statistics-1.4.3/0000755000000000000000000000000014153320774012105 5ustar0000000000000000statistics-1.4.3/COPYING0000644000000000000000000001255414153320774013147 0ustar0000000000000000inst/private/tbl_delim.m.m GPLv3+ inst/anderson_darling_cdf.m public domain inst/anderson_darling_test.m public domain inst/anovan.m GPLv3+ inst/bbscdf.m GPLv3+ inst/bbsinv.m GPLv3+ inst/bbspdf.m GPLv3+ inst/bbsrnd.m GPLv3+ inst/betastat.m GPLv3+ inst/binostat.m GPLv3+ inst/binotest.m GPLv3+ inst/boxplot.m GPLv3+ inst/burrcdf.m GPLv3+ inst/burrinv.m GPLv3+ inst/burrpdf.m GPLv3+ inst/burrrnd.m GPLv3+ inst/caseread.m GPLv3+ inst/casewrite.m GPLv3+ inst/cdf.m GPLv3+ inst/chi2stat.m GPLv3+ inst/cl_multinom.m GPLv3+ inst/cmdscale.m GPLv3+ inst/combnk.m GPLv3+ inst/copulacdf.m GPLv3+ inst/copulapdf.m GPLv3+ inst/copularnd.m GPLv3+ inst/crossval.m GPLv3+ inst/dcov.m GPLv3+ inst/dendogram.m GPLv3+ inst/expstat.m GPLv3+ inst/ff2n.m public domain inst/fitgmdist.m GPLv3+ inst/fstat.m GPLv3+ inst/fullfact.m public domain inst/gamfit.m public domain inst/gamlike.m public domain inst/gamstat.m GPLv3+ inst/geomean.m GPLv3+ inst/geostat.m GPLv3+ inst/gevcdf.m GPLv3+ inst/gevfit_lmom.m GPLv3+ inst/gevfit.m GPLv3+ inst/gevinv.m GPLv3+ inst/gevlike.m GPLv3+ inst/gevpdf.m GPLv3+ inst/gevrnd.m GPLv3+ inst/gevstat.m GPLv3+ inst/gmdistribution.m GPLv3+ inst/gpcdf.m GPLv3+ inst/gpinv.m GPLv3+ inst/gppdf.m GPLv3+ inst/gprnd.m GPLv3+ inst/grp2idx.m GPLv3+ inst/harmmean.m GPLv3+ inst/hist3.m GPLv3+ inst/histfit.m GPLv3+ inst/hmmestimate.m GPLv3+ inst/hmmgenerate.m GPLv3+ inst/hmmviterbi.m GPLv3+ inst/iwishpdf.m GPLv3+ inst/iwishrnd.m GPLv3+ inst/hygestat.m GPLv3+ inst/jackknife.m GPLv3+ inst/jsucdf.m GPLv3+ inst/jsupdf.m GPLv3+ inst/kmeans.m GPLv3+ inst/linkage.m GPLv3+ inst/lognstat.m GPLv3+ inst/mad.m GPLv3+ inst/mahal.m GPLv3+ inst/mnpdf.m GPLv3+ inst/mnrnd.m GPLv3+ inst/monotone_smooth.m GPLv3+ inst/mvncdf.m GPLv3+ inst/mvnpdf.m public domain inst/mvnrnd.m GPLv3+ inst/mvtcdf.m GPLv3+ inst/mvtpdf.m GPLv3+ inst/mvtrnd.m GPLv3+ inst/nakacdf.m GPLv3+ inst/nakainv.m GPLv3+ inst/nakapdf.m GPLv3+ inst/nakarnd.m GPLv3+ inst/nanmax.m GPLv3+ inst/nanmean.m GPLv3+ inst/nanmedian.m GPLv3+ inst/nanmin.m GPLv3+ inst/nanstd.m GPLv3+ inst/nansum.m GPLv3+ inst/nanvar.m GPLv3+ inst/nbinstat.m GPLv3+ inst/normalise_distribution.m GPLv3+ inst/normplot.m public domain inst/normstat.m GPLv3+ inst/pcacov.m GPLv3+ inst/pcares.m GPLv3+ inst/pdf.m GPLv3+ inst/pdist.m GPLv3+ inst/pdist2.m GPLv3+ inst/plsregress.m GPLv3+ inst/poisstat.m GPLv3+ inst/princomp.m public domain inst/qrandn.m GPLv3+ inst/random.m GPLv3+ inst/randsample.m GPLv3+ inst/raylcdf.m GPLv3+ inst/raylinv.m GPLv3+ inst/raylpdf.m GPLv3+ inst/raylrnd.m GPLv3+ inst/raylstat.m GPLv3+ inst/regress_gp.m GPLv3+ inst/regress.m GPLv3+ inst/repanova.m.m GPLv3+ inst/runtest.m GPLv3+ inst/signtest.m GPLv3+ inst/squareform.m GPLv3+ inst/stepwisefit.m GPLv3+ inst/tabulate.m GPLv3+ inst/tblread.m GPLv3+ inst/tblwrite.m GPLv3+ inst/tricdf.m GPLv3+ inst/triinv.m GPLv3+ inst/trimmean.m GPLv3+ inst/tripdf.m GPLv3+ inst/trirnd.m GPLv3+ inst/tstat.m GPLv3+ inst/ttest.m GPLv3+ inst/ttest2.m GPLv3+ inst/unidstat.m GPLv3+ inst/unifstat.m GPLv3+ inst/vartest.m GPLv3+ inst/vartest2.m GPLv3+ inst/violin.m GPLv3+ inst/vmpdf.m GPLv3+ inst/vmrnd.m GPLv3+ inst/wblstat.m GPLv3+ inst/wishpdf.m GPLv3+ inst/wishrnd.m GPLv3+ inst/ztest.m GPLv3+ statistics-1.4.3/DESCRIPTION0000644000000000000000000000051314153320774013612 0ustar0000000000000000Name: statistics Version: 1.4.3 Date: 2021-12-03 Author: various authors Maintainer: Octave-Forge community Title: Statistics Description: Additional statistics functions for Octave. Categories: Statistics Depends: octave (>= 4.0.0), io (>= 1.0.18) License: GPLv3+, public domain Url: http://octave.sf.net statistics-1.4.3/INDEX.in0000644000000000000000000000366414153320774013315 0ustar0000000000000000statistics >> Statistics Distributions anderson_darling_cdf bbscdf bbsinv bbspdf bbsrnd betastat binostat binotest burrcdf burrinv burrpdf burrrnd cdf chi2stat cl_multinom copulacdf copulapdf copularnd datasample expfit explike expstat fstat gamlike gamstat geostat gevcdf gevfit gevfit_lmom gevinv gevlike gevpdf gevrnd gevstat gmdistribution gpcdf gpinv gppdf gprnd hygestat iwishpdf iwishrnd jsucdf jsupdf lognstat mnpdf mnrnd mvnpdf mvnrnd mvncdf mvtcdf mvtpdf mvtrnd nakacdf nakainv nakapdf nakarnd nbinstat ncx2pdf normalise_distribution normstat pdf poisstat qrandn random randsample raylcdf raylinv raylpdf raylrnd raylstat tricdf triinv tripdf trirnd tstat unidstat unifstat vmpdf vmrnd wblstat wishpdf wishrnd Descriptive statistics combnk dcov geomean harmmean jackknife nanmax nanmean nanmedian nanmin nanstd nansum nanvar trimmean tabulate Experimental design fullfact ff2n Regression anova1 anovan canoncorr crossval monotone_smooth pca pcacov pcares plsregress princomp regress regress_gp stepwisefit Plots boxplot confusionchart dendrogram gscatter histfit hist3 normplot repanova silhouette violin wblplot Models hmmestimate hmmgenerate hmmviterbi mhsample slicesample Hypothesis testing anderson_darling_test kruskalwallis runstest signtest ttest ttest2 vartest vartest2 ztest Fitting fitgmdist gamfit Clustering cluster clusterdata cmdscale cophenet evalclusters inconsistent kmeans linkage mahal optimalleaforder pdist pdist2 squareform Reading and Writing caseread casewrite tblread tblwrite Cvpartition (class of set partitions for cross-validation, used in crossval) @cvpartition/cvpartition @cvpartition/display @cvpartition/get @cvpartition/repartition @cvpartition/set @cvpartition/test @cvpartition/training Categorical data grp2idx Classification Performance Evaluation confusionchart confusionmat Other sigma_pts statistics-1.4.3/Makefile0000644000000000000000000002235714153320774013556 0ustar0000000000000000## Copyright 2015-2016 CarnĂ« Draug ## Copyright 2015-2016 Oliver Heimlich ## Copyright 2017 Julien Bect ## Copyright 2017 Olaf Till ## Copyright 2018 John Donoghue ## ## Copying and distribution of this file, with or without modification, ## are permitted in any medium without royalty provided the copyright ## notice and this notice are preserved. This file is offered as-is, ## without any warranty. TOPDIR := $(shell pwd) ## Some basic tools (can be overriden using environment variables) SED ?= sed TAR ?= tar GREP ?= grep CUT ?= cut TR ?= tr ## Note the use of ':=' (immediate set) and not just '=' (lazy set). ## http://stackoverflow.com/a/448939/1609556 package := $(shell $(GREP) "^Name: " DESCRIPTION | $(CUT) -f2 -d" " | \ $(TR) '[:upper:]' '[:lower:]') version := $(shell $(GREP) "^Version: " DESCRIPTION | $(CUT) -f2 -d" ") ## These are the paths that will be created for the releases. target_dir := target release_dir := $(target_dir)/$(package)-$(version) release_tarball := $(target_dir)/$(package)-$(version).tar.gz html_dir := $(target_dir)/$(package)-html html_tarball := $(target_dir)/$(package)-html.tar.gz ## Using $(realpath ...) avoids problems with symlinks due to bug ## #50994 in Octaves scripts/pkg/private/install.m. But at least the ## release directory above is needed in the relative form, for 'git ## archive --format=tar --prefix=$(release_dir). real_target_dir := $(realpath .)/$(target_dir) installation_dir := $(real_target_dir)/.installation package_list := $(installation_dir)/.octave_packages install_stamp := $(installation_dir)/.install_stamp ## These can be set by environment variables which allow to easily ## test with different Octave versions. ifndef OCTAVE OCTAVE := octave endif OCTAVE := $(OCTAVE) --no-gui --silent --no-history --norc MKOCTFILE ?= mkoctfile ## Command used to set permissions before creating tarballs FIX_PERMISSIONS ?= chmod -R a+rX,u+w,go-w,ug-s ## Detect which VCS is used vcs := $(if $(wildcard .hg),hg,$(if $(wildcard .git),git,unknown)) ifeq ($(vcs),hg) release_dir_dep := .hg/dirstate endif ifeq ($(vcs),git) release_dir_dep := .git/index endif HG := hg HG_CMD = $(HG) --config alias.$(1)=$(1) --config defaults.$(1)= $(1) HG_ID := $(shell $(call HG_CMD,identify) --id | sed -e 's/+//' ) HG_TIMESTAMP := $(firstword $(shell $(call HG_CMD,log) --rev $(HG_ID) --template '{date|hgdate}')) TAR_REPRODUCIBLE_OPTIONS := --sort=name --mtime="@$(HG_TIMESTAMP)" --owner=0 --group=0 --numeric-owner TAR_OPTIONS := --format=ustar $(TAR_REPRODUCIBLE_OPTIONS) ## .PHONY indicates targets that are not filenames ## (https://www.gnu.org/software/make/manual/html_node/Phony-Targets.html) .PHONY: help ## make will display the command before runnning them. Use @command ## to not display it (makes specially sense for echo). help: @echo "Targets:" @echo " dist - Create $(release_tarball) for release." @echo " html - Create $(html_tarball) for release." @echo " release - Create both of the above and show md5sums." @echo " install - Install the package in $(installation_dir), where it is not visible in a normal Octave session." @echo " check - Execute package tests." @echo " doctest - Test the help texts with the doctest package." @echo " run - Run Octave with the package installed in $(installation_dir) in the path." @echo " clean - Remove everything made with this Makefile." ## ## Recipes for release tarballs (package + html) ## .PHONY: release dist html clean-tarballs clean-unpacked-release ## To make a release, build the distribution and html tarballs. release: dist html md5sum $(release_tarball) $(html_tarball) @echo "Upload @ https://sourceforge.net/p/octave/package-releases/new/" @echo " and note the changeset the release corresponds to" ## dist and html targets are only PHONY/alias targets to the release ## and html tarballs. dist: $(release_tarball) html: $(html_tarball) ## An implicit rule with a recipe to build the tarballs correctly. %.tar.gz: % $(TAR) -cf - $(TAR_OPTIONS) -C "$(target_dir)/" "$(notdir $<)" | gzip -9n > "$@" clean-tarballs: @echo "## Cleaning release tarballs (package + html)..." -$(RM) $(release_tarball) $(html_tarball) @echo ## Create the unpacked package. ## ## Notes: ## * having ".hg/dirstate" (or ".git/index") as a prerequesite means it is ## only rebuilt if we are at a different commit. ## * the variable RM usually defaults to "rm -f" ## * having this recipe separate from the one that makes the tarball ## makes it easy to have packages in alternative formats (such as zip) ## * note that if a commands needs to be run in a specific directory, ## the command to "cd" needs to be on the same line. Each line restores ## the original working directory. $(release_dir): $(release_dir_dep) -$(RM) -r "$@" ifeq (${vcs},hg) hg archive --exclude ".hg*" --type files "$@" endif ifeq (${vcs},git) git archive --format=tar --prefix="$@/" HEAD | $(TAR) -x $(RM) "$@/.gitignore" endif ## Don't fall back to run the supposed necessary contents of ## 'bootstrap' here. Users are better off if they provide ## 'bootstrap'. Administrators, checking build reproducibility, can ## put in the missing 'bootstrap' file if they feel they know its ## necessary contents. ifneq (,$(wildcard src/bootstrap)) cd "$@/src" && ./bootstrap && $(RM) -r "autom4te.cache" endif ## Uncomment this if your src/Makefile.in has these targets for ## pre-building something for the release (e.g. documentation). # cd "$@/src" && ./configure && $(MAKE) prebuild && \ # $(MAKE) distclean && $(RM) Makefile ## ${FIX_PERMISSIONS} "$@" run_in_place = $(OCTAVE) --eval ' pkg ("local_list", "$(package_list)"); ' \ --eval ' pkg ("load", "$(package)"); ' html_options = --eval 'options = get_html_options ("octave-forge");' ## Uncomment this for package documentation. # html_options = --eval 'options = get_html_options ("octave-forge");' \ # --eval 'options.package_doc = "$(package).texi";' $(html_dir): $(install_stamp) $(RM) -r "$@"; $(run_in_place) \ --eval ' pkg load generate_html; ' \ $(html_options) \ --eval ' generate_package_html ("$(package)", "$@", options); '; $(FIX_PERMISSIONS) "$@"; clean-unpacked-release: @echo "## Cleaning unpacked release tarballs (package + html)..." -$(RM) -r $(release_dir) $(html_dir) @echo ## ## Recipes for installing the package. ## .PHONY: install clean-install octave_install_commands = \ ' llist_path = pkg ("local_list"); \ mkdir ("$(installation_dir)"); \ load (llist_path); \ local_packages(cellfun (@ (x) strcmp ("$(package)", x.name), local_packages)) = []; \ save ("$(package_list)", "local_packages"); \ pkg ("local_list", "$(package_list)"); \ pkg ("prefix", "$(installation_dir)", "$(installation_dir)"); \ pkg ("install", "-local", "-verbose", "$(release_tarball)"); ' ## Install unconditionally. Maybe useful for testing installation with ## different versions of Octave. install: $(release_tarball) @echo "Installing package under $(installation_dir) ..." $(OCTAVE) --eval $(octave_install_commands) touch $(install_stamp) ## Install only if installation (under target/...) is not current. $(install_stamp): $(release_tarball) @echo "Installing package under $(installation_dir) ..." $(OCTAVE) --eval $(octave_install_commands) touch $(install_stamp) clean-install: @echo "## Cleaning installation under $(installation_dir) ..." -$(RM) -r $(installation_dir) @echo ## ## Recipes for testing purposes ## .PHONY: run doctest check clean-check ## Start an Octave session with the package directories on the path for ## interactice test of development sources. run: $(install_stamp) $(run_in_place) --persist ## Test example blocks in the documentation. Needs doctest package ## https://octave.sourceforge.io/doctest/index.html doctest: $(install_stamp) $(run_in_place) --eval 'pkg load doctest;' \ --eval "targets = '$(shell (ls inst; ls src | $(GREP) .oct) | $(CUT) -f2 -d@ | $(CUT) -f1 -d.)';" \ --eval "targets = strsplit (targets, ' '); doctest (targets);" ## Test package. orig_octave_test_commands = \ ' dirs = {"inst", "src"}; \ dirs(cellfun (@ (x) ! isdir (x), dirs)) = []; \ if (isempty (dirs)) error ("no \"inst\" or \"src\" directory"); exit (1); \ else __run_test_suite__ (dirs, {}); endif ' octave_test_commands = \ ' pkgs = pkg("list", "$(package)"); \ dirs = {pkgs{1}.dir}; \ __run_test_suite__ (dirs, {}); ' ## the following works, too, but provides no overall summary output as ## __run_test_suite__ does: ## ## else cellfun (@runtests, horzcat (cellfun (@ (dir) ostrsplit (([~, dirs] = system (sprintf ("find %s -type d", dir))), "\n\r", true), dirs, "UniformOutput", false){:})); endif ' check: $(install_stamp) $(run_in_place) --eval $(octave_test_commands) clean-check: @echo "## Removing fntests.log ..." test -e $(target_dir)/fntests.log && rm -f $(target_dir)/fntests.log || true ## ## CLEAN ## .PHONY: clean clean: clean-tarballs clean-unpacked-release clean-install clean-check @echo "## Removing target directory (if empty)..." test -e $(target_dir) && rmdir $(target_dir) || true @echo @echo "## Cleaning done" @echo statistics-1.4.3/NEWS0000644000000000000000000002760014153320774012611 0ustar0000000000000000Summary of important user-visible changes for statistics 1.4.3: ------------------------------------------------------------------- New functions: ============== ** anova1 (patch #10127) kruskalwallis ** cluster (patch #10009) ** clusterdata (patch #10012) ** confusionchart (patch #9985) ** confusionmat (patch #9971) ** cophenet (patch #10040) ** datasample (patch #10050) ** evalclusters (patch #10052) ** expfit (patch #10092) explike ** gscatter (patch #10043) ** ismissing (patch #10102) ** inconsistent (patch #10008) ** mhsample.m (patch #10016) ** ncx2pdf (patch #9711) ** optimalleaforder.m (patch #10034) ** pca (patch #10104) ** rmmissing (patch #10102) ** silhouette (patch #9743) ** slicesample (patch #10019) ** wblplot (patch #8579) Improvements: ============= ** anovan.m: use double instead of toascii (bug #60514) ** binocdf: new option "upper" (bug #43721) ** boxplot: better Matlab compatibility; several Matlab-compatible plot options added (OutlierTags, Sample_IDs, BoxWidth, Widths, BoxStyle, Positions, Labels, Colors) and an Octave-specific one (CapWidhts); demos added; texinfo improved (patch #9930) ** auto MPG (carbig) sample dataset added from https://archive.ics.uci.edu/ml/datasets/Auto+MPG (patch #10045) ** crosstab.m: make n-dimensional (patch #10014) ** dendrogram.m: many improvements (patch #10036) ** fitgmdist.m: fix typo in ComponentProportion (bug #59386) ** gevfit: change orientation of results for Matlab compatibility (bug #47369) ** hygepdf: avoid overflow for certain inputs (bug #35827) ** kmeans: efficiency and compatibility tweaks (patch #10042) ** pdist: option for squared Euclidean distance (patch #10051) ** stepwisefit.m: give another option to select predictors (patch #8584) ** tricdf, triinv: fixes (bug #60113) Summary of important user-visible changes for statistics 1.4.2: ------------------------------------------------------------------- ** canoncorr: allow more variables than observations ** fitgmdist: return fitgmdist parameters (Bug #57917) ** gamfit: invert parameter per docs (Bug #57849) ** geoXXX: update docs 'number of failures (X-1)' => 'number of failures (X)' (Bug #57606) ** kolmogorov_smirnov_test.m: update function handle usage from octave6+ (Bug #57351) ** linkage.m: fix octave6+ parse error (Bug #57348) ** unifrnd: changed unifrnd(a,a) to return a 0 rather than NaN (Bug #56342) ** updates for usage of depreciated octave functions Summary of important user-visible changes for statistics 1.4.1: ------------------------------------------------------------------- ** update install scripts for octave 5.0 depreciated functions ** bug fixes to the following functions: pdist2.m: use max in distEucSq (Bug #50377) normpdf: use eps tolerance in tests (Bug #51963) fitgmdist: fix an output bug in fitgmdist t_test: Set tolerance on t_test BISTS (Bug #54557) gpXXXXX: change order of inputs to match matlab (Bug #54009) bartlett_test: df = k-1 (Bug #45894) gppdf: apply scale factor (Bug #54009) gmdistribution: updates for bug #54278, ##54279 wishrnd: Bug #55860 Summary of important user-visible changes for statistics 1.4.0: ------------------------------------------------------------------- ** The following functions are new: canoncorr fitgmdist gmdistribution sigma_pts ** The following functions have been moved from the statistics package but are conditionally installed: mad ** The following functions have been moved from octave to be conditionally installed: BASE cloglog logit prctile probit qqplot table (renamed to crosstab) DISTRIBUTIONS betacdf betainv betapdf betarnd binocdf binoinv binopdf binornd cauchy_cdf cauchy_inv cauchy_pdf cauchy_rnd chi2cdf chi2inv chi2pdf chi2rnd expcdf expinv exppdf exprnd fcdf finv fpdf frnd gamcdf gaminv gampdf gamrnd geocdf geoinv geopdf geornd hygecdf hygeinv hygepdf hygernd kolmogorov_smirnov_cdf laplace_cdf laplace_inv laplace_pdf laplace_rnd logistic_cdf logistic_inv logistic_pdf logistic_rnd logncdf logninv lognpdf lognrnd nbincdf nbininv nbinpdf nbinrnd normcdf norminv normpdf normrnd poisscdf poissinv poisspdf poissrnd stdnormal_cdf stdnormal_inv stdnormal_pdf stdnormal_rnd tcdf tinv tpdf trnd unidcdf unidinv unidpdf unidrnd unifcdf unifinv unifpdf unifrnd wblcdf wblinv wblpdf wblrnd wienrnd MODELS logistic_regression TESTS anova bartlett_test chisquare_test_homogeneity chisquare_test_independence cor_test f_test_regression hotelling_test hotelling_test_2 kolmogorov_smirnov_test kolmogorov_smirnov_test_2 kruskal_wallis_test manova mcnemar_test prop_test_2 run_test sign_test t_test t_test_2 t_test_regression u_test var_test welch_test wilcoxon_test z_test z_test_2 ** Functions marked with known test failures: grp2idx: bug #51928 gevfir_lmom: bug #31070 ** Other functions that have been changed for smaller bugfixes, increased Matlab compatibility, or performance: dcov: returned dcov instead of dcor. added demo. violin: can be used with subplots. violin quality improved. princomp: Fix expected values of tsquare in unit tests fitgmdist: test number inputs to function hist3: fix removal of rows with NaN values ** added the packages test data to install Summary of important user-visible changes for statistics 1.3.0: ------------------------------------------------------------------- ** The following functions are new: bbscdf bbsinv bbspdf bbsrnd binotest burrcdf burrinv burrpdf burrrnd gpcdf gpinv gppdf gprnd grp2idx mahal mvtpdf nakacdf nakainv nakapdf nakarnd pdf tricdf triinv tripdf trirnd violin ** Other functions that have been changed for smaller bugfixes, increased Matlab compatibility, or performance: betastat binostat cdf combnk gevfit hist3 kmeans linkage randsample squareform ttest Summary of important user-visible changes for statistics 1.2.4: ------------------------------------------------------------------- ** Made princomp work with nargout < 2. ** Renamed dendogram to dendrogram. ** Added isempty check to kmeans. ** Transposed output of hist3. ** Converted calculation in hmmviterbi to log space. ** Bug fixes for stepwisefit wishrnd. ** Rewrite of cmdscale for improved compatibility. ** Fix in squareform for improved compatibility. ** New cvpartition class, with methods: display repartition test training ** New sample data file fisheriris.txt for tests ** The following functions are new: cdf crossval dcov pdist2 qrandn randsample signtest ttest ttest2 vartest vartest2 ztest Summary of important user-visible changes for statistics 1.2.3: ------------------------------------------------------------------- ** Made sure that output of nanstd is real. ** Fixed second output of nanmax and nanmin. ** Corrected handle for outliers in boxplot. ** Bug fix and enhanced functionality for mvnrnd. ** The following functions are new: wishrnd iwishrnd wishpdf iwishpdf cmdscale Summary of important user-visible changes for statistics 1.2.2: ------------------------------------------------------------------- ** Fixed documentation of dendogram and hist3 to work with TexInfo 5. Summary of important user-visible changes for statistics 1.2.1: ------------------------------------------------------------------- ** The following functions are new: pcares pcacov runstest stepwisefit hist3 ** dendogram now returns the leaf node numbers and order that the nodes were displayed in. ** New faster implementation of princomp. Summary of important user-visible changes for statistics 1.2.0: ------------------------------------------------------------------- ** The following functions are new: regress_gp dendogram plsregress ** New functions for the generalized extreme value (GEV) distribution: gevcdf gevfit gevfit_lmom gevinv gevlike gevpdf gevrnd gevstat ** The interface of the following functions has been modified: mvnrnd ** `kmeans' has been fixed to deal with clusters that contain only one element. ** `normplot' has been fixed to avoid use of functions that have been removed from Octave core. Also, the plot produced should now display some aesthetic elements and appropriate legends. ** The help text of `mvtrnd' has been improved. ** Package is no longer autoloaded. Summary of important user-visible changes for statistics 1.1.3: ------------------------------------------------------------------- ** The following functions are new in 1.1.3: copularnd mvtrnd ** The functions mnpdf and mnrnd are now also usable for greater numbers of categories for which the rows do not exactly sum to 1. Summary of important user-visible changes for statistics 1.1.2: ------------------------------------------------------------------- ** The following functions are new in 1.1.2: mnpdf mnrnd ** The package is now dependent on the io package (version 1.0.18 or later) since the functions that it depended of from miscellaneous package have been moved to io. ** The function `kmeans' now accepts the 'emptyaction' property with the 'singleton' value. This allows for the kmeans algorithm to handle empty cluster better. It also throws an error if the user does not request an empty cluster handling, and there is an empty cluster. Plus, the returned items are now a closer match to Matlab. Summary of important user-visible changes for statistics 1.1.1: ------------------------------------------------------------------- ** The following functions are new in 1.1.1: monotone_smooth kmeans jackknife ** Bug fixes on the functions: normalise_distribution combnk repanova ** The following functions were removed since equivalents are now part of GNU octave core: zscore ** boxplot.m now returns a structure with handles to the plot elemenets. Summary of important user-visible changes for statistics 1.1.0: ------------------------------------------------------------------- ** IMPORTANT note about `fstat' shadowing core library function: GNU octave's 3.2 release added a new function `fstat' to return information of a file. Statistics' `fstat' computes F mean and variance. Since MatLab's `fstat' is the equivalent to statistics' `fstat' (not to core's `fstat'), and to avoid problems with the statistics package, `fstat' has been deprecated in octave 3.4 and will be removed in Octave 3.8. In the mean time, please ignore this warning when installing the package. ** The following functions are new in 1.1.0: normalise_distribution repanova combnk ** The following functions were removed since equivalents are now part of GNU octave core: prctile ** The __tbl_delim__ function is now private. ** The function `boxplot' now accepts named arguments. ** Bug fixes on the functions: harmmean nanmax nanmin regress ** Small improvements on help text. statistics-1.4.3/PKG_ADD0000644000000000000000000000145414153320774013125 0ustar0000000000000000## three problems: ## - the directory returned by 'mfilename' must not be added also ## (endless loop) ## - 'genpath' of Octave 4.0 includes directories indiscriminately, ## e.g. 'private' directories ## - PKG_ADD (and PKG_DEL?) is run during installation, too, from the ## root directory of the package, where no such subdirectories ## exist. if exist ("isfolder") == 0 if (isdir (fullfile (fileparts (mfilename ("fullpath")), "base"))) addpath (fullfile (fileparts (mfilename ("fullpath")), {"base", "distributions", "models", "tests"}){:}); endif else if (isfolder (fullfile (fileparts (mfilename ("fullpath")), "base"))) addpath (fullfile (fileparts (mfilename ("fullpath")), {"base", "distributions", "models", "tests"}){:}); endif endif statistics-1.4.3/PKG_DEL0000644000000000000000000000144414153320774013140 0ustar0000000000000000## three problems: ## - the directory returned by 'mfilename' must not be added also ## (endless loop) ## - 'genpath' of Octave 4.0 includes directories indiscriminately, ## e.g. 'private' directories ## - PKG_ADD (and PKG_DEL?) is run during installation, too, from the ## root directory of the package, where no such subdirectories ## exist. if exist ("isfolder") == 0 if (isdir (fullfile (fileparts (mfilename ("fullpath")), "base"))) rmpath (fullfile (fileparts (mfilename ("fullpath")), {"base", "distributions", "models", "tests"}){:}); endif else if (isfolder (fullfile (fileparts (mfilename ("fullpath")), "base"))) rmpath (fullfile (fileparts (mfilename ("fullpath")), {"base", "distributions", "models", "tests"}){:}); endif endif statistics-1.4.3/README.crosscompilation0000644000000000000000000000011314153320774016347 0ustar0000000000000000Instructions for cross-compiling are in utils/conditional_installation.m . statistics-1.4.3/inst/0000755000000000000000000000000014153320774013062 5ustar0000000000000000statistics-1.4.3/inst/@cvpartition/0000755000000000000000000000000014153320774015524 5ustar0000000000000000statistics-1.4.3/inst/@cvpartition/cvpartition.m0000644000000000000000000001406514153320774020252 0ustar0000000000000000## Copyright (C) 2014 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; If not, see . ## -*- texinfo -*- ## @deftypefn{Function File}{@var{C} =} cvpartition (@var{X}, [@var{partition_type}, [@var{k}]]) ## Create a partition object for cross validation. ## ## @var{X} may be a positive integer, interpreted as the number of values @var{n} to partition, or a vector of length @var{n} containing class designations for the elements, in which case the partitioning types @var{KFold} and @var{HoldOut} attempt to ensure each partition represents the classes proportionately. ## ## @var{partition_type} must be one of the following: ## ## @table @asis ## @item @samp{KFold} ## Divide set into @var{k} equal-size subsets (this is the default, with @var{k}=10). ## @item @samp{HoldOut} ## Divide set into two subsets, "training" and "validation". If @var{k} is a fraction, that is the fraction of values put in the validation subset; if it is a positive integer, that is the number of values in the validation subset (by default @var{k}=0.1). ## @item @samp{LeaveOut} ## Leave-one-out partition (each element is placed in its own subset). ## @item @samp{resubstitution} ## Training and validation subsets that both contain all the original elements. ## @item @samp{Given} ## Subset indices are as given in @var{X}. ## @end table ## ## The following fields are defined for the @samp{cvpartition} class: ## ## @table @asis ## @item @samp{classes} ## Class designations for the elements. ## @item @samp{inds} ## Subset indices for the elements. ## @item @samp{n_classes} ## Number of different classes. ## @item @samp{NumObservations} ## @var{n}, number of elements in data set. ## @item @samp{NumTestSets} ## Number of testing subsets. ## @item @samp{TestSize} ## Number of elements in (each) testing subset. ## @item @samp{TrainSize} ## Number of elements in (each) training subset. ## @item @samp{Type} ## Partition type. ## @end table ## ## @seealso{crossval} ## @end deftypefn ## Author: Nir Krakauer function C = cvpartition (X, partition_type = 'KFold', k = []) if (nargin < 1 || nargin > 3 || !isvector(X)) print_usage (); endif if isscalar (X) n = X; n_classes = 1; else n = numel (X); endif switch tolower(partition_type) case {'kfold' 'holdout' 'leaveout' 'resubstitution' 'given'} otherwise warning ('unrecognized type, using KFold') partition_type = 'KFold'; endswitch switch tolower(partition_type) case {'kfold' 'holdout' 'given'} if !isscalar (X) [y, ~, j] = unique (X(:)); n_per_class = accumarray (j, 1); n_classes = numel (n_per_class); endif endswitch C = struct ("classes", [], "inds", [], "n_classes", [], "NumObservations", [], "NumTestSets", [], "TestSize", [], "TrainSize", [], "Type", []); #The non-Matlab fields classes, inds, n_classes are only useful for some methods switch tolower(partition_type) case 'kfold' if isempty (k) k = 10; endif if n_classes == 1 inds = floor((0:(n-1))' * (k / n)) + 1; else inds = nan(n, 1); for i = 1:n_classes if mod (i, 2) #alternate ordering over classes so that the subsets are more nearly the same size inds(j == i) = floor((0:(n_per_class(i)-1))' * (k / n_per_class(i))) + 1; else inds(j == i) = floor(((n_per_class(i)-1):-1:0)' * (k / n_per_class(i))) + 1; endif endfor endif C.inds = inds; C.NumTestSets = k; [~, ~, jj] = unique (inds); n_per_subset = accumarray (jj, 1); C.TrainSize = n - n_per_subset; C.TestSize = n_per_subset; case 'given' C.inds = j; C.NumTestSets = n_classes; C.TrainSize = n - n_per_class; C.TestSize = n_per_class; case 'holdout' if isempty (k) k = 0.1; endif if k < 1 f = k; #target fraction to sample k = round (k * n); #number of samples else f = k / n; endif inds = zeros (n, 1, "logical"); if n_classes == 1 inds(randsample(n, k)) = true; #indices for test set else #sample from each class k_check = 0; for i = 1:n_classes ki = round(f*n_per_class(i)); inds(find(j == i)(randsample(n_per_class(i), ki))) = true; k_check += ki; endfor if k_check < k #add random elements to test set to make it k inds(find(!inds)(randsample(n - k_check, k - k_check))) = true; elseif k_check > k #remove random elements from test set inds(find(inds)(randsample(k_check, k_check - k))) = false; endif C.classes = j; endif C.n_classes = n_classes; C.TrainSize = n - k; C.TestSize = k; C.NumTestSets = 1; C.inds = inds; case 'leaveout' C.TrainSize = ones (n, 1); C.TestSize = (n-1) * ones (n, 1); C.NumTestSets = n; case 'resubstitution' C.TrainSize = C.TestSize = n; C.NumTestSets = 1; endswitch C.NumObservations = n; C.Type = tolower (partition_type); C = class (C, "cvpartition"); endfunction %!demo %! # Partition with Fisher iris dataset (n = 150) %! # Stratified by species %! load fisheriris.txt %! y = fisheriris(:, 1); %! # 10-fold cross-validation partition %! c = cvpartition (y, 'KFold', 10) %! # leave-10-out partition %! c1 = cvpartition (y, 'HoldOut', 10) %! idx1 = test (c, 2); %! idx2 = training (c, 2); %! # another leave-10-out partition %! c2 = repartition (c1) #plot(struct(c).inds, '*') statistics-1.4.3/inst/@cvpartition/display.m0000644000000000000000000000265614153320774017360 0ustar0000000000000000## Copyright (C) 2014 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; If not, see . ## -*- texinfo -*- ## @deftypefn{Function File} display (@var{C}) ## Display a cvpartition object. ## ## @seealso{cvpartition} ## @end deftypefn ## Author: Nir Krakauer function display (C) if nargin != 1 print_usage (); endif switch C.Type case 'kfold' str = 'K-fold'; case 'given' str = 'Given'; case 'holdout' str = 'HoldOut'; case 'leaveout' str = 'Leave-One-Out'; case 'resubstitution' str = 'Resubstitution'; otherwise str = 'Unknown-type'; endswitch disp([str ' cross validation partition']) disp([' N: ' num2str(C.NumObservations)]) disp(['NumTestSets: ' num2str(C.NumTestSets)]) disp([' TrainSize: ' num2str(C.TrainSize')]) disp([' TestSize: ' num2str(C.TestSize')]) statistics-1.4.3/inst/@cvpartition/get.m0000644000000000000000000000247014153320774016464 0ustar0000000000000000## Copyright (C) 2014 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; If not, see . ## -*- texinfo -*- ## @deftypefn{Function File}@var{s} = get (@var{c}, [@var{f}]) ## Get a field from a @samp{cvpartition} object. ## ## @seealso{cvpartition} ## @end deftypefn function s = get (c, f) if (nargin == 1) s = c; elseif (nargin == 2) if (ischar (f)) switch (f) case {"classes", "inds", "n_classes", "NumObservations", "NumTestSets", "TestSize", "TrainSize", "Type"} s = eval(["struct(c)." f]); otherwise error ("get: invalid property %s", f); endswitch else error ("get: expecting the property to be a string"); endif else print_usage (); endif endfunction statistics-1.4.3/inst/@cvpartition/repartition.m0000644000000000000000000000453414153320774020250 0ustar0000000000000000## Copyright (C) 2014 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; If not, see . ## -*- texinfo -*- ## @deftypefn{Function File}{@var{Cnew} =} repartition (@var{C}) ## Return a new cvpartition object. ## ## @var{C} should be a cvpartition object. @var{Cnew} will use the same partition_type as @var{C} but redo any randomization performed (currently, only the HoldOut type uses randomization). ## ## @seealso{cvpartition} ## @end deftypefn ## Author: Nir Krakauer function Cnew = repartition (C) if (nargin < 1 || nargin > 2) print_usage (); endif Cnew = C; switch C.Type case 'kfold' case 'given' case 'holdout' #currently, only the HoldOut method uses randomization n = C.NumObservations; k = C.TestSize; n_classes = C.n_classes; if k < 1 f = k; #target fraction to sample k = round (k * n); #number of samples else f = k / n; endif inds = zeros (n, 1, "logical"); if n_classes == 1 inds(randsample(n, k)) = true; #indices for test set else #sample from each class j = C.classes; #integer class labels n_per_class = accumarray (j, 1); n_classes = numel (n_per_class); k_check = 0; for i = 1:n_classes ki = round(f*n_per_class(i)); inds(find(j == i)(randsample(n_per_class(i), ki))) = true; k_check += ki; endfor if k_check < k #add random elements to test set to make it k inds(find(!inds)(randsample(n - k_check, k - k_check))) = true; elseif k_check > k #remove random elements from test set inds(find(inds)(randsample(k_check, k_check - k))) = false; endif endif Cnew.inds = inds; case 'leaveout' case 'resubstitution' endswitch statistics-1.4.3/inst/@cvpartition/set.m0000644000000000000000000000302114153320774016471 0ustar0000000000000000## Copyright (C) 2014 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; If not, see . ## -*- texinfo -*- ## @deftypefn{Function File}@var{s} = set (@var{c}, @var{varargin}) ## Set field(s) in a @samp{cvpartition} object. ## ## @seealso{cvpartition} ## @end deftypefn function s = set (c, varargin) s = struct(c); if (length (varargin) < 2 || rem (length (varargin), 2) != 0) error ("set: expecting property/value pairs"); endif while (length (varargin) > 1) prop = varargin{1}; val = varargin{2}; varargin(1:2) = []; if (ischar (prop)) switch (prop) case {"classes", "inds", "n_classes", "NumObservations", "NumTestSets", "TestSize", "TrainSize", "Type"} s = setfield (s, prop, val); otherwise error ("set: invalid property %s", f); endswitch else error ("set: expecting the property to be a string"); endif endwhile s = class (s, "cvpartition"); endfunction statistics-1.4.3/inst/@cvpartition/test.m0000644000000000000000000000270314153320774016663 0ustar0000000000000000## Copyright (C) 2014 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; If not, see . ## -*- texinfo -*- ## @deftypefn{Function File}{@var{inds} =} test (@var{C}, [@var{i}]) ## Return logical vector for testing-subset indices from a cvpartition object. ## ## @var{C} should be a cvpartition object. @var{i} is the fold index (default is 1). ## ## @seealso{cvpartition, @@cvpartition/training} ## @end deftypefn ## Author: Nir Krakauer function inds = test (C, i = []) if (nargin < 1 || nargin > 2) print_usage (); endif if nargin < 2 || isempty (i) i = 1; endif switch C.Type case {'kfold' 'given'} inds = C.inds == i; case 'holdout' inds = C.inds; case 'leaveout' inds = zeros(C.NumObservations, 1, "logical"); inds(i) = true; case 'resubstitution' inds = ones(C.NumObservations, 1, "logical"); endswitch statistics-1.4.3/inst/@cvpartition/training.m0000644000000000000000000000271414153320774017521 0ustar0000000000000000## Copyright (C) 2014 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; If not, see . ## -*- texinfo -*- ## @deftypefn{Function File}{@var{inds} =} training (@var{C}, [@var{i}]) ## Return logical vector for training-subset indices from a cvpartition object. ## ## @var{C} should be a cvpartition object. @var{i} is the fold index (default is 1). ## ## @seealso{cvpartition, @@cvpartition/test} ## @end deftypefn ## Author: Nir Krakauer function inds = training (C, i = []) if (nargin < 1 || nargin > 2) print_usage (); endif if nargin < 2 || isempty (i) i = 1; endif switch C.Type case {'kfold' 'given'} inds = C.inds != i; case 'holdout' inds = !C.inds; case 'leaveout' inds = ones (C.NumObservations, 1, "logical"); inds(i) = false; case 'resubstitution' inds = ones (C.NumObservations, 1, "logical"); endswitch statistics-1.4.3/inst/ConfusionMatrixChart.m0000644000000000000000000007025014153320774017356 0ustar0000000000000000## Copyright (C) 2020-2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## ## Author: Stefano Guidoni classdef ConfusionMatrixChart < handle ## -*- texinfo -*- ## @deftypefn {} {@var{p} =} ConfusionMatrixChart () ## Create object @var{p}, a Confusion Matrix Chart object. ## ## @table @asis ## @item @qcode{"DiagonalColor"} ## The color of the patches on the diagonal, default is [0.0, 0.4471, 0.7412]. ## ## @item @qcode{"OffDiagonalColor"} ## The color of the patches off the diagonal, default is [0.851, 0.3255, 0.098]. ## ## @item @qcode{"GridVisible"} ## Available values: @qcode{on} (default), @qcode{off}. ## ## @item @qcode{"Normalization"} ## Available values: @qcode{absolute} (default), @qcode{column-normalized}, ## @qcode{row-normalized}, @qcode{total-normalized}. ## ## @item @qcode{"ColumnSummary"} ## Available values: @qcode{off} (default), @qcode{absolute}, ## @qcode{column-normalized},@qcode{total-normalized}. ## ## @item @qcode{"RowSummary"} ## Available values: @qcode{off} (default), @qcode{absolute}, ## @qcode{row-normalized}, @qcode{total-normalized}. ## @end table ## ## MATLAB compatibility -- the not implemented properties are: FontColor, ## PositionConstraint, InnerPosition, Layout. ## ## @seealso{confusionchart} ## @end deftypefn properties (Access = public) ## text properties XLabel = "Predicted Class"; YLabel = "True Class"; Title = ""; FontName = ""; FontSize = 0; ## chart colours DiagonalColor = [0 0.4471 0.7412]; OffDiagonalColor = [0.8510 0.3255 0.0980]; ## data visualization Normalization = "absolute"; ColumnSummary = "off"; RowSummary = "off"; GridVisible = "on"; HandleVisibility = ""; OuterPosition = []; Position = []; Units = ""; endproperties properties (GetAccess = public, SetAccess = private) ClassLabels = {}; # a string cell array of classes NormalizedValues = []; # the normalized confusion matrix Parent = 0; # a handle to the parent object endproperties properties (Access = protected) hax = 0.0; # a handle to the axes ClassN = 0; # the number of classes AbsoluteValues = []; # the original confusion matrix ColumnSummaryAbsoluteValues = []; # default values of the column summary RowSummaryAbsoluteValues = []; # default values of the row summary endproperties methods (Access = public) ## class constructor ## inputs: axis handle, a confusion matrix, a list of class labels, ## an array of optional property-value pairs. function this = ConfusionMatrixChart (hax, cm, cl, args) ## class initialization this.hax = hax; this.Parent = get (this.hax, "parent"); this.ClassLabels = cl; this.NormalizedValues = cm; this.AbsoluteValues = cm; this.ClassN = rows (cm); this.FontName = get (this.hax, "fontname"); this.FontSize = get (this.hax, "fontsize"); set (this.hax, "xlabel", this.XLabel); set (this.hax, "ylabel", this.YLabel); ## draw the chart draw (this); ## apply paired properties if (! isempty (args)) pair_idx = 1; while (pair_idx < length (args)) switch (args{pair_idx}) case "XLabel" this.XLabel = args{pair_idx + 1}; case "YLabel" this.YLabel = args{pair_idx + 1}; case "Title" this.Title = args{pair_idx + 1}; case "FontName" this.FontName = args{pair_idx + 1}; case "FontSize" this.FontSize = args{pair_idx + 1}; case "DiagonalColor" this.DiagonalColor = args{pair_idx + 1}; case "OffDiagonalColor" this.OffDiagonalColor = args{pair_idx + 1}; case "Normalization" this.Normalization = args{pair_idx + 1}; case "ColumnSummary" this.ColumnSummary = args{pair_idx + 1}; case "RowSummary" this.RowSummary = args{pair_idx + 1}; case "GridVisible" this.GridVisible = args{pair_idx + 1}; case "HandleVisibility" this.HandleVisibility = args{pair_idx + 1}; case "OuterPosition" this.OuterPosition = args{pair_idx + 1}; case "Position" this.Position = args{pair_idx + 1}; case "Units" this.Units = args{pair_idx + 1}; otherwise close (this.Parent); error ("confusionchart: invalid property %s", args{pair_idx}); endswitch pair_idx += 2; endwhile endif ## init the color map updateColorMap (this); endfunction ## set functions function set.XLabel (this, string) if (! ischar (string)) close (this.Parent); error ("confusionchart: XLabel must be a string."); endif this.XLabel = updateAxesProperties (this, "xlabel", string); endfunction function set.YLabel (this, string) if (! ischar (string)) close (this.Parent); error ("confusionchart: YLabel must be a string."); endif this.YLabel = updateAxesProperties (this, "ylabel", string); endfunction function set.Title (this, string) if (! ischar (string)) close (this.Parent); error ("confusionchart: Title must be a string."); endif this.Title = updateAxesProperties (this, "title", string); endfunction function set.FontName (this, string) if (! ischar (string)) close (this.Parent); error ("confusionchart: FontName must be a string."); endif this.FontName = updateTextProperties (this, "fontname", string); endfunction function set.FontSize (this, value) if (! isnumeric (value)) close (this.Parent); error ("confusionchart: FontSize must be numeric."); endif this.FontSize = updateTextProperties (this, "fontsize", value); endfunction function set.DiagonalColor (this, color) if (ischar (color)) color = this.convertNamedColor (color); endif if (! (isvector (color) && length (color) == 3 )) close (this.Parent); error ("confusionchart: DiagonalColor must be a color."); endif this.DiagonalColor = color; updateColorMap (this); endfunction function set.OffDiagonalColor (this, color) if (ischar (color)) color = this.convertNamedColor (color); endif if (! (isvector (color) && length (color) == 3)) close (this.Parent); error ("confusionchart: OffDiagonalColor must be a color."); endif this.OffDiagonalColor = color; updateColorMap (this); endfunction function set.Normalization (this, string) if (! any (strcmp (string, {"absolute", "column-normalized",... "row-normalized", "total-normalized"}))) close (this.Parent); error ("confusionchart: invalid value for Normalization."); endif this.Normalization = string; updateChart (this); endfunction function set.ColumnSummary (this, string) if (! any (strcmp (string, {"off", "absolute", "column-normalized",... "total-normalized"}))) close (this.Parent); error ("confusionchart: invalid value for ColumnSummary."); endif this.ColumnSummary = string; updateChart (this); endfunction function set.RowSummary (this, string) if (! any (strcmp (string, {"off", "absolute", "row-normalized",... "total-normalized"}))) close (this.Parent); error ("confusionchart: invalid value for RowSummary."); endif this.RowSummary = string; updateChart (this); endfunction function set.GridVisible (this, string) if (! any (strcmp (string, {"off", "on"}))) close (this.Parent); error ("confusionchart: invalid value for GridVisible."); endif this.GridVisible = string; setGridVisibility (this); endfunction function set.HandleVisibility (this, string) if (! any (strcmp (string, {"off", "on", "callback"}))) close (this.Parent); error ("confusionchart: invalid value for HandleVisibility"); endif set (this.hax, "handlevisibility", string); endfunction function set.OuterPosition (this, vector) if (! isvector (vector) || ! isnumeric (vector) || length (vector) != 4) close (this.Parent); error ("confusionchart: invalid value for OuterPosition"); endif set (this.hax, "outerposition", vector); endfunction function set.Position (this, vector) if (! isvector (vector) || ! isnumeric (vector) || length (vector) != 4) close (this.Parent); error ("confusionchart: invalid value for Position"); endif set (this.hax, "position", vector); endfunction function set.Units (this, string) if (! any (strcmp (string, {"centimeters", "characters", "inches", ... "normalized", "pixels", "points"}))) close (this.Parent); error ("confusionchart: invalid value for Units"); endif set (this.hax, "units", string); endfunction ## display method ## MATLAB compatibility, this tries to mimic the MATLAB behaviour function disp (this) nv_sizes = size (this.NormalizedValues); cl_sizes = size (this.ClassLabels); printf ("%s with properties:\n\n", class (this)); printf ("\tNormalizedValues: [ %dx%d %s ]\n", nv_sizes(1), nv_sizes(2),... class (this.NormalizedValues)); printf ("\tClassLabels: { %dx%d %s }\n\n", cl_sizes(1), cl_sizes(2),... class (this.ClassLabels)); endfunction ## sortClasses ## reorder the chart function sortClasses (this, order) ## -*- texinfo -*- ## @deftypefn {} {} sortClasses (@var{cm},@var{order}) ## Sort the classes of the @code{ConfusionMatriChart} object @var{cm} ## according to @var{order}. ## ## Valid values for @var{order} can be an array or cell array including ## the same class labels as @var{cm}, or a value like @code{'auto'}, ## @code{'ascending-diagonal'}, @code{'descending-diagonal'} and ## @code{'cluster'}. ## ## @end deftypefn ## ## @seealso{confusionchart, linkage, pdist} ## check the input parameters if (nargin != 2) print_usage (); endif cl = this.ClassLabels; cm_size = this.ClassN; nv = this.NormalizedValues; av = this.AbsoluteValues; cv = this.ColumnSummaryAbsoluteValues; rv = this.RowSummaryAbsoluteValues; scl = {}; Idx = []; if (strcmp (order, "auto")) [scl, Idx] = sort (cl); elseif (strcmp (order, "ascending-diagonal")) [s, Idx] = sort (diag (nv)); scl = cl(Idx); elseif (strcmp (order, "descending-diagonal")) [s, Idx] = sort (diag (nv)); Idx = flip (Idx); scl = cl(Idx); elseif (strcmp (order, "cluster")) ## the classes are all grouped together ## this way one can visually evaluate which are the most similar classes ## according to the learning algorithm D = zeros (1, ((cm_size - 1) * cm_size / 2)); # a pdist like vector maxD = 2 * max (max (av)); k = 1; # better than computing the index at every cycle for i = 1 : (cm_size - 1) for j = (i + 1) : cm_size D(k++) = maxD - (av(i, j) + av(j, i)); # distance endfor endfor tree = linkage (D, "average"); # clustering ## we could have optimal leaf ordering with Idx = optimalleaforder (tree, D); # optimal clustering ## [sorted_v Idx] = sort (cluster (tree, )); nodes_to_visit = 2 * cm_size - 1; nodecount = 0; while (! isempty (nodes_to_visit)) current_node = nodes_to_visit(1); nodes_to_visit(1) = []; if (current_node > cm_size) node = current_node - cm_size; nodes_to_visit = [tree(node,[2 1]) nodes_to_visit]; end if (current_node <= cm_size) nodecount++; Idx(nodecount) = current_node; end end ## scl = cl(Idx); else ## must be an array or cell array of labels if (! iscellstr (order)) if (! ischar (order)) if (isrow (order)) order = vec (order); endif order = num2str (order); endif scl = cellstr (order); endif if (length (scl) != length (cl)) error ("sortClasses: wrong size for order.") endif Idx = zeros (length (scl), 1); for i = 1 : length (scl) Idx(i) = find (strcmp (cl, scl{i})); endfor endif ## rearrange the normalized values... nv = nv(Idx, :); nv = nv(:, Idx); this.NormalizedValues = nv; ## ...and the absolute values... av = av(Idx, :); av = av(:, Idx); this.AbsoluteValues = av; cv = cv([Idx ( Idx + cm_size )]); this.ColumnSummaryAbsoluteValues = cv; rv = rv([Idx ( Idx + cm_size )]); this.RowSummaryAbsoluteValues = rv; ## ...and the class labels this.ClassLabels = scl; ## update the axes set (this.hax, "xtick", (0.5 : 1 : (cm_size - 0.5)), "xticklabel", scl,... "ytick", (0.5 : 1 : (cm_size - 0.5)), "yticklabel", scl); ## get text and patch handles kids = get (this.hax, "children"); t_kids = kids(find (isprop (kids, "fontname"))); # hack to find texts m_kid = kids(find (strcmp (get (kids, "userdata"), "MainChart"))); c_kid = kids(find (strcmp (get (kids, "userdata"), "ColumnSummary"))); r_kid = kids(find (strcmp (get (kids, "userdata"), "RowSummary"))); ## re-assign colors to the main chart cdata_m = reshape (get (m_kid, "cdata"), cm_size, cm_size); cdata_m = cdata_m(Idx, :); cdata_m = cdata_m(:, Idx); cdata_v = vec (cdata_m); set (m_kid, "cdata", cdata_v); ## re-assign colors to the column summary cdata_m = reshape (transpose (get (c_kid, "cdata")), cm_size, 2); cdata_m = cdata_m(Idx, :); cdata_v = vec (cdata_m); set (c_kid, "cdata", cdata_v); ## re-assign colors to the row summary cdata_m = reshape (get (r_kid, "cdata"), cm_size, 2); cdata_m = cdata_m(Idx, :); cdata_v = vec (cdata_m); set (r_kid, "cdata", cdata_v); ## move the text labels for i = 1:length (t_kids) t_pos = get (t_kids(i), "userdata"); if (t_pos(2) > cm_size) ## row summary t_pos(1) = find (Idx == (t_pos(1) + 1)) - 1; set (t_kids(i), "userdata", t_pos); t_pos = t_pos([2 1]) + 0.5; set (t_kids(i), "position", t_pos); elseif (t_pos(1) > cm_size) ## column summary t_pos(2) = find (Idx == (t_pos(2) + 1)) - 1; set (t_kids(i), "userdata", t_pos); t_pos = t_pos([2 1]) + 0.5; set (t_kids(i), "position", t_pos); else ## main chart t_pos(1) = find (Idx == (t_pos(1) + 1)) - 1; t_pos(2) = find (Idx == (t_pos(2) + 1)) - 1; set (t_kids(i), "userdata", t_pos); t_pos = t_pos([2 1]) + 0.5; set (t_kids(i), "position", t_pos); endif endfor updateChart (this); endfunction endmethods methods (Access = private) ## convertNamedColor ## convert a named colour to a colour triplet function ret = convertNamedColor (this, color) vColorNames = ["ymcrgbwk"]'; vColorTriplets = [1 1 0; 1 0 1; 0 1 1; 1 0 0; 0 1 0; 0 0 1; 1 1 1; 0 0 0]; if (strcmp (color, "black")) color = 'k'; endif index = find (vColorNames == color(1)); if (! isempty (index)) ret = vColorTriplets(index, :); else ret = []; # trigger an error message endif endfunction ## updateAxesProperties ## update the properties of the axes function ret = updateAxesProperties (this, prop, value) set (this.hax, prop, value); ret = value; endfunction ## updateTextProperties ## set the properties of the texts function ret = updateTextProperties (this, prop, value) hax_kids = get (this.hax, "children"); text_kids = hax_kids(isprop (hax_kids , "fontname")); # hack to find texts text_kids(end + 1) = get (this.hax, "xlabel"); text_kids(end + 1) = get (this.hax, "ylabel"); text_kids(end + 1) = get (this.hax, "title"); updateAxesProperties (this, prop, value); set (text_kids, prop, value); ret = value; endfunction ## setGridVisibility ## toggle the visibility of the grid function setGridVisibility (this) kids = get (this.hax, "children"); kids = kids(find (isprop (kids, "linestyle"))); if (strcmp (this.GridVisible, "on")) set (kids, "linestyle", "-"); else set (kids, "linestyle", "none"); endif endfunction ## updateColorMap ## change the colormap and, accordingly, the text colors function updateColorMap (this) cm_size = this.ClassN; d_color = this.DiagonalColor; o_color = this.OffDiagonalColor; ## quick hack d_color(find (d_color == 1.0)) = 0.999; o_color(find (o_color == 1.0)) = 0.999; ## 64 shades for each color cm_colormap(1:64,:) = [1.0 : (-(1.0 - o_color(1)) / 63) : o_color(1);... 1.0 : (-(1.0 - o_color(2)) / 63) : o_color(2);... 1.0 : (-(1.0 - o_color(3)) / 63) : o_color(3)]'; cm_colormap(65:128,:) = [1.0 : (-(1.0 - d_color(1)) / 63) : d_color(1);... 1.0 : (-(1.0 - d_color(2)) / 63) : d_color(2);... 1.0 : (-(1.0 - d_color(3)) / 63) : d_color(3)]'; colormap (this.hax, cm_colormap); ## update text colors kids = get (this.hax, "children"); t_kids = kids(find (isprop (kids, "fontname"))); # hack to find texts m_patch = kids(find (strcmp (get (kids, "userdata"), "MainChart"))); c_patch = kids(find (strcmp (get (kids, "userdata"), "ColumnSummary"))); r_patch = kids(find (strcmp (get (kids, "userdata"), "RowSummary"))); m_colors = get (m_patch, "cdata"); c_colors = get (c_patch, "cdata"); r_colors = get (r_patch, "cdata"); ## when a patch is dark, let's use a pale color for the text for i = 1 : length (t_kids) t_pos = get (t_kids(i), "userdata"); color_idx = 1; if (t_pos(2) > cm_size) ## row summary idx = (t_pos(2) - cm_size - 1) * cm_size + t_pos(1) + 1; color_idx = r_colors(idx) + 1; elseif (t_pos(1) > cm_size) ## column summary idx = (t_pos(1) - cm_size - 1) * cm_size + t_pos(2) + 1; color_idx = c_colors(idx) + 1; else ## main chart idx = t_pos(2) * cm_size + t_pos(1) + 1; color_idx = m_colors(idx) + 1; endif if (sum (cm_colormap(color_idx, :)) < 1.8) set (t_kids(i), "color", [.97 .97 1.0]); else set (t_kids(i), "color", [.15 .15 .15]); endif endfor endfunction ## updateChart ## update the text labels and the NormalizedValues property function updateChart (this) cm_size = this.ClassN; cm = this.AbsoluteValues; l_cs = this.ColumnSummaryAbsoluteValues; l_rs = this.RowSummaryAbsoluteValues; kids = get (this.hax, "children"); t_kids = kids(find (isprop (kids, "fontname"))); # hack to find texts normalization = this.Normalization; column_summary = this.ColumnSummary; row_summary = this.RowSummary; ## normalization for labelling row_totals = sum (cm, 2); col_totals = sum (cm, 1); mat_total = sum (col_totals); cm_labels = cm; add_percent = true; if (strcmp (normalization, "column-normalized")) for i = 1 : cm_size cm_labels(:,i) = cm_labels(:,i) ./ col_totals(i); endfor elseif (strcmp (normalization, "row-normalized")) for i = 1 : cm_size cm_labels(i,:) = cm_labels(i,:) ./ row_totals(i); endfor elseif (strcmp (normalization, "total-normalized")) cm_labels = cm_labels ./ mat_total; else add_percent = false; endif ## update NormalizedValues this.NormalizedValues = cm_labels; ## update axes last_row = cm_size; last_col = cm_size; userdata = cell2mat (get (t_kids, "userdata")); cs_kids = t_kids(find (userdata(:,1) > cm_size)); cs_kids(end + 1) = kids(find (strcmp (get (kids, "userdata"),... "ColumnSummary"))); if (! strcmp ("off", column_summary)) set (cs_kids, "visible", "on"); last_row += 3; else set (cs_kids, "visible", "off"); endif rs_kids = t_kids(find (userdata(:,2) > cm_size)); rs_kids(end + 1) = kids(find (strcmp (get (kids, "userdata"),... "RowSummary"))); if (! strcmp ("off", row_summary)) set (rs_kids, "visible", "on"); last_col += 3; else set (rs_kids, "visible", "off"); endif axis (this.hax, [0 last_col 0 last_row]); ## update column summary data cs_add_percent = true; if (! strcmp (column_summary, "off")) if (strcmp (column_summary, "column-normalized")) for i = 1 : cm_size if (col_totals(i) == 0) ## avoid division by zero l_cs([i (cm_size + i)]) = 0; else l_cs([i, cm_size + i]) = l_cs([i, cm_size + i]) ./ col_totals(i); endif endfor elseif strcmp (column_summary, "total-normalized") l_cs = l_cs ./ mat_total; else cs_add_percent = false; endif endif ## update row summary data rs_add_percent = true; if (! strcmp (row_summary, "off")) if (strcmp (row_summary, "row-normalized")) for i = 1 : cm_size if (row_totals(i) == 0) ## avoid division by zero l_rs([i (cm_size + i)]) = 0; else l_rs([i, cm_size + i]) = l_rs([i, cm_size + i]) ./ row_totals(i); endif endfor elseif (strcmp (row_summary, "total-normalized")) l_rs = l_rs ./ mat_total; else rs_add_percent = false; endif endif ## update text label_list = vec (cm_labels); for i = 1 : length (t_kids) t_pos = get (t_kids(i), "userdata"); new_string = ""; if (t_pos(2) > cm_size) ## this is the row summary idx = (t_pos(2) - cm_size - 1) * cm_size + t_pos(1) + 1; if (rs_add_percent) new_string = num2str (100.0 * l_rs(idx), "%3.1f"); new_string = [new_string "%"]; else new_string = num2str (l_rs(idx)); endif elseif (t_pos(1) > cm_size) ## this is the column summary idx = (t_pos(1) - cm_size - 1) * cm_size + t_pos(2) + 1; if (cs_add_percent) new_string = num2str (100.0 * l_cs(idx), "%3.1f"); new_string = [new_string "%"]; else new_string = num2str (l_cs(idx)); endif else ## this is the main chart idx = t_pos(2) * cm_size + t_pos(1) + 1; if (add_percent) new_string = num2str (100.0 * label_list(idx), "%3.1f"); new_string = [new_string "%"]; else new_string = num2str (label_list(idx)); endif endif set (t_kids(i), "string", new_string); endfor endfunction ## draw ## draw the chart function draw (this) cm = this.AbsoluteValues; cl = this.ClassLabels; cm_size = this.ClassN; ## set up the axes set (this.hax, "xtick", (0.5 : 1 : (cm_size - 0.5)), "xticklabel", cl,... "ytick", (0.5 : 1 : (cm_size - 0.5)), "yticklabel", cl ); axis ("ij"); axis (this.hax, [0 cm_size 0 cm_size]); ## prepare the patches indices_b = 0 : (cm_size -1); indices_v = repmat (indices_b, cm_size, 1); indices_vx = transpose (vec (indices_v)); indices_vy = vec (indices_v', 2); indices_ex = vec ((cm_size + 1) * [1; 2] .* ones (2, cm_size), 2); ## normalization for colorization ## it is used a colormap of 128 shades of two colors, 64 shades for each ## color normal = max (max (cm)); cm_norm = round (63 * cm ./ normal); cm_norm = cm_norm + 64 * eye (cm_size); ## default normalization: absolute cm_labels = vec (cm); ## the patches of the main chart x_patch = [indices_vx; ( indices_vx + 1 ); ( indices_vx + 1 ); indices_vx]; y_patch = [indices_vy; indices_vy; ( indices_vy + 1 ); ( indices_vy + 1 )]; c_patch = vec (cm_norm(1 : cm_size, 1 : cm_size)); ## display the patches ph = patch (this.hax, x_patch, y_patch, c_patch); set (ph, "userdata", "MainChart"); ## display the labels userdata = [indices_vy; indices_vx]'; nonzero_idx = find (cm_labels != 0); th = text ((x_patch(1, nonzero_idx) + 0.5), (y_patch(1, nonzero_idx) +... 0.5), num2str (cm_labels(nonzero_idx)), "parent", this.hax ); set (th, "horizontalalignment", "center"); for i = 1 : length (nonzero_idx) set (th(i), "userdata", userdata(nonzero_idx(i), :)); endfor ## patches for the summaries main_values = diag (cm); ct_values = sum (cm)'; rt_values = sum (cm, 2); cd_values = ct_values - main_values; rd_values = rt_values - main_values; ## column summary x_cs = [[indices_b indices_b]; ( [indices_b indices_b] + 1 ); ( [indices_b indices_b] + 1 ); [indices_b indices_b]]; y_cs = [(repmat ([1 1 2 2]', 1, cm_size)) (repmat ([2 2 3 3]', 1, cm_size))] +... cm_size; c_cs = [(round (63 * (main_values ./ ct_values)) + 64); (round (63 * (cd_values ./ ct_values)))]; c_cs(isnan (c_cs)) = 0; l_cs = [main_values; cd_values]; ph = patch (this.hax, x_cs, y_cs, c_cs); set (ph, "userdata", "ColumnSummary"); set (ph, "visible", "off" ); userdata = [y_cs(1,:); x_cs(1,:)]'; nonzero_idx = find (l_cs != 0); th = text ((x_cs(1,nonzero_idx) + 0.5), (y_cs(1,nonzero_idx) + 0.5),... num2str (l_cs(nonzero_idx)), "parent", this.hax); set (th, "horizontalalignment", "center"); for i = 1 : length (nonzero_idx) set (th(i), "userdata", userdata(nonzero_idx(i), :)); endfor set (th, "visible", "off"); ## row summary x_rs = y_cs; y_rs = x_cs; c_rs = [(round (63 * (main_values ./ rt_values)) + 64); (round (63 * (rd_values ./ rt_values)))]; c_rs(isnan (c_rs)) = 0; l_rs = [main_values; rd_values]; ph = patch (this.hax, x_rs, y_rs, c_rs); set (ph, "userdata", "RowSummary"); set (ph, "visible", "off"); userdata = [y_rs(1,:); x_rs(1,:)]'; nonzero_idx = find (l_rs != 0); th = text ((x_rs(1,nonzero_idx) + 0.5), (y_rs(1,nonzero_idx) + 0.5),... num2str (l_rs(nonzero_idx)), "parent", this.hax); set (th, "horizontalalignment", "center"); for i = 1 : length (nonzero_idx) set (th(i), "userdata", userdata(nonzero_idx(i), :)); endfor set (th, "visible", "off"); this.ColumnSummaryAbsoluteValues = l_cs; this.RowSummaryAbsoluteValues = l_rs; endfunction endmethods endclassdef statistics-1.4.3/inst/anderson_darling_cdf.m0000644000000000000000000000726614153320774017400 0ustar0000000000000000## Author: Paul Kienzle ## This program is granted to the public domain. ## -*- texinfo -*- ## @deftypefn {Function File} @var{p} = anderson_darling_cdf (@var{A}, @var{n}) ## ## Return the CDF for the given Anderson-Darling coefficient @var{A} ## computed from @var{n} values sampled from a distribution. For a ## vector of random variables @var{x} of length @var{n}, compute the CDF ## of the values from the distribution from which they are drawn. ## You can uses these values to compute @var{A} as follows: ## ## @example ## @var{A} = -@var{n} - sum( (2*i-1) .* (log(@var{x}) + log(1 - @var{x}(@var{n}:-1:1,:))) )/@var{n}; ## @end example ## ## From the value @var{A}, @code{anderson_darling_cdf} returns the probability ## that @var{A} could be returned from a set of samples. ## ## The algorithm given in [1] claims to be an approximation for the ## Anderson-Darling CDF accurate to 6 decimal points. ## ## Demonstrate using: ## ## @example ## n = 300; reps = 10000; ## z = randn(n, reps); ## x = sort ((1 + erf (z/sqrt (2)))/2); ## i = [1:n]' * ones (1, size (x, 2)); ## A = -n - sum ((2*i-1) .* (log (x) + log (1 - x (n:-1:1, :))))/n; ## p = anderson_darling_cdf (A, n); ## hist (100 * p, [1:100] - 0.5); ## @end example ## ## You will see that the histogram is basically flat, which is to ## say that the probabilities returned by the Anderson-Darling CDF ## are distributed uniformly. ## ## You can easily determine the extreme values of @var{p}: ## ## @example ## [junk, idx] = sort (p); ## @end example ## ## The histograms of various @var{p} aren't very informative: ## ## @example ## histfit (z (:, idx (1)), linspace (-3, 3, 15)); ## histfit (z (:, idx (end/2)), linspace (-3, 3, 15)); ## histfit (z (:, idx (end)), linspace (-3, 3, 15)); ## @end example ## ## More telling is the qqplot: ## ## @example ## qqplot (z (:, idx (1))); hold on; plot ([-3, 3], [-3, 3], ';;'); hold off; ## qqplot (z (:, idx (end/2))); hold on; plot ([-3, 3], [-3, 3], ';;'); hold off; ## qqplot (z (:, idx (end))); hold on; plot ([-3, 3], [-3, 3], ';;'); hold off; ## @end example ## ## Try a similarly analysis for @var{z} uniform: ## ## @example ## z = rand (n, reps); x = sort(z); ## @end example ## ## and for @var{z} exponential: ## ## @example ## z = rande (n, reps); x = sort (1 - exp (-z)); ## @end example ## ## [1] Marsaglia, G; Marsaglia JCW; (2004) "Evaluating the Anderson Darling ## distribution", Journal of Statistical Software, 9(2). ## ## @seealso{anderson_darling_test} ## @end deftypefn function y = anderson_darling_cdf(z,n) y = ADinf(z); y += ADerrfix(y,n); end function y = ADinf(z) y = zeros(size(z)); idx = (z < 2); if any(idx(:)) p = [.00168691, -.0116720, .0347962, -.0649821, .247105, 2.00012]; z1 = z(idx); y(idx) = exp(-1.2337141./z1)./sqrt(z1).*polyval(p,z1); end idx = (z >= 2); if any(idx(:)) p = [-.0003146, +.008056, -.082433, +.43424, -2.30695, 1.0776]; y(idx) = exp(-exp(polyval(p,z(idx)))); end end function y = ADerrfix(x,n) if isscalar(n), n = n*ones(size(x)); elseif isscalar(x), x = x*ones(size(n)); end y = zeros(size(x)); c = .01265 + .1757./n; idx = (x >= 0.8); if any(idx(:)) p = [255.7844, -1116.360, 1950.646, -1705.091, 745.2337, -130.2137]; g3 = polyval(p,x(idx)); y(idx) = g3./n(idx); end idx = (x < 0.8 & x > c); if any(idx(:)) p = [1.91864, -8.259, 14.458, -14.6538, 6.54034, -.00022633]; n1 = 1./n(idx); c1 = c(idx); g2 = polyval(p,(x(idx)-c1)./(.8-c1)); y(idx) = (.04213 + .01365*n1).*n1 .* g2; end idx = (x <= c); if any(idx(:)) x1 = x(idx)./c(idx); n1 = 1./n(idx); g1 = sqrt(x1).*(1-x1).*(49*x1-102); y(idx) = ((.0037*n1+.00078).*n1+.00006).*n1 .* g1; end end statistics-1.4.3/inst/anderson_darling_test.m0000644000000000000000000001235014153320774017611 0ustar0000000000000000## Author: Paul Kienzle ## This program is granted to the public domain. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{q}, @var{Asq}, @var{info}] = } = @ ## anderson_darling_test (@var{x}, @var{distribution}) ## ## Test the hypothesis that @var{x} is selected from the given distribution ## using the Anderson-Darling test. If the returned @var{q} is small, reject ## the hypothesis at the @var{q}*100% level. ## ## The Anderson-Darling @math{@var{A}^2} statistic is calculated as follows: ## ## @example ## @iftex ## A^2_n = -n - \sum_{i=1}^n (2i-1)/n log(z_i (1-z_{n-i+1})) ## @end iftex ## @ifnottex ## n ## A^2_n = -n - SUM (2i-1)/n log(@math{z_i} (1 - @math{z_@{n-i+1@}})) ## i=1 ## @end ifnottex ## @end example ## ## where @math{z_i} is the ordered position of the @var{x}'s in the CDF of the ## distribution. Unlike the Kolmogorov-Smirnov statistic, the ## Anderson-Darling statistic is sensitive to the tails of the ## distribution. ## ## The @var{distribution} argument must be a either @t{"uniform"}, @t{"normal"}, ## or @t{"exponential"}. ## ## For @t{"normal"}' and @t{"exponential"} distributions, estimate the ## distribution parameters from the data, convert the values ## to CDF values, and compare the result to tabluated critical ## values. This includes an correction for small @var{n} which ## works well enough for @var{n} >= 8, but less so from smaller @var{n}. The ## returned @code{info.Asq_corrected} contains the adjusted statistic. ## ## For @t{"uniform"}, assume the values are uniformly distributed ## in (0,1), compute @math{@var{A}^2} and return the corresponding @math{p}-value from ## @code{1-anderson_darling_cdf(A^2,n)}. ## ## If you are selecting from a known distribution, convert your ## values into CDF values for the distribution and use @t{"uniform"}. ## Do not use @t{"uniform"} if the distribution parameters are estimated ## from the data itself, as this sharply biases the @math{A^2} statistic ## toward smaller values. ## ## [1] Stephens, MA; (1986), "Tests based on EDF statistics", in ## D'Agostino, RB; Stephens, MA; (eds.) Goodness-of-fit Techinques. ## New York: Dekker. ## ## @seealso{anderson_darling_cdf} ## @end deftypefn function [q,Asq,info] = anderson_darling_test(x,dist) if size(x,1) == 1, x=x(:); end x = sort(x); n = size(x,1); use_cdf = 0; # Compute adjustment and critical values to use for stats. switch dist case 'normal', # This expression for adj is used in R. # Note that the values from NIST dataplot don't work nearly as well. adj = 1 + (.75 + 2.25/n)/n; qvals = [ 0.1, 0.05, 0.025, 0.01 ]; Acrit = [ 0.631, 0.752, 0.873, 1.035]; x = stdnormal_cdf(zscore(x)); case 'uniform', ## Put invalid data at the limits of the distribution ## This will drive the statistic to infinity. x(x<0) = 0; x(x>1) = 1; adj = 1.; qvals = [ 0.1, 0.05, 0.025, 0.01 ]; Acrit = [ 1.933, 2.492, 3.070, 3.857 ]; use_cdf = 1; case 'XXXweibull', adj = 1 + 0.2/sqrt(n); qvals = [ 0.1, 0.05, 0.025, 0.01 ]; Acrit = [ 0.637, 0.757, 0.877, 1.038]; ## XXX FIXME XXX how to fit alpha and sigma? x = wblcdf (x, ones(n,1)*sigma, ones(n,1)*alpha); case 'exponential', adj = 1 + 0.6/n; qvals = [ 0.1, 0.05, 0.025, 0.01 ]; # Critical values depend on n. Choose the appropriate critical set. # These values come from NIST dataplot/src/dp8.f. Acritn = [ 0, 1.022, 1.265, 1.515, 1.888 11, 1.045, 1.300, 1.556, 1.927; 21, 1.062, 1.323, 1.582, 1.945; 51, 1.070, 1.330, 1.595, 1.951; 101, 1.078, 1.341, 1.606, 1.957; ]; # FIXME: consider interpolating in the critical value table. Acrit = Acritn(lookup(Acritn(:,1),n),2:5); lambda = 1./mean(x); # exponential parameter estimation x = expcdf(x, 1./(ones(n,1)*lambda)); otherwise # FIXME consider implementing more of distributions; a number # of them are defined in NIST dataplot/src/dp8.f. error("Anderson-Darling test for %s not implemented", dist); endswitch if any(x<0 | x>1) error('Anderson-Darling test requires data in CDF form'); endif i = [1:n]'*ones(1,size(x,2)); Asq = -n - sum( (2*i-1) .* (log(x) + log(1-x(n:-1:1,:))) )/n; # Lookup adjusted critical value in the cdf (if uniform) or in the # the critical table. if use_cdf q = 1-anderson_darling_cdf(Asq*adj, n); else idx = lookup([-Inf,Acrit],Asq*adj); q = [1,qvals](idx); endif if nargout > 2, info.Asq = Asq; info.Asq_corrected = Asq*adj; info.Asq_critical = [100*(1-qvals); Acrit]'; info.p = 1-q; info.p_is_precise = use_cdf; endif endfunction %!demo %! c = anderson_darling_test(10*rande(12,10000),'exponential'); %! tabulate(100*c,100*[unique(c),1]); %! % The Fc column should report 100, 250, 500, 1000, 10000 more or less. %!demo %! c = anderson_darling_test(randn(12,10000),'normal'); %! tabulate(100*c,100*[unique(c),1]); %! % The Fc column should report 100, 250, 500, 1000, 10000 more or less. %!demo %! c = anderson_darling_test(rand(12,10000),'uniform'); %! hist(100*c,1:2:99); %! % The histogram should be flat more or less. statistics-1.4.3/inst/anova1.m0000644000000000000000000002250514153320774014431 0ustar0000000000000000## Copyright (C) 2021 Andreas Bertsatos ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} =} anova1 (@var{x}) ## @deftypefnx {Function File} {@var{p} =} anova1 (@var{x}, @var{group}) ## @deftypefnx {Function File} {@var{p} =} anova1 (@var{x}, @var{group}, @var{displayopt}) ## @deftypefnx {Function File} {[@var{p}, @var{atab}] =} anova1 (@var{x}, @dots{}) ## @deftypefnx {Function File} {[@var{p}, @var{atab}, @var{stats}] =} anova1 (@var{x}, @dots{}) ## ## Perform a one-way analysis of variance (ANOVA) for comparing the means of two ## or more groups of data under the null hypothesis that the groups are drawn ## from the same distribution, i.e. the group means are equal. ## ## anova1 can take up to three input arguments: ## ## @itemize ## @item ## @var{x} contains the data and it can either be a vector or matrix. ## If @var{x} is a matrix, then each column is treated as a separate group. ## If @var{x} is a vector, then the @var{group} argument is mandatory. ## @item ## @var{group} contains the names for each group. If @var{x} is a matrix, then ## @var{group} can either be a cell array of strings of a character array, with ## one row per column of @var{x}. If you want to omit this argument, enter an ## empty array ([]). If @var{x} is a vector, then @var{group} must be a vector ## of the same length, or a string array or cell array of strings with one row ## for each element of @var{x}. @var{x} values corresponding to the same value ## of @var{group} are placed in the same group. ## @item ## @var{displayopt} is an optional parameter for displaying the groups contained ## in the data in a boxplot. If omitted, it is 'on' by default. If group names ## are defined in @var{group}, these are used to identify the groups in the ## boxplot. Use 'off' to omit displaying this figure. ## @end itemize ## ## anova1 can return up to three output arguments: ## ## @itemize ## @item ## @var{p} is the p-value of the null hypothesis that all group means are equal. ## @item ## @var{atab} is a cell array containing the results in a standard ANOVA table. ## @item ## @var{stats} is a structure containing statistics useful for performing ## a multiple comparison of means with the MULTCOMPARE function. ## @end itemize ## ## If anova1 is called without any output arguments, then it prints the results ## in a one-way ANOVA table to the standard output. It is also printed when ## @var{displayopt} is 'on'. ## ## ## Examples: ## ## @example ## x = meshgrid (1:6); ## x = x + normrnd (0, 1, 6, 6); ## anova1 (x, [], 'off'); ## [p, atab] = anova1(x); ## @end example ## ## ## @example ## x = ones (50, 4) .* [-2, 0, 1, 5]; ## x = x + normrnd (0, 2, 50, 4); ## groups = @{"A", "B", "C", "D"@}; ## anova1 (x, groups); ## @end example ## ## @end deftypefn function [p, anovatab, stats] = anova1 (x, group, displayopt) ## check for valid number of input arguments narginchk (1, 3); ## add defaults if (nargin < 2) group = []; endif if (nargin < 3) displayopt = 'on'; endif plotdata = ~(strcmp (displayopt, 'off')); ## Convert group to cell array from character array, make it a column if (! isempty (group) && ischar (group)) group = cellstr(group); endif if (size (group, 1) == 1) group = group'; endif ## If X is a matrix, convert it to column vector and create a ## corresponging column vector for groups if (length (x) < prod (size (x))) [n, m] = size (x); x = x(:); gi = reshape (repmat ((1:m), n, 1), n*m, 1); if (length (group) == 0) ## no group names are provided group = gi; elseif (size (group, 1) == m) ## group names exist and match columns group = group(gi,:); else error("X columns and GROUP length do not match."); endif endif ## Identify NaN values (if any) and remove them from X along with ## their corresponding values from group vector nonan = ~isnan (x); x = x(nonan); group = group(nonan, :); ## Convert group to indices and separate names [group_id, group_names] = grp2idx (group); group_id = group_id(:); named = 1; ## Center data to improve accuracy and keep uncentered data for ploting xorig = x; mu = mean(x); x = x - mu; xr = x; ## Get group size and mean for each group groups = size (group_names, 1); xs = zeros (1, groups); xm = xs; for j = 1:groups group_size = find (group_id == j); xs(j) = length (group_size); xm(j) = mean (xr(group_size)); endfor ## Calculate statistics lx = length (xr); ## Number of samples in groups gm = mean (xr); ## Grand mean of groups dfm = length (xm) - 1; ## degrees of freedom for model dfe = lx - dfm - 1; ## degrees of freedom for error SSM = xs .* (xm - gm) * (xm - gm)'; ## Sum of Squares for Model SST = (xr(:) - gm)' * (xr(:) - gm); ## Sum of Squares Total SSE = SST - SSM; ## Sum of Squares Error if (dfm > 0) MSM = SSM / dfm; ## Mean Square for Model else MSM = NaN; endif if (dfe > 0) MSE = SSE / dfe; ## Mean Square for Error else MSE = NaN; endif ## Calculate F statistic if (SSE != 0) ## Regular Matrix case. F = (SSM / dfm) / MSE; p = 1 - fcdf (F, dfm, dfe); ## Probability of F given equal means. elseif (SSM == 0) ## Constant Matrix case. F = 0; p = 1; else ## Perfect fit case. F = Inf; p = 0; end ## Create results table (if requested) if (nargout > 1) anovatab = {"Source", "SS", "df", "MS", "F", "Prob>F"; ... "Groups", SSM, dfm, MSM, F, p; ... "Error", SSE, dfe, MSE, "", ""; ... "Total", SST, dfm + dfe, "", "", ""}; endif ## Create stats structure (if requested) for MULTCOMPARE if (nargout > 2) if (length (group_names) > 0) stats.gnames = group_names; else stats.gnames = strjust (num2str ((1:length (xm))'), 'left'); end stats.n = xs; stats.source = 'anova1'; stats.means = xm + mu; stats.df = dfe; stats.s = sqrt (MSE); endif ## Print results table on screen if no output argument was requested if (nargout == 0 || plotdata) printf(" ANOVA Table\n"); printf("Source SS df MS F Prob>F\n"); printf("------------------------------------------------------\n"); printf("Columns %10.4f %5.0f %10.4f %8.2f %9.4f\n", SSM, dfm, MSM, F, p); printf("Error %10.4f %5.0f %10.4f\n", SSE, dfe, MSE); printf("Total %10.4f %5.0f\n", SST, dfm + dfe); endif ## Plot data using BOXPLOT (unless opted out) if (plotdata) boxplot (x, group_id, 'Notch', "on", 'Labels', group_names); endif endfunction %!demo %! x = meshgrid (1:6); %! x = x + normrnd (0, 1, 6, 6); %! anova1 (x, [], 'off'); %!demo %! x = meshgrid (1:6); %! x = x + normrnd (0, 1, 6, 6); %! [p, atab] = anova1(x); %!demo %! x = ones (50, 4) .* [-2, 0, 1, 5]; %! x = x + normrnd (0, 2, 50, 4); %! groups = {"A", "B", "C", "D"}; %! anova1 (x, groups); ## testing against GEAR.DAT data file and results for one-factor ANOVA from ## https://www.itl.nist.gov/div898/handbook/eda/section3/eda354.htm %!test %! data = [1.006, 0.996, 0.998, 1.000, 0.992, 0.993, 1.002, 0.999, 0.994, 1.000, ... %! 0.998, 1.006, 1.000, 1.002, 0.997, 0.998, 0.996, 1.000, 1.006, 0.988, ... %! 0.991, 0.987, 0.997, 0.999, 0.995, 0.994, 1.000, 0.999, 0.996, 0.996, ... %! 1.005, 1.002, 0.994, 1.000, 0.995, 0.994, 0.998, 0.996, 1.002, 0.996, ... %! 0.998, 0.998, 0.982, 0.990, 1.002, 0.984, 0.996, 0.993, 0.980, 0.996, ... %! 1.009, 1.013, 1.009, 0.997, 0.988, 1.002, 0.995, 0.998, 0.981, 0.996, ... %! 0.990, 1.004, 0.996, 1.001, 0.998, 1.000, 1.018, 1.010, 0.996, 1.002, ... %! 0.998, 1.000, 1.006, 1.000, 1.002, 0.996, 0.998, 0.996, 1.002, 1.006, ... %! 1.002, 0.998, 0.996, 0.995, 0.996, 1.004, 1.004, 0.998, 0.999, 0.991, ... %! 0.991, 0.995, 0.984, 0.994, 0.997, 0.997, 0.991, 0.998, 1.004, 0.997]; %! group = [1:10] .* ones (10,10); %! group = group(:); %! [p, tbl] = anova1 (data, group, "off"); %! assert (p, 0.022661, 1e-6); %! assert (tbl{2,5}, 2.2969, 1e-4); %! assert (tbl{2,3}, 9, 0); %! assert (tbl{4,2}, 0.003903, 1e-6); %! data = reshape (data, 10, 10); %! [p, tbl, stats] = anova1 (data, [], "off"); %! assert (p, 0.022661, 1e-6); %! assert (tbl{2,5}, 2.2969, 1e-4); %! assert (tbl{2,3}, 9, 0); %! assert (tbl{4,2}, 0.003903, 1e-6); %! means = [0.998, 0.9991, 0.9954, 0.9982, 0.9919, 0.9988, 1.0015, 1.0004, 0.9983, 0.9948]; %! N = 10 * ones (1, 10); %! assert (stats.means, means, 1e-6); %! assert (length (stats.gnames), 10, 0); %! assert (stats.n, N, 0); statistics-1.4.3/inst/anovan.m0000644000000000000000000002737414153320774014537 0ustar0000000000000000## Copyright (C) 2003-2005 Andy Adler ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{pval}, @var{f}, @var{df_b}, @var{df_e}] =} anovan (@var{data}, @var{grps}) ## @deftypefnx {Function File} {[@var{pval}, @var{f}, @var{df_b}, @var{df_e}] =} anovan (@var{data}, @var{grps}, 'param1', @var{value1}) ## Perform a multi-way analysis of variance (ANOVA). The goal is to test ## whether the population means of data taken from @var{k} different ## groups are all equal. ## ## Data is a single vector @var{data} with groups specified by ## a corresponding matrix of group labels @var{grps}, where @var{grps} ## has the same number of rows as @var{data}. For example, if ## @var{data} = [1.1;1.2]; @var{grps}= [1,2,1; 1,5,2]; ## then data point 1.1 was measured under conditions 1,2,1 and ## data point 1.2 was measured under conditions 1,5,2. ## Note that groups do not need to be sequentially numbered. ## ## By default, a 'linear' model is used, computing the N main effects ## with no interactions. this may be modified by param 'model' ## ## p= anovan(data,groups, 'model', modeltype) ## - modeltype = 'linear': compute N main effects ## - modeltype = 'interaction': compute N effects and ## N*(N-1) two-factor interactions ## - modeltype = 'full': compute interactions at all levels ## ## Under the null of constant means, the statistic @var{f} follows an F ## distribution with @var{df_b} and @var{df_e} degrees of freedom. ## ## The p-value (1 minus the CDF of this distribution at @var{f}) is ## returned in @var{pval}. ## ## If no output argument is given, the standard one-way ANOVA table is ## printed. ## ## BUG: DFE is incorrect for modeltypes != full ## @end deftypefn ## Author: Andy Adler ## Based on code by: KH ## $Id$ ## ## TESTING RESULTS: ## 1. ANOVA ACCURACY: www.itl.nist.gov/div898/strd/anova/anova.html ## Passes 'easy' test. Comes close on 'Average'. Fails 'Higher'. ## This could be fixed with higher precision arithmetic ## 2. Matlab anova2 test ## www.mathworks.com/access/helpdesk/help/toolbox/stats/anova2.html ## % From web site: ## popcorn= [ 5.5 4.5 3.5; 5.5 4.5 4.0; 6.0 4.0 3.0; ## 6.5 5.0 4.0; 7.0 5.5 5.0; 7.0 5.0 4.5]; ## % Define groups so reps = 3 ## groups = [ 1 1;1 2;1 3;1 1;1 2;1 3;1 1;1 2;1 3; ## 2 1;2 2;2 3;2 1;2 2;2 3;2 1;2 2;2 3 ]; ## anovan( vec(popcorn'), groups, 'model', 'full') ## % Results same as Matlab output ## 3. Matlab anovan test ## www.mathworks.com/access/helpdesk/help/toolbox/stats/anovan.html ## % From web site ## y = [52.7 57.5 45.9 44.5 53.0 57.0 45.9 44.0]'; ## g1 = [1 2 1 2 1 2 1 2]; ## g2 = {'hi';'hi';'lo';'lo';'hi';'hi';'lo';'lo'}; ## g3 = {'may'; 'may'; 'may'; 'may'; 'june'; 'june'; 'june'; 'june'}; ## anovan( y', [g1',g2',g3']) ## % Fails because we always do interactions function [PVAL, FSTAT, DF_B, DFE] = anovan (data, grps, varargin) if nargin <= 1 usage ("anovan (data, grps)"); end # test supplied parameters modeltype= 'linear'; for idx= 3:2:nargin param= varargin{idx-2}; value= varargin{idx-1}; if strcmp(param, 'model') modeltype= value; # elseif strcmp(param # add other parameters here else error(sprintf('parameter %s is not supported', param)); end end if ~isvector (data) error ("anova: for `anova (data, grps)', data must be a vector"); endif nd = size (grps,1); # number of data points nw = size (grps,2); # number of anova "ways" if (~ isvector (data) || (length(data) ~= nd)) error ("anova: grps must be a matrix of the same number of rows as data"); endif [g,grp_map] = relabel_groups (grps); if strcmp(modeltype, 'linear') max_interact = 1; elseif strcmp(modeltype,'interaction') max_interact = 2; elseif strcmp(modeltype,'full') max_interact = rows(grps); else error(sprintf('modeltype %s is not supported', modeltype)); end ng = length(grp_map); int_tbl = interact_tbl (nw, ng, max_interact ); [gn, gs, gss] = raw_sums(data, g, ng, int_tbl); stats_tbl = int_tbl(2:size(int_tbl,1),:)>0; nstats= size(stats_tbl,1); stats= zeros( nstats+1, 5); # SS, DF, MS, F, p for i= 1:nstats [SS, DF, MS]= factor_sums( gn, gs, gss, stats_tbl(i,:), ng, nw); stats(i,1:3)= [SS, DF, MS]; end # The Mean squared error is the data - avg for each possible measurement # This calculation doesn't work unless there is replication for all grps # SSE= sum( gss(sel) ) - sum( gs(sel).^2 ./ gn(sel) ); SST= gss(1) - gs(1)^2/gn(1); SSE= SST - sum(stats(:,1)); sel = select_pat( ones(1,nw), ng, nw); %incorrect for modeltypes != full DFE= sum( (gn(sel)-1).*(gn(sel)>0) ); MSE= SSE/DFE; stats(nstats+1,1:3)= [SSE, DFE, MSE]; for i= 1:nstats MS= stats(i,3); DF= stats(i,2); F= MS/MSE; pval = 1 - fcdf (F, DF, DFE); stats(i,4:5)= [F, pval]; end if nargout==0; printout( stats, stats_tbl ); else PVAL= stats(1:nstats,5); FSTAT=stats(1:nstats,4); DF_B= stats(1:nstats,2); DF_E= DFE; end endfunction # relabel groups to a mapping from 1 to ng # Input # grps input grouping # Output # g relabelled grouping # grp_map map from output to input grouping function [g,grp_map] = relabel_groups(grps) grp_vec= vec(grps); s= sort (grp_vec); uniq = 1+[0;find(diff(s))]; # mapping from new grps to old groups grp_map = s(uniq); # create new group g ngroups= length(uniq); g= zeros(size(grp_vec)); for i = 1:ngroups g( find( grp_vec== grp_map(i) ) ) = i; end g= reshape(g, size(grps)); endfunction # Create interaction table # # Input: # nw number of "ways" # ng number of ANOVA groups # max_interact maximum number of interactions to consider # default is nw function int_tbl =interact_tbl(nw, ng, max_interact) combin= 2^nw; inter_tbl= zeros( combin, nw); idx= (0:combin-1)'; for i=1:nw; inter_tbl(:,i) = ( rem(idx,2^i) >= 2^(i-1) ); end # find elements with more than max_interact 1's idx = ( sum(inter_tbl',1) > max_interact ); inter_tbl(idx,:) =[]; combin= size(inter_tbl,1); # update value #scale inter_tbl # use ng+1 to map combinations of groups to integers # this would be lots easier with a hash data structure int_tbl = inter_tbl .* (ones(combin,1) * (ng+1).^(0:nw-1) ); endfunction # Calculate sums for each combination # # Input: # g relabelled grouping matrix # ng number of ANOVA groups # max_interact # # Output (virtual (ng+1)x(nw) matrices): # gn number of data sums in each group # gs sum of data in each group # gss sumsqr of data in each group function [gn, gs, gss] = raw_sums(data, g, ng, int_tbl); nw= size(g,2); ndata= size(g,1); gn= gs= gss= zeros((ng+1)^nw, 1); for i=1:ndata # need offset by one for indexing datapt= data(i); idx = 1+ int_tbl*g(i,:)'; gn(idx) +=1; gs(idx) +=datapt; gss(idx) +=datapt^2; end endfunction # Calcualte the various factor sums # Input: # gn number of data sums in each group # gs sum of data in each group # gss sumsqr of data in each group # select binary vector of factor for this "way"? # ng number of ANOVA groups # nw number of ways function [SS,DF]= raw_factor_sums( gn, gs, gss, select, ng, nw); sel= select_pat( select, ng, nw); ss_raw= gs(sel).^2 ./ gn(sel); SS= sum( ss_raw( ~isnan(ss_raw) )); if length(find(select>0))==1 DF= sum(gn(sel)>0)-1; else DF= 1; #this isn't the real DF, but needed to multiply end endfunction function [SS, DF, MS]= factor_sums( gn, gs, gss, select, ng, nw); SS=0; DF=1; ff = find(select); lff= length(ff); # zero terms added, one term subtracted, two added, etc for i= 0:2^lff-1 remove= find( rem( floor( i * 2.^(-lff+1:0) ), 2) ); sel1= select; if ~isempty(remove) sel1( ff( remove ) )=0; end [raw_sum,raw_df]= raw_factor_sums(gn,gs,gss,sel1,ng,nw); add_sub= (-1)^length(remove); SS+= add_sub*raw_sum; DF*= raw_df; end MS= SS/DF; endfunction # Calcualte the various factor sums # Input: # select binary vector of factor for this "way"? # ng number of ANOVA groups # nw number of ways function sel= select_pat( select, ng, nw); # if select(i) is zero, remove nonzeros # if select(i) is zero, remove zero terms for i field=[]; if length(select) ~= nw; error("length of select must be = nw"); end ng1= ng+1; if isempty(field) # expand 0:(ng+1)^nw in base ng+1 field= (0:(ng1)^nw-1)'* ng1.^(-nw+1:0); field= rem( floor( field), ng1); # select zero or non-zero elements field= field>0; end sel= find( all( field == ones(ng1^nw,1)*select(:)', 2) ); endfunction function printout( stats, stats_tbl ); nw= size( stats_tbl,2); [jnk,order]= sort( sum(stats_tbl,2) ); printf('\n%d-way ANOVA Table (Factors A%s):\n\n', nw, ... sprintf(',%c',double('A')+(1:nw-1)) ); printf('Source of Variation Sum Sqr df MeanSS Fval p-value\n'); printf('*********************************************************************\n'); printf('Error %10.2f %4d %10.2f\n', stats( size(stats,1),1:3)); for i= order(:)' str= sprintf(' %c x',double('A')+find(stats_tbl(i,:)>0)-1 ); str= str(1:length(str)-2); # remove x printf('Factor %15s %10.2f %4d %10.2f %7.3f %7.6f\n', ... str, stats(i,:) ); end printf('\n'); endfunction #{ # Test Data from http://maths.sci.shu.ac.uk/distance/stats/14.shtml data=[7 9 9 8 12 10 ... 9 8 10 11 13 13 ... 9 10 10 12 10 12]'; grp = [1,1; 1,1; 1,2; 1,2; 1,3; 1,3; 2,1; 2,1; 2,2; 2,2; 2,3; 2,3; 3,1; 3,1; 3,2; 3,2; 3,3; 3,3]; data=[7 9 9 8 12 10 9 8 ... 9 8 10 11 13 13 10 11 ... 9 10 10 12 10 12 10 12]'; grp = [1,4; 1,4; 1,5; 1,5; 1,6; 1,6; 1,7; 1,7; 2,4; 2,4; 2,5; 2,5; 2,6; 2,6; 2,7; 2,7; 3,4; 3,4; 3,5; 3,5; 3,6; 3,6; 3,7; 3,7]; # Test Data from http://maths.sci.shu.ac.uk/distance/stats/9.shtml data=[9.5 11.1 11.9 12.8 ... 10.9 10.0 11.0 11.9 ... 11.2 10.4 10.8 13.4]'; grp= [1:4,1:4,1:4]'; # Test Data from http://maths.sci.shu.ac.uk/distance/stats/13.shtml data=[7.56 9.68 11.65 ... 9.98 9.69 10.69 ... 7.23 10.49 11.77 ... 8.22 8.55 10.72 ... 7.59 8.30 12.36]'; grp = [1,1;1,2;1,3; 2,1;2,2;2,3; 3,1;3,2;3,3; 4,1;4,2;4,3; 5,1;5,2;5,3]; # Test Data from www.mathworks.com/ # access/helpdesk/help/toolbox/stats/linear10.shtml data=[23 27 43 41 15 17 3 9 20 63 55 90]; grp= [ 1 1 1 1 2 2 2 2 3 3 3 3; 1 1 2 2 1 1 2 2 1 1 2 2]'; #} statistics-1.4.3/inst/bbscdf.m0000644000000000000000000000762714153320774014477 0ustar0000000000000000## Copyright (C) 2018 John Donoghue ## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} bbscdf (@var{x}, @var{shape}, @var{scale}, @var{location}) ## For each element of @var{x}, compute the cumulative distribution function ## (CDF) at @var{x} of the Birnbaum-Saunders distribution with parameters ## @var{location}, @var{scale} and @var{shape}. ## @end deftypefn ## Author: Dag Lyberg ## Description: CDF of the Birnbaum-Saunders distribution function cdf = bbscdf (x, shape, scale, location) if (nargin != 4) print_usage (); endif if (! isscalar (location) || ! isscalar (scale) || ! isscalar(shape)) [retval, x, location, scale, shape] = ... common_size (x, location, scale, shape); if (retval > 0) error ("bbscdf: X, LOCATION, SCALE and SHAPE must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (location) || iscomplex (scale) ... || iscomplex(shape)) error ("bbscdf: X, LOCATION, SCALE and SHAPE must not be complex"); endif if (isa (x, "single") || isa (location, "single") || isa (scale, "single") ... || isa (shape, "single")) cdf = zeros (size (x), "single"); else cdf = zeros (size (x)); endif k = isnan(x) | ! (-Inf < location) | ! (location < Inf) ... | ! (scale > 0) | ! (scale < Inf) | ! (shape > 0) | ! (shape < Inf); cdf(k) = NaN; k = (x > location) & (x <= Inf) & (-Inf < location) & (location < Inf) ... & (0 < scale) & (scale < Inf) & (0 < shape) & (shape < Inf); if (isscalar (location) && isscalar(scale) && isscalar(shape)) a = x(k) - location; b = sqrt(a ./ scale); cdf(k) = normcdf ((b - b.^-1) / shape); else a = x(k) - location(k); b = sqrt(a ./ scale(k)); cdf(k) = normcdf ((b - b.^-1) ./ shape(k)); endif endfunction %!shared x,y %! x = [-1, 0, 1, 2, Inf]; %! y = [0, 0, 1/2, 0.76024993890652337, 1]; %!assert (bbscdf (x, ones (1,5), ones (1,5), zeros (1,5)), y, eps) %!assert (bbscdf (x, 1, 1, zeros (1,5)), y, eps) %!assert (bbscdf (x, 1, ones (1,5), 0), y, eps) %!assert (bbscdf (x, ones (1,5), 1, 0), y, eps) %!assert (bbscdf (x, 1, 1, 0), y, eps) %!assert (bbscdf (x, 1, 1, [0, 0, NaN, 0, 0]), [y(1:2), NaN, y(4:5)], eps) %!assert (bbscdf (x, 1, [1, 1, NaN, 1, 1], 0), [y(1:2), NaN, y(4:5)], eps) %!assert (bbscdf (x, [1, 1, NaN, 1, 1], 1, 0), [y(1:2), NaN, y(4:5)], eps) %!assert (bbscdf ([x, NaN], 1, 1, 0), [y, NaN], eps) ## Test class of input preserved %!assert (bbscdf (single ([x, NaN]), 1, 1, 0), single ([y, NaN]), eps('single')) %!assert (bbscdf ([x, NaN], 1, 1, single (0)), single ([y, NaN]), eps('single')) %!assert (bbscdf ([x, NaN], 1, single (1), 0), single ([y, NaN]), eps('single')) %!assert (bbscdf ([x, NaN], single (1), 1, 0), single ([y, NaN]), eps('single')) ## Test input validation %!error bbscdf () %!error bbscdf (1) %!error bbscdf (1,2,3) %!error bbscdf (1,2,3,4,5) %!error bbscdf (ones (3), ones (2), ones(2), ones(2)) %!error bbscdf (ones (2), ones (3), ones(2), ones(2)) %!error bbscdf (ones (2), ones (2), ones(3), ones(2)) %!error bbscdf (ones (2), ones (2), ones(2), ones(3)) %!error bbscdf (i, 4, 3, 2) %!error bbscdf (1, i, 3, 2) %!error bbscdf (1, 4, i, 2) %!error bbscdf (1, 4, 3, i) statistics-1.4.3/inst/bbsinv.m0000644000000000000000000001025614153320774014527 0ustar0000000000000000## Copyright (C) 2018 John Donoghue ## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} bbsinv (@var{x}, @var{shape}, @var{scale}, @var{location}) ## For each element of @var{x}, compute the quantile (the inverse of the CDF) ## at @var{x} of the Birnbaum-Saunders distribution with parameters ## @var{location}, @var{scale}, and @var{shape}. ## @end deftypefn ## Author: Dag Lyberg ## Description: Quantile function of the Birnbaum-Saunders distribution function inv = bbsinv (x, shape, scale, location) if (nargin != 4) print_usage (); endif if (! isscalar (location) || ! isscalar (scale) || ! isscalar(shape)) [retval, x, location, scale, shape] = ... common_size (x, location, scale, shape); if (retval > 0) error ("bbsinv: X, LOCATION, SCALE and SHAPE must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (location) ... || iscomplex (scale) || iscomplex(shape)) error ("bbsinv: X, LOCATION, SCALE and SHAPE must not be complex"); endif if (isa (x, "single") || isa (location, "single") ... || isa (scale, "single") || isa (shape, "single")) inv = zeros (size (x), "single"); else inv = zeros (size (x)); endif k = isnan (x) | (x < 0) | (x > 1) | ! (-Inf < location) | ! (location < Inf) ... | ! (scale > 0) | ! (scale < Inf) | ! (shape > 0) | ! (shape < Inf); inv(k) = NaN; k = (x <= 0) & (-Inf < location) & (location < Inf) ... & (scale > 0) & (scale < Inf) & (shape > 0) & (shape < Inf); inv(k) = 0; k = (x == 1) & (-Inf < location) & (location < Inf) ... & (scale > 0) & (scale < Inf) & (shape > 0) & (shape < Inf); inv(k) = Inf; k = (0 < x) & (x < 1) & (location < Inf) & (0 < scale) & (scale < Inf) ... & (0 < shape) & (shape < Inf); if (isscalar (location) && isscalar(scale) && isscalar(shape)) y = shape * norminv (x(k)); inv(k) = location + scale * (y + sqrt (4 + y.^2)).^2 / 4; else y = shape(k) .* norminv (x(k)); inv(k) = location(k) + scale(k) .* (y + sqrt (4 + y.^2)).^2 ./ 4; endif endfunction %!shared x,y,f %! f = @(x,a,b,c) (a + b * (c * norminv (x) + sqrt (4 + (c * norminv(x))^2))^2) / 4; %! x = [-1, 0, 1/4, 1/2, 1, 2]; %! y = [0, 0, f(1/4, 0, 1, 1), 1, Inf, NaN]; %!assert (bbsinv (x, ones (1,6), ones (1,6), zeros (1,6)), y) %!assert (bbsinv (x, 1, 1, zeros (1,6)), y) %!assert (bbsinv (x, 1, ones (1,6), 0), y) %!assert (bbsinv (x, ones (1,6), 1, 0), y) %!assert (bbsinv (x, 1, 1, 0), y) %!assert (bbsinv (x, 1, 1, [0, 0, 0, NaN, 0, 0]), [y(1:3), NaN, y(5:6)]) %!assert (bbsinv (x, 1, [1, 1, 1, NaN, 1, 1], 0), [y(1:3), NaN, y(5:6)]) %!assert (bbsinv (x, [1, 1, 1, NaN, 1, 1], 1, 0), [y(1:3), NaN, y(5:6)]) %!assert (bbsinv ([x, NaN], 1, 1, 0), [y, NaN]) ## Test class of input preserved %!assert (bbsinv (single ([x, NaN]), 1, 1, 0), single ([y, NaN])) %!assert (bbsinv ([x, NaN], 1, 1, single (0)), single ([y, NaN])) %!assert (bbsinv ([x, NaN], 1, single (1), 0), single ([y, NaN])) %!assert (bbsinv ([x, NaN], single (1), 1, 0), single ([y, NaN])) ## Test input validation %!error bbsinv () %!error bbsinv (1) %!error bbsinv (1,2,3) %!error bbsinv (1,2,3,4,5) %!error bbsinv (ones (3), ones (2), ones(2), ones(2)) %!error bbsinv (ones (2), ones (3), ones(2), ones(2)) %!error bbsinv (ones (2), ones (2), ones(3), ones(2)) %!error bbsinv (ones (2), ones (2), ones(2), ones(3)) %!error bbsinv (i, 4, 3, 2) %!error bbsinv (1, i, 3, 2) %!error bbsinv (1, 4, i, 2) %!error bbsinv (1, 4, 3, i) statistics-1.4.3/inst/bbspdf.m0000644000000000000000000001003214153320774014474 0ustar0000000000000000## Copyright (C) 2018 John Donoghue ## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} bbspdf (@var{x}, @var{shape}, @var{scale}, @var{location}) ## For each element of @var{x}, compute the probability density function (PDF) ## at @var{x} of the Birnbaum-Saunders distribution with parameters ## @var{location}, @var{scale} and @var{shape}. ## @end deftypefn ## Author: Dag Lyberg ## Description: PDF of the Birnbaum-Saunders distribution function pdf = bbspdf (x, shape, scale, location) if (nargin != 4) print_usage (); endif if (! isscalar (location) || ! isscalar (scale) || ! isscalar(shape)) [retval, x, location, scale, shape] = ... common_size (x, location, scale, shape); if (retval > 0) error ("bbspdf: X, LOCATION, SCALE and SHAPE must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (location) ... || iscomplex (scale) || iscomplex(shape)) error ("bbspdf: X, LOCATION, SCALE and SHAPE must not be complex"); endif if (isa (x, "single") || isa (location, "single") || isa (scale, "single") ... || isa (shape, "single")) pdf = zeros (size (x), "single"); else pdf = zeros (size (x)); endif k = isnan (x) | ! (-Inf < location) | ! (location < Inf) ... | ! (scale > 0) | ! (scale < Inf) ... | ! (shape > 0) | ! (shape < Inf); pdf(k) = NaN; k = (x > location) & (x < Inf) & (-Inf < location) ... & (location < Inf) & (0 < scale) & (scale < Inf) ... & (0 < shape) & (shape < Inf); if (isscalar (location) && isscalar(scale) && isscalar(shape)) a = x(k) - location; b = sqrt(a ./ scale); pdf(k) = ((b + b.^-1) ./ (2 * shape * a)) ... .* normpdf ((b - b.^-1) / shape); else a = x(k) - location(k); b = sqrt(a ./ scale(k)); pdf(k) = ((b + b.^-1) ./ (2 * shape(k).* a)) ... .* normpdf ((b - b.^-1) ./ shape(k)); endif endfunction %!shared x,y %! x = [-1, 0, 1, 2, Inf]; %! y = [0, 0, 0.3989422804014327, 0.1647717335503959, 0]; %!assert (bbspdf (x, ones (1,5), ones (1,5), zeros (1,5)), y, eps) %!assert (bbspdf (x, 1, 1, zeros (1,5)), y, eps) %!assert (bbspdf (x, 1, ones (1,5), 0), y, eps) %!assert (bbspdf (x, ones (1,5), 1, 0), y, eps) %!assert (bbspdf (x, 1, 1, 0), y, eps) %!assert (bbspdf (x, 1, 1, [0, 0, NaN, 0, 0]), [y(1:2), NaN, y(4:5)], eps) %!assert (bbspdf (x, 1, [1, 1, NaN, 1, 1], 0), [y(1:2), NaN, y(4:5)], eps) %!assert (bbspdf (x, [1, 1, NaN, 1, 1], 1, 0), [y(1:2), NaN, y(4:5)], eps) %!assert (bbspdf ([x, NaN], 1, 1, 0), [y, NaN], eps) ## Test class of input preserved %!assert (bbspdf (single ([x, NaN]), 1, 1, 0), single ([y, NaN]), eps('single')) %!assert (bbspdf ([x, NaN], 1, 1, single (0)), single ([y, NaN]), eps('single')) %!assert (bbspdf ([x, NaN], 1, single (1), 0), single ([y, NaN]), eps('single')) %!assert (bbspdf ([x, NaN], single (1), 1, 0), single ([y, NaN]), eps('single')) ## Test input validation %!error bbspdf () %!error bbspdf (1) %!error bbspdf (1,2,3) %!error bbspdf (1,2,3,4,5) %!error bbspdf (ones (3), ones (2), ones(2), ones(2)) %!error bbspdf (ones (2), ones (3), ones(2), ones(2)) %!error bbspdf (ones (2), ones (2), ones(3), ones(2)) %!error bbspdf (ones (2), ones (2), ones(2), ones(3)) %!error bbspdf (i, 4, 3, 2) %!error bbspdf (1, i, 3, 2) %!error bbspdf (1, 4, i, 2) %!error bbspdf (1, 4, 3, i) statistics-1.4.3/inst/bbsrnd.m0000644000000000000000000001244114153320774014514 0ustar0000000000000000## Copyright (C) 2018 John Donoghue ## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} bbsrnd (@var{shape}, @var{scale}, @var{location}) ## @deftypefnx {} {} bbsrnd (@var{shape}, @var{scale}, @var{location}, @var{r}) ## @deftypefnx {} {} bbsrnd (@var{shape}, @var{scale}, @var{location}, @var{r}, @var{c}, @dots{}) ## @deftypefnx {} {} bbsrnd (@var{shape}, @var{scale}, @var{location}, [@var{sz}]) ## Return a matrix of random samples from the Birnbaum-Saunders ## distribution with parameters @var{location}, @var{scale} and @var{shape}. ## ## When called with a single size argument, return a square matrix with ## the dimension specified. When called with more than one scalar argument the ## first two arguments are taken as the number of rows and columns and any ## further arguments specify additional matrix dimensions. The size may also ## be specified with a vector of dimensions @var{sz}. ## ## If no size arguments are given then the result matrix is the common size of ## @var{location}, @var{scale} and @var{shape}. ## @end deftypefn ## Author: Dag Lyberg ## Description: Random deviates from the Birnbaum-Saunders distribution function rnd = bbsrnd (shape, scale, location, varargin) if (nargin < 3) print_usage (); endif if (! isscalar (location) || ! isscalar (scale) || ! isscalar (shape)) [retval, location, scale, shape] = common_size (location, scale, shape); if (retval > 0) error ("bbsrnd: LOCATION, SCALE and SHAPE must be of common size or scalars"); endif endif if (iscomplex (location) || iscomplex (scale) || iscomplex (shape)) error ("bbsrnd: LOCATION, SCALE and SHAPE must not be complex"); endif if (nargin == 3) sz = size (location); elseif (nargin == 4) if (isscalar (varargin{1}) && varargin{1} >= 0) sz = [varargin{1}, varargin{1}]; elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) sz = varargin{1}; else error ("bbsrnd: dimension vector must be row vector of non-negative integers"); endif elseif (nargin > 3) if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) error ("bbsrnd: dimensions must be non-negative integers"); endif sz = [varargin{:}]; endif if (! isscalar (location) && ! isequal (size (location), sz)) error ("bbsrnd: LOCATION, SCALE and SHAPE must be scalar or of size SZ"); endif if (isa (location, "single") || isa (scale, "single") || isa (shape, "single")) cls = "single"; else cls = "double"; endif if (isscalar (location) && isscalar (scale) && isscalar (shape)) if ((-Inf < location) && (location < Inf) ... && (0 < scale) && (scale < Inf) ... && (0 < shape) && (shape < Inf)) rnd = rand(sz,cls); y = shape * norminv (rnd); rnd = location + scale * (y + sqrt (4 + y.^2)).^2 / 4; else rnd = NaN (sz, cls); endif else rnd = NaN (sz, cls); k = (-Inf < location) & (location < Inf) ... & (0 < scale) & (scale < Inf) ... & (0 < shape) & (shape < Inf); rnd(k) = rand(sum(k(:)),1); y = shape(k) .* norminv (rnd(k)); rnd(k) = location(k) + scale(k) .* (y + sqrt (4 + y.^2)).^2 / 4; endif endfunction %!assert (size (bbsrnd (1, 1, 0)), [1 1]) %!assert (size (bbsrnd (1, 1, zeros (2,1))), [2, 1]) %!assert (size (bbsrnd (1, 1, zeros (2,2))), [2, 2]) %!assert (size (bbsrnd (1, ones (2,1), 0)), [2, 1]) %!assert (size (bbsrnd (1, ones (2,2), 0)), [2, 2]) %!assert (size (bbsrnd (ones (2,1), 1, 0)), [2, 1]) %!assert (size (bbsrnd (ones (2,2), 1, 0)), [2, 2]) %!assert (size (bbsrnd (1, 1, 0, 3)), [3, 3]) %!assert (size (bbsrnd (1, 1, 0, [4 1])), [4, 1]) %!assert (size (bbsrnd (1, 1, 0, 4, 1)), [4, 1]) ## Test class of input preserved %!assert (class (bbsrnd (1,1,0)), "double") %!assert (class (bbsrnd (1, 1, single (0))), "single") %!assert (class (bbsrnd (1, 1, single ([0 0]))), "single") %!assert (class (bbsrnd (1, single (1), 0)), "single") %!assert (class (bbsrnd (1, single ([1 1]), 0)), "single") %!assert (class (bbsrnd (single (1), 1, 0)), "single") %!assert (class (bbsrnd (single ([1 1]), 1, 0)), "single") ## Test input validation %!error bbsrnd () %!error bbsrnd (1) %!error bbsrnd (1,2) %!error bbsrnd (ones (3), ones (2), ones (2), 2) %!error bbsrnd (ones (2), ones (3), ones (2), 2) %!error bbsrnd (ones (2), ones (2), ones (3), 2) %!error bbsrnd (i, 2, 3) %!error bbsrnd (1, i, 3) %!error bbsrnd (1, 2, i) %!error bbsrnd (1,2,3, -1) %!error bbsrnd (1,2,3, ones (2)) %!error bbsrnd (1,2,3, [2 -1 2]) %!error bbsrnd (2, 1, ones (2), 3) %!error bbsrnd (2, 1, ones (2), [3, 2]) %!error bbsrnd (2, 1, ones (2), 3, 2) statistics-1.4.3/inst/betastat.m0000644000000000000000000000710014153320774015045 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} betastat (@var{a}, @var{b}) ## Compute mean and variance of the beta distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{a} is the first parameter of the beta distribution. @var{a} must be ## positive ## ## @item ## @var{b} is the second parameter of the beta distribution. @var{b} must be ## positive ## @end itemize ## @var{a} and @var{b} must be of common size or one of them must be scalar ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the beta distribution ## ## @item ## @var{v} is the variance of the beta distribution ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## a = 1:6; ## b = 1:0.2:2; ## [m, v] = betastat (a, b) ## @end group ## ## @group ## [m, v] = betastat (a, 1.5) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the beta distribution function [m, v] = betastat (a, b) if (nargin != 2) print_usage (); elseif (! isscalar (a) && ! isscalar (b) && ! size_equal (a, b)) error ("betastat: a and b must be of common size or scalar"); endif k = find (! (a > 0 & b > 0)); # Calculate moments a_b = a + b; m = a ./ (a_b); m(k) = NaN; if (nargout > 1) v = (a .* b) ./ ((a_b .^ 2) .* (a_b + 1)); v(k) = NaN; endif endfunction %!test %! a = -2:6; %! b = 0.4:0.2:2; %! [m, v] = betastat (a, b); %! expected_m = [NaN NaN NaN 1/2 2/3.2 3/4.4 4/5.6 5/6.8 6/8]; %! expected_v = [NaN NaN NaN 0.0833, 0.0558, 0.0402, 0.0309, 0.0250, 0.0208]; %! assert (m, expected_m, eps*100); %! assert (v, expected_v, 0.001); %!test %! a = -2:1:6; %! [m, v] = betastat (a, 1.5); %! expected_m = [NaN NaN NaN 1/2.5 2/3.5 3/4.5 4/5.5 5/6.5 6/7.5]; %! expected_v = [NaN NaN NaN 0.0686, 0.0544, 0.0404, 0.0305, 0.0237, 0.0188]; %! assert (m, expected_m); %! assert (v, expected_v, 0.001); %!test %! a = [14 Inf 10 NaN 10]; %! b = [12 9 NaN Inf 12]; %! [m, v] = betastat (a, b); %! expected_m = [14/26 NaN NaN NaN 10/22]; %! expected_v = [168/18252 NaN NaN NaN 120/11132]; %! assert (m, expected_m); %! assert (v, expected_v); %!assert (nthargout (1:2, @betastat, 5, []), {[], []}) %!assert (nthargout (1:2, @betastat, [], 5), {[], []}) %!assert (nthargout (1:2, @betastat, "", 5), {[], []}) %!assert (nthargout (1:2, @betastat, true, 5), {1/6, 5/252}) %!assert (size (betastat (rand (10, 5, 4), rand (10, 5, 4))), [10 5 4]) %!assert (size (betastat (rand (10, 5, 4), 7)), [10 5 4]) statistics-1.4.3/inst/binostat.m0000644000000000000000000000726614153320774015076 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## Copyright (C) 2015 CarnĂ« Draug ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} binostat (@var{n}, @var{p}) ## Compute mean and variance of the binomial distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{n} is the first parameter of the binomial distribution. The elements ## of @var{n} must be natural numbers ## ## @item ## @var{p} is the second parameter of the binomial distribution. The ## elements of @var{p} must be probabilities ## @end itemize ## @var{n} and @var{p} must be of common size or one of them must be scalar ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the binomial distribution ## ## @item ## @var{v} is the variance of the binomial distribution ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## n = 1:6; ## p = 0:0.2:1; ## [m, v] = binostat (n, p) ## @end group ## ## @group ## [m, v] = binostat (n, 0.5) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the binomial distribution function [m, v] = binostat (n, p) if (nargin != 2) print_usage (); elseif (! isscalar (n) && ! isscalar (p) && ! size_equal (n, p)) error ("binostat: N and P must be of common size or scalar"); endif k = find (! (n > 0 & fix (n) == n & p >= 0 & p <= 1)); # Calculate moments m = n .* p; m(k) = NaN; if (nargout > 1) v = m .* (1 - p); v(k) = NaN; endif endfunction %!test %! n = 1:6; %! p = 0:0.2:1; %! [m, v] = binostat (n, p); %! expected_m = [0.00, 0.40, 1.20, 2.40, 4.00, 6.00]; %! expected_v = [0.00, 0.32, 0.72, 0.96, 0.80, 0.00]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); %!test %! n = 1:6; %! [m, v] = binostat (n, 0.5); %! expected_m = [0.50, 1.00, 1.50, 2.00, 2.50, 3.00]; %! expected_v = [0.25, 0.50, 0.75, 1.00, 1.25, 1.50]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); %!test %! n = [-Inf -3 5 0.5 3 NaN 100, Inf]; %! [m, v] = binostat (n, 0.5); %! assert (isnan (m), [true true false true false true false false]) %! assert (isnan (v), [true true false true false true false false]) %! assert (m(end), Inf); %! assert (v(end), Inf); %!assert (nthargout (1:2, @binostat, 5, []), {[], []}) %!assert (nthargout (1:2, @binostat, [], 5), {[], []}) %!assert (nthargout (1:2, @binostat, "", 5), {[], []}) %!assert (nthargout (1:2, @binostat, true, 5), {NaN, NaN}) %!assert (nthargout (1:2, @binostat, 5, true), {5, 0}) %!assert (size (binostat (randi (100, 10, 5, 4), rand (10, 5, 4))), [10 5 4]) %!assert (size (binostat (randi (100, 10, 5, 4), 7)), [10 5 4]) statistics-1.4.3/inst/binotest.m0000644000000000000000000001225614153320774015075 0ustar0000000000000000## Copyright (C) 2016 Andreas Stahel ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{h}, @var{pval}, @var{ci}] =} binotest (@var{pos},@var{N},@var{p0}) ## @deftypefnx {Function File} {[@var{h}, @var{pval}, @var{ci}] =} binotest (@var{pos},@var{N},@var{p0},@var{Name},@var{Value}) ## Test for probability @var{p} of a binomial sample ## ## Perform a test of the null hypothesis @var{p} == @var{p0} for a sample ## of size @var{N} with @var{pos} positive results ## ## ## Name-Value pair arguments can be used to set various options. ## @qcode{"alpha"} can be used to specify the significance level ## of the test (the default value is 0.05). The option @qcode{"tail"}, ## can be used to select the desired alternative hypotheses. If the ## value is @qcode{"both"} (default) the null is tested against the two-sided ## alternative @code{@var{p} != @var{p0}}. The value of @var{pval} is ## determined by adding the probabilities of all event less or equally ## likely than the observed number @var{pos} of positive events. ## If the value of @qcode{"tail"} is @qcode{"right"} ## the one-sided alternative @code{@var{p} > @var{p0}} is considered. ## Similarly for @qcode{"left"}, the one-sided alternative ## @code{@var{p} < @var{p0}} is considered. ## ## If @var{h} is 0 the null hypothesis is accepted, if it is 1 the null ## hypothesis is rejected. The p-value of the test is returned in @var{pval}. ## A 100(1-alpha)% confidence interval is returned in @var{ci}. ## ## @end deftypefn ## Author: Andreas Stahel function [h, p, ci] = binotest(pos,n,p0,varargin) % Set default arguments alpha = 0.05; tail = 'both'; i = 1; while ( i <= length(varargin) ) switch lower(varargin{i}) case 'alpha' i = i + 1; alpha = varargin{i}; case 'tail' i = i + 1; tail = varargin{i}; otherwise error('Invalid Name argument.',[]); end i = i + 1; end if ~isa(tail,'char') error('tail argument to vartest must be a string\n',[]); end if (n<=0) error('binotest: required n>0\n',[]); end if (p0<0)|(p0>1) error('binotest: required 0<= p0 <= 1\n',[]); end if (pos<0)|(pos>n) error('binotest: required 0<= pos <= n\n',[]); end % Based on the "tail" argument determine the P-value, the critical values, % and the confidence interval. switch lower(tail) case 'both' A_low = binoinv(alpha/2,n,p0)/n; A_high = binoinv(1-alpha/2,n,p0)/n; p_pos = binopdf(pos,n,p0); p_all = binopdf([0:n],n,p0); ind = find(p_all <=p_pos); % p = min(1,sum(p_all(ind))); p = sum(p_all(ind)); if pos==0 p_low = 0; else p_low = fzero(@(pl)1-binocdf(pos-1,n,pl)-alpha/2,[0 1]); endif if pos==n p_high = 1; else p_high = fzero(@(ph) binocdf(pos,n,ph) -alpha/2,[0,1]); endif ci = [p_low,p_high]; case 'left' p = 1-binocdf(pos-1,n,p0); if pos==n p_high = 1; else p_high = fzero(@(ph) binocdf(pos,n,ph) -alpha,[0,1]); endif ci = [0, p_high]; case 'right' p = binocdf(pos,n,p0); if pos==0 p_low = 0; else p_low = fzero(@(pl)1-binocdf(pos-1,n,pl)-alpha,[0 1]); endif ci = [p_low 1]; otherwise error('Invalid fifth (tail) argument to binotest\n',[]); end % Determine the test outcome % MATLAB returns this a double instead of a logical array h = double(p < alpha); end %!demo %! % flip a coin 1000 times, showing 475 heads %! % Hypothesis: coin is fair, i.e. p=1/2 %! [h,p_val,ci] = binotest(475,1000,0.5) %! % Result: h = 0 : null hypothesis not rejected, coin could be fair %! % P value 0.12, i.e. hypothesis not rejected for alpha up to 12% %! % 0.444 <= p <= 0.506 with 95% confidence %!demo %! % flip a coin 100 times, showing 65 heads %! % Hypothesis: coin shows less than 50% heads, i.e. p<=1/2 %! [h,p_val,ci] = binotest(65,100,0.5,'tail','left','alpha',0.01) %! % Result: h = 1 : null hypothesis is rejected, i.e. coin shows more heads than tails %! % P value 0.0018, i.e. hypothesis not rejected for alpha up to 0.18% %! % 0 <= p <= 0.76 with 99% confidence %!test #example from https://en.wikipedia.org/wiki/Binomial_test %! [h,p_val,ci] = binotest (51,235,1/6); %! assert (p_val, 0.0437, 0.00005) %! [h,p_val,ci] = binotest (51,235,1/6,'tail','left'); %! assert (p_val, 0.027, 0.0005) statistics-1.4.3/inst/boxplot.m0000644000000000000000000010274314153320774014736 0ustar0000000000000000## Copyright (C) 2002 Alberto Terruzzi ## Copyright (C) 2006 Alberto Pose ## Copyright (C) 2011 Pascal Dupuis ## Copyright (C) 2012 Juan Pablo Carbajal ## Copyright (C) 2016 Pascal Dupuis ## Copyright (C) 2020 Andreas Bertsatos ## Copyright (C) 2020 Philip Nienhuis (prnienhuis@users.sf.net) ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{s} =} boxplot (@var{data}) ## @deftypefnx {Function File} {@var{s} =} boxplot (@var{data}, @var{group}) ## @deftypefnx {Function File} {@var{s} =} boxplot (@var{data}, @var{notched}, @var{symbol}, @var{orientation}, @var{whisker}, @dots{}) ## @deftypefnx {Function File} {@var{s} =} boxplot (@var{data}, @var{group}, @var{notched}, @var{symbol}, @var{orientation}, @var{whisker}, @dots{}) ## @deftypefnx {Function File} {@var{s} =} boxplot (@var{data}, @var{options}) ## @deftypefnx {Function File} {@var{s} =} boxplot (@var{data}, @var{group}, @var{options}, @dots{}) ## @deftypefnx {Function File} {[@dots{} @var{h}]=} boxplot (@var{data}, @dots{}) ## Produce a box plot. ## ## A box plot is a graphical display that simultaneously describes several ## important features of a data set, such as center, spread, departure from ## symmetry, and identification of observations that lie unusually far from ## the bulk of the data. ## ## Input arguments (case-insensitive) recognized by boxplot are: ## ## @itemize ## @item ## @var{data} is a matrix with one column for each data set, or a cell vector ## with one cell for each data set. Each cell must contain a numerical row or ## column vector (NaN and NA are ignored) and not a nested vector of cells. ## ## @item ## @var{notched} = 1 produces a notched-box plot. Notches represent a robust ## estimate of the uncertainty about the median. ## ## @var{notched} = 0 (default) produces a rectangular box plot. ## ## @var{notched} within the interval (0,1) produces a notch of the specified ## depth. Notched values outside (0,1) are amusing if not exactly impractical. ## ## @item ## @var{symbol} sets the symbol for the outlier values. The default symbol ## for points that lie outside 3 times the interquartile range is 'o'; ## the default symbol for points between 1.5 and 3 times the interquartile ## range is '+'. @* ## Alternative @var{symbol} settings: ## ## @var{symbol} = '.': points between 1.5 and 3 times the IQR are marked with ## '.' and points outside 3 times IQR with 'o'. ## ## @var{symbol} = ['x','*']: points between 1.5 and 3 times the IQR are marked ## with 'x' and points outside 3 times IQR with '*'. ## ## @item ## @var{orientation} = 0 makes the boxes horizontally. @* ## @var{orientation} = 1 plots the boxes vertically (default). Alternatively, ## orientation can be passed as a string, e.g., 'vertical' or 'horizontal'. ## ## @item ## @var{whisker} defines the length of the whiskers as a function of the IQR ## (default = 1.5). If @var{whisker} = 0 then @code{boxplot} displays all data ## values outside the box using the plotting symbol for points that lie ## outside 3 times the IQR. ## ## @item ## @var{group} may be passed as an optional argument only in the second ## position after @var{data}. @var{group} contains a numerical vector defining ## separate categories, each plotted in a different box, for each set of ## @var{DATA} values that share the same @var{group} value or values. With ## the formalism (@var{data}, @var{group}), both must be vectors of the same ## length. ## ## @item ## @var{options} are additional paired arguments passed with the formalism ## (Name, Value) that provide extra functionality as listed below. ## @var{options} can be passed at any order after the initial arguments and ## are case-insensitive. ## ## @multitable {Name} {Value} {description} @columnfractions .2 .2 .6 ## @item 'Notch' @tab 'on' @tab Notched by 0.25 of the boxes width. ## @item @tab 'off' @tab Produces a straight box. ## @item @tab scalar @tab Proportional width of the notch. ## ## @item 'Symbol' @tab '.' @tab Defines only outliers between 1.5 and 3 IQR. ## @item @tab ['x','*'] @tab 2nd character defines outliers > 3 IQR ## ## @item 'Orientation' @tab 'vertical' @tab Default value, can also be defined ## with numerical 1. ## @item @tab 'horizontal' @tab Can also be defined with numerical 0. ## ## @item 'Whisker' @tab scalar @tab Multiplier of IQR (default is 1.5). ## ## @item 'OutlierTags' @tab 'on' or 1 @tab Plot the vector index of the outlier ## value next to its point. ## @item @tab 'off' or 0 @tab No tags are plotted (default value). ## ## @item 'Sample_IDs' @tab 'cell' @tab A cell vector with one cell for each ## data set containing a nested cell vector with each sample's ID (should be ## a string). If this option is passed, then all outliers are tagged with ## their respective sample's ID string instead of their vector's index. ## ## @item 'BoxWidth' @tab 'proportional' @tab Create boxes with their width ## proportional to the number of samples in their respective dataset (default ## value). ## @item @tab 'fixed' @tab Make all boxes with equal width. ## ## @item 'Widths' @tab scalar @tab Scaling factor for box widths (default ## value is 0.4). ## ## @item 'CapWidths' @tab scalar @tab Scaling factor for whisker cap widths ## (default value is 1, which results to 'Widths'/8 halflength) ## ## @item 'BoxStyle' @tab 'outline' @tab Draw boxes as outlines (default value). ## @item @tab 'filled' @tab Fill boxes with a color (outlines are still ## plotted). ## ## @item 'Positions' @tab vector @tab Numerical vector that defines the ## position of each data set. It must have the same length as the number of ## groups in a desired manner. This vector merely defines the points along ## the group axis, which by default is [1:number of groups]. ## ## @item 'Labels' @tab cell @tab A cell vector of strings containing the names ## of each group. By default each group is labeled numerically according to ## its order in the data set ## ## @item 'Colors' @tab character string or Nx3 numerical matrix @tab If just ## one character or 1x3 vector of RGB values, specify the fill color of all ## boxes when BoxStyle = 'filled'. If a character string or Nx3 matrix is ## entered, box #1's fill color corrresponds to the first character or first ## matrix row, and the next boxes' fill colors corresponds to the next ## characters or rows. If the char string or Nx3 array is exhausted the color ## selection wraps around. ## @end multitable ## @end itemize ## ## Supplemental arguments not described above (@dots{}) are concatenated and ## passed to the plot() function. ## ## The returned matrix @var{s} has one column for each data set as follows: ## ## @multitable @columnfractions .1 .8 ## @item 1 @tab Minimum ## @item 2 @tab 1st quartile ## @item 3 @tab 2nd quartile (median) ## @item 4 @tab 3rd quartile ## @item 5 @tab Maximum ## @item 6 @tab Lower confidence limit for median ## @item 7 @tab Upper confidence limit for median ## @end multitable ## ## The returned structure @var{h} contains handles to the plot elements, ## allowing customization of the visualization using set/get functions. ## ## Example ## ## @example ## title ("Grade 3 heights"); ## axis ([0,3]); ## set(gca (), "xtick", [1 2], "xticklabel", @{"girls", "boys"@}); ## boxplot (@{randn(10,1)*5+140, randn(13,1)*8+135@}); ## @end example ## ## @end deftypefn function [s_o, hs_o] = boxplot (data, varargin) ## Assign parameter defaults if (nargin < 1) print_usage; endif ## Check data if (! (isnumeric (data) || iscell (data))) error ("boxplot: numerical array or cell array containing data expected."); elseif (iscell (data)) ## Check if cell contain numerical data if (! all (cellfun ("isnumeric", data))) error ("boxplot: data cells must contain numerical data."); endif endif ## Default values maxwhisker = 1.5; orientation = 1; symbol = ["+", "o"]; notched = 0; plot_opts = {}; groups = []; sample_IDs = {}; outlier_tags = 0; box_width = "proportional"; widths = 0.4; capwid = 1; box_style = 0; positions = []; labels = {}; nug = 0; bcolor = "y"; ## Optional arguments analysis numarg = nargin - 1; indopt = 1; group_exists = 0; while (numarg) dummy = varargin{indopt++}; if ((! ischar (dummy) || iscellstr (dummy)) && indopt < 6) ## MATLAB allows passing the second argument as a grouping vector if (length (dummy) > 1) if (2 != indopt) error ("boxplot: grouping vector may only be passed as second arg."); endif if (isnumeric (dummy)) groups = dummy; group_exists = 1; else error ("boxplot: grouping vector must be numerical"); endif elseif (length (dummy) == 1) ## Old way: positional argument switch indopt - group_exists case 2 notched = dummy; case 4 orientation = dummy; case 5 maxwhisker = dummy; otherwise error("boxplot: no positional argument allowed at position %d", ... --indopt); endswitch endif numarg--; continue; else if (3 == (indopt - group_exists) && length (dummy) <= 2) symbol = dummy; numarg--; continue; else ## Check for additional paired arguments switch lower (dummy) case "notch" notched = varargin{indopt}; ## Check for string input: "on" or "off" if (ischar (notched)) if (strcmpi (notched, "on")) notched = 1; elseif (strcmpi (notched, "off")) notched = 0; else msg = ["boxplot: 'Notch' input argument accepts only 'on',", ... " 'off' or a numeric scalar as value"]; error (msg); endif elseif (! (isnumeric (notched) && isreal (notched))) error ("boxplot: illegal Notch value"); endif case "symbol" symbol = varargin{indopt}; if (! ischar (symbol)) error ("boxplot; Symbol(s) must be character(s)"); endif case "orientation" orientation = varargin{indopt}; if (ischar (orientation)) ## Check for string input: "vertical" or "horizontal" if (strcmpi (orientation, "vertical")) orientation = 1; elseif (strcmpi (orientation, "horizontal")) orientation = 0; else msg = ["boxplot: 'Orientation' input argument accepts only", ... " 'vertical' (or 1) or 'horizontal' (or 0) as value"]; error (msg); endif elseif (! (isnumeric (orientation) && isreal (orientation))) error ("boxplot: illegal Orientation value"); endif case "whisker" maxwhisker = varargin{indopt}; if (! isscalar (maxwhisker) || ... ! (isnumeric (maxwhisker) && isreal (maxwhisker))) msg = ["boxplot: 'Whisker' input argument accepts only", ... " a real scalar value as input parameter"]; error(msg); endif case "outliertags" outlier_tags = varargin{indopt}; ## Check for string input: "on" or "off" if (ischar (outlier_tags)) if (strcmpi (outlier_tags, "on")) outlier_tags = 1; elseif (strcmpi (outlier_tags, "off")) outlier_tags = 0; else msg = ["boxplot: 'OutlierTags' input argument accepts only", ... " 'on' (or 1) or 'off' (or 0) as value"]; error (msg); endif elseif (! (isnumeric (outlier_tags) && isreal (outlier_tags))) error ("boxplot: illegal OutlierTags value"); endif case "sample_ids" sample_IDs = varargin{indopt}; if (! iscell (sample_IDs)) msg = ["boxplot: 'Sample_IDs' input argument accepts only", ... " a cell array as value"]; error (msg); endif outlier_tags = 1; case "boxwidth" box_width = varargin{indopt}; ## Check for string input: "fixed" or "proportional" if (! ischar (box_width) || ... ! ismember (lower (box_width), {"fixed", "proportional"})) msg = ["boxplot: 'BoxWidth' input argument accepts only", ... " 'fixed' or 'proportional' as value"]; error (msg); endif box_width = lower (box_width); case "widths" widths = varargin{indopt}; if (! isscalar (widths) || ! (isnumeric (widths) && isreal (widths))) msg = ["boxplot: 'Widths' input argument accepts only", ... " a real scalar value as value"]; error (msg); endif case "capwidths" capwid = varargin{indopt}; if (! isscalar (capwid) || ! (isnumeric (capwid) && isreal (capwid))) msg = ["boxplot: 'CapWidths' input argument accepts only", ... " a real scalar value as value"]; error (msg); endif case "boxstyle" box_style = varargin{indopt}; ## Check for string input: "outline" or "filled" if (! ischar (box_style) || ... ! ismember (lower (box_style), {"outline", "filled"})) msg = ["boxplot: 'BoxStyle' input argument accepts only", ... " 'outline' or 'filled' as value"]; error (msg); endif box_style = lower (box_style); case "positions" positions = varargin{indopt}; if (! isvector (positions) || ! isnumeric (positions)) msg = ["boxplot: 'Positions' input argument accepts only", ... " a numeric vector as value"]; error (msg); endif case "labels" labels = varargin{indopt}; if (! iscellstr (labels)) msg = ["boxplot: 'Labels' input argument accepts only", ... " a cellstr array as value"]; error (msg); endif case "colors" bcolor = varargin{indopt}; if (! (ischar (bcolor) || ... (isnumeric (bcolor) && size (bcolor, 2) == 3))) msg = ["boxplot: 'Colors' input argument accepts only", ... " a character (string) or Nx3 numeric array as value"]; error (msg); endif otherwise ## Take two args and append them to plot_opts plot_opts(1, end+1:end+2) = {dummy, varargin{indopt}}; endswitch endif numarg -= 2; indopt++; endif endwhile if (1 == length (symbol)) symbol(2) = symbol(1); endif if (1 == notched) notched = 0.25; endif a = 1-notched; ## Figure out how many data sets we have if (isempty (groups)) if (iscell (data)) nc = nug = length (data); for ind_c = (1:nc) lc(ind_c) = length (data{ind_c}); endfor else if (isvector (data)) data = data(:); endif nc = nug = columns (data); lc = ones (1, nc) * rows (data); endif groups = (1:nc); ## In case sample_IDs exists. check that it has same size as data if (! isempty (sample_IDs) && length (sample_IDs) == 1) for ind_c = (1:nc) if (lc(ind_c) != length (sample_IDs)) error ("boxplot: Sample_IDs must match the data"); endif endfor elseif (! isempty (sample_IDs) && length (sample_IDs) == nc) for ind_c = (1:nc) if (lc(ind_c) != length (sample_IDs{ind_c})) error ("boxplot: Sample_IDs must match the data"); endif endfor elseif (! isempty (sample_IDs) && length (sample_IDs) != nc) error ("boxplot: Sample_IDs must match the data"); endif ## Create labels according to number of datasets as ordered in data ## in case they are not provided by the user as optional argument if (isempty (labels)) for i = 1:nc column_label = num2str (groups(i)); labels(i) = {column_label}; endfor endif else if (! isvector (data)) error ("boxplot: with the formalism (data, group), both must be vectors"); endif ## If sample IDs given, check that their size matches the data if (! isempty (sample_IDs)) if (length (sample_IDs) != 1 || length (sample_IDs{1}) != length (data)) error ("boxplot: Sample_IDs must match the data"); endif nug = unique (groups); dummy_data = cell (1, length (nug)); dummy_sIDs = cell (1, length (nug)); ## Check if groups are parsed as a numeric vector if (isnumeric (groups)) for ind_c = (1:length (nug)) dummy_data(ind_c) = data(groups == nug(ind_c)); dummy_sIDs(ind_c) = {sample_IDs{1}(groups == nug(ind_c))}; endfor ## Create labels according to unique numeric groups in case ## they are not provided by the user as optional argument if (isempty (labels)) for i = 1:nug column_label = num2str (groups(i)); labels(i) = {column_label}; endfor endif ## Check if groups are parsed as a cell string vector elseif iscellstr (groups) for ind_c = (1:length (nug)) dummy_data(ind_c) = data(ismember (group, nug(ind_c))); dummy_sIDs(ind_c) = {sample_IDs{1}(ismember (group, nug(ind_c)))}; endfor ## Create labels according to unique cell string groups in case ## they are not provided by the user as optional argument if (isempty (labels)) labels = nug; endif else error ("boxplot: group argument must be numeric or cell string vector"); endif data = dummy_data; groups = nug(:).'; nc = length (nug); sample_IDs = dummy_sIDs; else nug = unique (groups); dummy_data = cell (1, length (nug)); ## Check if groups are parsed as a numeric vector if (isnumeric (groups)) for ind_c = (1:length (nug)) dummy_data(ind_c) = data(groups == nug(ind_c)); endfor ## Create labels according to unique numeric groups in case ## they are not provided by the user as optional argument if (isempty (labels)) for i = 1:nug column_label = num2str (groups(i)); labels(i) = {column_label}; endfor endif ## Check if groups are parsed as a cell string vector elseif (iscellstr (groups)) for ind_c = (1:length (nug)) dummy_data(ind_c) = data(ismember (group, nug(ind_c))); endfor ## Create labels according to unique cell string groups in case ## they are not provided by the user as optional argument if (isempty (labels)) labels = nug; endif else error ("boxplot: group argument must be numeric vector or cell string"); endif data = dummy_data; nc = length (nug); if (iscell (groups)) groups = [1:nc]; else groups = nug(:).'; endif endif endif ## Compute statistics. ## s will contain ## 1,5 min and max ## 2,3,4 1st, 2nd and 3rd quartile ## 6,7 lower and upper confidence intervals for median s = zeros (7, nc); box = zeros (1, nc); ## Arrange the boxes into desired positions (if requested, otherwise leave ## default 1:nc) if (! isempty (positions)) groups = positions; endif ## Initialize whisker matrices to correct size and all necessary outlier ## variables whisker_x = ones (2, 1) * [groups, groups]; whisker_y = zeros (2, 2 * nc); outliers_x = []; outliers_y = []; outliers_idx = []; outliers_IDs = {}; outliers2_x = []; outliers2_y = []; outliers2_idx = []; outliers2_IDs = {}; for indi = (1:nc) ## Get the next data set from the array or cell array if (iscell (data)) col = data{indi}(:); if (!isempty (sample_IDs)) sIDs = sample_IDs{indi}; else sIDs = num2cell([1:length(col)]); endif else col = data(:, indi); sIDs = num2cell([1:length(col)]); endif ## Skip missing data (NaN, NA) and remove respective sample IDs. ## Do this only on nonempty data if (length (col) > 0) remove_samples = find (col(isnan (col) | isna (col))); if (length (remove_samples) > 0) col(remove_samples) = []; sIDs(remove_samples) = []; endif endif ## Remember data length nd = length (col); box(indi) = nd; if (nd > 1) ## Min, max and quartiles s(1:5, indi) = statistics (col)(1:5); ## Confidence interval for the median est = 1.57 * (s(4, indi) - s(2, indi)) / sqrt (nd); s(6, indi) = max ([s(3, indi) - est, s(2, indi)]); s(7, indi) = min ([s(3, indi) + est, s(4, indi)]); ## Whiskers out to the last point within the desired inter-quartile range IQR = maxwhisker * (s(4, indi) - s(2, indi)); whisker_y(:, indi) = [min(col(col >= s(2, indi) - IQR)); s(2, indi)]; whisker_y(:, nc+indi) = [max(col(col <= s(4, indi) + IQR)); s(4, indi)]; ## Outliers beyond 1 and 2 inter-quartile ranges outliers = col((col < s(2, indi) - IQR & col >= s(2, indi) - 2 * IQR) | ... (col > s(4, indi) + IQR & col <= s(4, indi) + 2 * IQR)); outliers2 = col(col < s(2, indi) - 2 * IQR | col > s(4, indi) + 2 * IQR); ## Get outliers indices from this dataset if (length (outliers) > 0) for out_i = 1:length (outliers) outliers_idx = [outliers_idx; (find (col == outliers(out_i)))]; outliers_IDs = {outliers_IDs{:}, sIDs{(find (col == outliers(out_i)))}}; endfor endif if (length (outliers2) > 0) for out_i = 1:length (outliers2) outliers2_idx = [outliers2_idx; find(col == outliers2(out_i))]; outliers2_IDs = {outliers2_IDs{:}, sIDs{find(col == outliers2(out_i))}}; endfor endif outliers_x = [outliers_x; (groups(indi) * ones (size (outliers)))]; outliers_y = [outliers_y; outliers]; outliers2_x = [outliers2_x; (groups(indi) * ones (size (outliers2)))]; outliers2_y = [outliers2_y; outliers2]; elseif (1 == nd) ## All statistics collapse to the value of the point s(:, indi) = col; ## Single point data sets are plotted as outliers. outliers_x = [outliers_x; groups(indi)]; outliers_y = [outliers_y; col]; ## Append the single point's index to keep the outliers' vector aligned outliers_idx = [outliers_idx; 1]; outliers_IDs = {outliers_IDs{:}, sIDs{:}}; else ## No statistics if no points s(:, indi) = NaN; endif endfor ## Note which boxes don't have enough stats chop = find (box <= 1); ## Replicate widths (if scalar or shorter vector) to match the number of boxes widths = widths(repmat (1:length (widths), 1, nc)); ## Truncate just in case :) widths([nc+1:end]) = []; ## Draw a box around the quartiles, with box width being fixed or proportional ## to the number of items in the box. if (strcmpi (box_width, "proportional")) box = box .* (widths ./ max (box)); else box = box .* (widths ./ box); endif ## Draw notches if desired. quartile_x = ones (11, 1) * groups + ... [-a; -1; -1; 1 ; 1; a; 1; 1; -1; -1; -a] * box; quartile_y = s([3, 7, 4, 4, 7, 3, 6, 2, 2, 6, 3], :); ## Draw a line through the median median_x = ones (2, 1) * groups + [-a; +a] * box; median_y = s([3, 3], :); ## Chop all boxes which don't have enough stats quartile_x(:, chop) = []; quartile_y(:, chop) = []; whisker_x(:, [chop, chop + nc]) = []; whisker_y(:, [chop, chop + nc]) = []; median_x(:, chop) = []; median_y(:, chop) = []; box(chop) = []; ## Add caps to the remaining whiskers cap_x = whisker_x; if (strcmpi (box_width, "proportional")) cap_x(1, :) -= repmat (((capwid * box .* (widths ./ max (box))) / 8), 1, 2); cap_x(2, :) += repmat (((capwid * box .* (widths ./ max (box))) / 8), 1, 2); else cap_x(1, :) -= repmat ((capwid * widths / 8), 1, 2); cap_x(2, :) += repmat ((capwid * widths / 8), 1, 2); endif cap_y = whisker_y([1, 1], :); ## Calculate coordinates for outlier tags outliers_tags_x = outliers_x + 0.08; outliers_tags_y = outliers_y; outliers2_tags_x = outliers2_x + 0.08; outliers2_tags_y = outliers2_y; ## Do the plot if (orientation) ## Define outlier_tags' vertical alignment outlier_tags_alignment = {"horizontalalignment", "left"}; if (box_style) f = fillbox (quartile_x, quartile_y, bcolor); endif h = plot (quartile_x, quartile_y, "b;;", whisker_x, whisker_y, "b;;", cap_x, cap_y, "b;;", median_x, median_y, "r;;", outliers_x, outliers_y, [symbol(1), "r;;"], outliers2_x, outliers2_y, [symbol(2), "r;;"], plot_opts{:}); ## Print outlier tags if (outlier_tags == 1 && outliers_x > 0) t1 = plot_tags (outliers_tags_x, outliers_tags_y, outliers_idx, outliers_IDs, sample_IDs, outlier_tags_alignment); endif if (outlier_tags == 1 && outliers2_x > 0) t2 = plot_tags (outliers2_tags_x, outliers2_tags_y, outliers2_idx, outliers2_IDs, sample_IDs, outlier_tags_alignment); endif else ## Define outlier_tags' horizontal alignment outlier_tags_alignment = {"horizontalalignment", "left", "rotation", 90}; if (box_style) f = fillbox (quartile_y, quartile_x, bcolor); endif h = plot (quartile_y, quartile_x, "b;;", whisker_y, whisker_x, "b;;", cap_y, cap_x, "b;;", median_y, median_x, "r;;", outliers_y, outliers_x, [symbol(1), "r;;"], outliers2_y, outliers2_x, [symbol(2), "r;;"], plot_opts{:}); ## Print outlier tags if (outlier_tags == 1 && outliers_x > 0) t1 = plot_tags (outliers_tags_y, outliers_tags_x, outliers_idx, outliers_IDs, sample_IDs, outlier_tags_alignment); endif if (outlier_tags == 1 && outliers2_x > 0) t2 = plot_tags (outliers2_tags_y, outliers2_tags_x, outliers2_idx, outliers2_IDs, sample_IDs, outlier_tags_alignment); endif endif ## Distribute handles for box outlines and box fill (if any) nq = 1 : size (quartile_x, 2); hs.box = h(nq); if (box_style) nf = 1 : length (groups); hs.box_fill = f(nf); else hs.box_fill = []; endif ## Distribute handles for whiskers (including caps) and median lines nw = nq(end) + [1 : 2 * (size (whisker_x, 2))]; hs.whisker = h(nw); nm = nw(end)+ [1 : (size (median_x, 2))]; hs.median = h(nm); ## Distribute handles for outliers (if any) and their respective tags ## (if applicable) no = nm; if (! isempty (outliers_y)) no = nm(end) + [1 : size(outliers_y, 2)]; hs.outliers = h(no); if (outlier_tags == 1) nt = 1 : length (outliers_tags_y); hs.out_tags = t1(nt); else hs.out_tags = []; endif else hs.outliers = []; hs.out_tags = []; endif ## Distribute handles for extreme outliers (if any) and their respective tags ## (if applicable) if (! isempty (outliers2_y)) no2 = no(end) + [1 : size(outliers2_y, 2)]; hs.outliers2 = h(no2); if (outlier_tags == 1) nt2 = 1 : length (outliers2_tags_y); hs.out_tags2 = t2(nt2); else hs.out_tags2 = []; endif else hs.outliers2 = []; hs.out_tags2 = []; end ## Redraw the median lines to avoid colour overlapping in case of 'filled' ## BoxStyle if (box_style) set (hs.median, "color", "r"); endif ## Print labels according to orientation and return handle if (orientation) set (gca(), "xtick", groups, "xticklabel", labels); hs.labels = get (gcf, "currentaxes"); else set (gca(), "ytick", groups, "yticklabel", labels); hs.labels = get (gcf, "currentaxes"); endif hold off; ## Return output arguments if desired if (nargout >= 1) s_o = s; endif if (nargout == 2) hs_o = hs; endif endfunction function htags = plot_tags (out_tags_x, out_tags_y, out_idx, out_IDs, ... sample_IDs, opt) for i=1 : length (out_tags_x) if (! isempty (sample_IDs)) htags(i) = text (out_tags_x(i), out_tags_y(i), out_IDs{i}, opt{:}); else htags(i) = text (out_tags_x(i), out_tags_y(i), num2str (out_idx(i)), ... opt{:}); endif endfor endfunction function f = fillbox (quartile_y, quartile_x, bcolor) f = []; for icol = 1 : columns (quartile_x) if (ischar (bcolor)) f = [ f; fill(quartile_y(:, icol), quartile_x(:, icol), ... bcolor(mod (icol-1, numel (bcolor))+1)) ]; else f = [ f; fill(quartile_y(:, icol), quartile_x(:, icol), ... bcolor(mod (icol-1, size (bcolor, 1))+1, :)) ]; endif hold on; endfor endfunction %!demo %! axis ([0, 3]); %! boxplot ({(randn(10, 1) * 5 + 140), (randn (13, 1) * 8 + 135)}); %! set (gca (), "xtick", [1 2], "xticklabel", {"girls", "boys"}) %! title ("Grade 3 heights"); %!demo %! data = [(randn (10, 1) * 5 + 140); (randn (25, 1) * 8 + 135); ... %! (randn (20, 1) * 6 + 165)]; %! groups = [(ones (10, 1)); (ones (25, 1) * 2); (ones (20, 1) * 3)]; %! labels = {"Team A", "Team B", "Team C"}; %! pos = [2, 1, 3]; %! boxplot (data, groups, "Notch", "on", "Labels", labels, "Positions", pos, ... %! "OutlierTags", "on", "BoxStyle", "filled"); %! title ("Example of Group splitting with paired vectors"); %!demo %! boxplot (randn (100, 9), "notch", "on", "boxstyle", "filled", ... %! "colors", "ygcwkmb", "whisker", 1.2); %! title ("Example of different colors specified with characters"); %!demo %! colors = [0.7 0.7 0.7; ... %! 0.0 0.4 0.9; ... %! 0.7 0.4 0.3; ... %! 0.7 0.1 0.7; ... %! 0.8 0.7 0.4; ... %! 0.1 0.8 0.5; ... %! 0.9 0.9 0.2]; %! boxplot (randn (100, 13), "notch", "on", "boxstyle", "filled", ... %! "colors", colors, "whisker", 1.3, "boxwidth", "proportional"); %! title ("Example of different colors specified as RGB values"); %% Input data validation %!error boxplot ("a") %!error boxplot ({[1 2 3], "a"}) %!error boxplot ([1 2 3], 1, {2, 3}) %!error boxplot ([1 2 3], {"a", "b"}) %!error <'Notch' input argument accepts> boxplot ([1:10], "notch", "any") %!error boxplot ([1:10], "notch", i) %!error boxplot ([1:10], "notch", {}) %!error boxplot (1, "symbol", 1) %!error <'Orientation' input argument accepts only> boxplot (1, "orientation", "diagonal") %!error boxplot (1, "orientation", {}) %!error <'Whisker' input argument accepts only> boxplot (1, "whisker", "a") %!error <'Whisker' input argument accepts only> boxplot (1, "whisker", [1 3]) %!error <'OutlierTags' input argument accepts only> boxplot (3, "OutlierTags", "maybe") %!error boxplot (3, "OutlierTags", {}) %!error <'Sample_IDs' input argument accepts only> boxplot (1, "sample_IDs", 1) %!error <'BoxWidth' input argument accepts only> boxplot (1, "boxwidth", 2) %!error <'BoxWidth' input argument accepts only> boxplot (1, "boxwidth", "anything") %!error <'Widths' input argument accepts only> boxplot (5, "widths", "a") %!error <'Widths' input argument accepts only> boxplot (5, "widths", [1:4]) %!error <'Widths' input argument accepts only> boxplot (5, "widths", []) %!error <'CapWidths' input argument accepts only> boxplot (5, "capwidths", "a") %!error <'CapWidths' input argument accepts only> boxplot (5, "capwidths", [1:4]) %!error <'CapWidths' input argument accepts only> boxplot (5, "capwidths", []) %!error <'BoxStyle' input argument accepts only> boxplot (1, "Boxstyle", 1) %!error <'BoxStyle' input argument accepts only> boxplot (1, "Boxstyle", "garbage") %!error <'Positions' input argument accepts only> boxplot (1, "positions", "aa") %!error <'Labels' input argument accepts only> boxplot (3, "labels", [1 5]) %!error <'Colors' input argument accepts only> boxplot (1, "colors", {}) %!error <'Colors' input argument accepts only> boxplot (2, "colors", [1 2 3 4]) %!error boxplot (randn (10, 3), 'Sample_IDs', {"a", "b"}) %!error boxplot (rand (3, 3), [1 2]) %!test %! h = figure ("visible", "off"); %! [a, b] = boxplot (rand (10, 3)); %! close (h); %! assert (size (a), [7, 3]); %! assert (numel (b.box), 3); %! assert (numel (b.whisker), 12); %! assert (numel (b.median), 3); %!test %! h = figure ("visible", "off"); %! [~, b] = boxplot (rand (10, 3), "BoxStyle", "filled", "colors", "ybc"); %! close (h); %! assert (numel (b.box_fill), 3); statistics-1.4.3/inst/burrcdf.m0000644000000000000000000000661114153320774014673 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} burrcdf (@var{x}, @var{c}, @var{k}) ## For each element of @var{x}, compute the cumulative distribution function ## (CDF) at @var{x} of the Burr distribution with scale parameter @var{alpha} ## and shape parameters @var{c} and @var{k}. ## @end deftypefn ## Author: Dag Lyberg ## Description: CDF of the Burr distribution function cdf = burrcdf (x, alpha, c, k) if (nargin != 4) print_usage (); endif if (! isscalar (alpha) || ! isscalar (c) || ! isscalar (k) ) [retval, x, alpha, c, k] = common_size (x, alpha, c, k); if (retval > 0) error ("burrcdf: X, ALPHA, C AND K must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex(alpha) || iscomplex (c) || iscomplex (k)) error ("burrcdf: X, ALPHA, C AND K must not be complex"); endif if (isa (x, "single") || isa (alpha, "single") || isa (c, "single") ... || isa (k, "single")) cdf = zeros (size (x), "single"); else cdf = zeros (size (x)); endif j = isnan (x) | ! (alpha > 0) | ! (c > 0) | ! (k > 0); cdf(j) = NaN; j = (x > 0) & (0 < alpha) & (alpha < Inf) & (0 < c) & (c < Inf) ... & (0 < k) & (k < Inf); if (isscalar (alpha) && isscalar(c) && isscalar(k)) cdf(j) = 1 - (1 + (x(j) / alpha).^c).^(-k); else cdf(j) = 1 - (1 + (x(j) ./ alpha(j)).^c(j)).^(-k(j)); endif endfunction %!shared x,y %! x = [-1, 0, 1, 2, Inf]; %! y = [0, 0, 1/2, 2/3, 1]; %!assert (burrcdf (x, ones(1,5), ones (1,5), ones (1,5)), y, eps) %!assert (burrcdf (x, 1, 1, 1), y, eps) %!assert (burrcdf (x, [1, 1, NaN, 1, 1], 1, 1), [y(1:2), NaN, y(4:5)], eps) %!assert (burrcdf (x, 1, [1, 1, NaN, 1, 1], 1), [y(1:2), NaN, y(4:5)], eps) %!assert (burrcdf (x, 1, 1, [1, 1, NaN, 1, 1]), [y(1:2), NaN, y(4:5)], eps) %!assert (burrcdf ([x, NaN], 1, 1, 1), [y, NaN], eps) ## Test class of input preserved %!assert (burrcdf (single ([x, NaN]), 1, 1, 1), single ([y, NaN]), eps('single')) %!assert (burrcdf ([x, NaN], single (1), 1, 1), single ([y, NaN]), eps('single')) %!assert (burrcdf ([x, NaN], 1, single (1), 1), single ([y, NaN]), eps('single')) %!assert (burrcdf ([x, NaN], 1, 1, single (1)), single ([y, NaN]), eps('single')) ## Test input validation %!error burrcdf () %!error burrcdf (1) %!error burrcdf (1,2) %!error burrcdf (1,2,3) %!error burrcdf (1,2,3,4,5) %!error burrcdf (ones (3), ones (2), ones(2), ones(2)) %!error burrcdf (ones (2), ones (3), ones(2), ones(2)) %!error burrcdf (ones (2), ones (2), ones(3), ones(2)) %!error burrcdf (ones (2), ones (2), ones(2), ones(3)) %!error burrcdf (i, 2, 2, 2) %!error burrcdf (2, i, 2, 2) %!error burrcdf (2, 2, i, 2) %!error burrcdf (2, 2, 2, i) statistics-1.4.3/inst/burrinv.m0000644000000000000000000000716614153320774014741 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} burrinv (@var{x}, @var{alpha}, @var{c}, @var{k}) ## For each element of @var{x}, compute the quantile (the inverse of the CDF) ## at @var{x} of the Burr distribution with scale parameter @var{alpha} and ## shape parameters @var{c} and @var{k}. ## @end deftypefn ## Author: Dag Lyberg ## Description: Quantile function of the Burr distribution function inv = burrinv (x, alpha, c, k) if (nargin != 4) print_usage (); endif if (! isscalar (alpha) || ! isscalar (c) || ! isscalar (k) ) [retval, x, alpha, c, k] = common_size (x, alpha, c, k); if (retval > 0) error ("burrinv: X, ALPHA, C AND K must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex(alpha) || iscomplex (c) || iscomplex (k)) error ("burrinv: X, ALPHA, C AND K must not be complex"); endif if (isa (x, "single") || isa (alpha, "single") || isa (c, "single") ... || isa (k, "single")) inv = zeros (size (x), "single"); else inv = zeros (size (x)); endif j = isnan (x) | (x < 0) | (x > 1) | ! (alpha > 0) | ! (c > 0) | ! (k > 0); inv(j) = NaN; j = (x == 1) & (0 < alpha) & (alpha < Inf) & (0 < c) & (c < Inf) ... & (0 < k) & (k < Inf); inv(j) = Inf; j = (0 < x) & (x < 1) & (0 < alpha) & (alpha < Inf) & (0 < c) & (c < Inf) ... & (0 < k) & (k < Inf); if (isscalar (alpha) && isscalar(c) && isscalar(k)) inv(j) = ((1 - x(j) / alpha).^(-1 / k) - 1).^(1 / c) ; else inv(j) = ((1 - x(j) ./ alpha(j)).^(-1 ./ k(j)) - 1).^(1 ./ c(j)) ; endif endfunction %!shared x,y %! x = [-Inf, -1, 0, 1/2, 1, 2, Inf]; %! y = [NaN, NaN, 0, 1 , Inf, NaN, NaN]; %!assert (burrinv (x, ones (1,7), ones (1,7), ones(1,7)), y, eps) %!assert (burrinv (x, 1, 1, 1), y, eps) %!assert (burrinv (x, [1, 1, 1, NaN, 1, 1, 1], 1, 1), [y(1:3), NaN, y(5:7)], eps) %!assert (burrinv (x, 1, [1, 1, 1, NaN, 1, 1, 1], 1), [y(1:3), NaN, y(5:7)], eps) %!assert (burrinv (x, 1, 1, [1, 1, 1, NaN, 1, 1, 1]), [y(1:3), NaN, y(5:7)], eps) %!assert (burrinv ([x, NaN], 1, 1, 1), [y, NaN], eps) ## Test class of input preserved %!assert (burrinv (single ([x, NaN]), 1, 1, 1), single ([y, NaN]), eps('single')) %!assert (burrinv ([x, NaN], single (1), 1, 1), single ([y, NaN]), eps('single')) %!assert (burrinv ([x, NaN], 1, single (1), 1), single ([y, NaN]), eps('single')) %!assert (burrinv ([x, NaN], 1, 1, single (1)), single ([y, NaN]), eps('single')) ## Test input validation %!error burrinv () %!error burrinv (1) %!error burrinv (1,2) %!error burrinv (1,2,3) %!error burrinv (1,2,3,4,5) %!error burrinv (ones (3), ones (2), ones(2), ones(2)) %!error burrinv (ones (2), ones (3), ones(2), ones(2)) %!error burrinv (ones (2), ones (2), ones(3), ones(2)) %!error burrinv (ones (2), ones (2), ones(2), ones(3)) %!error burrinv (i, 2, 2, 2) %!error burrinv (2, i, 2, 2) %!error burrinv (2, 2, i, 2) %!error burrinv (2, 2, 2, i) statistics-1.4.3/inst/burrpdf.m0000644000000000000000000000666014153320774014714 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} burrpdf (@var{x}, @var{alpha}, @var{c}, @var{k}) ## For each element of @var{x}, compute the probability density function (PDF) ## at @var{x} of the Burr distribution with scale parameter @var{alpha} and ## shape parameters @var{c} and @var{k}. ## @end deftypefn ## Author: Dag Lyberg ## Description: PDF of the Burr distribution function pdf = burrpdf (x, alpha, c, k) if (nargin != 4) print_usage (); endif if (! isscalar (alpha) || ! isscalar (c) || ! isscalar (k) ) [retval, x, alpha, c, k] = common_size (x, alpha, c, k); if (retval > 0) error ("burrpdf: X, ALPHA, C AND K must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex(alpha) || iscomplex (c) || iscomplex (k)) error ("burrpdf: X, ALPHA, C AND K must not be complex"); endif if (isa (x, "single") || isa (alpha, "single") ... || isa (c, "single") || isa (k, "single")) pdf = zeros (size (x), "single"); else pdf = zeros (size (x)); endif j = isnan (x) | ! (alpha > 0) | ! (c > 0) | ! (k > 0); pdf(j) = NaN; j = (x > 0) & (0 < alpha) & (alpha < Inf) & (0 < c) & (c < Inf) ... & (0 < k) & (k < Inf); if (isscalar (alpha) && isscalar (c) && isscalar(k)) pdf(j) = (c * k / alpha) .* (x(j) / alpha).^(c-1) ./ ... (1 + (x(j) / alpha).^c).^(k + 1); else pdf(j) = (c(j) .* k(j) ./ alpha(j) ).* x(j).^(c(j)-1) ./ ... (1 + (x(j) ./ alpha(j) ).^c(j) ).^(k(j) + 1); endif endfunction %!shared x,y %! x = [-1, 0, 1, 2, Inf]; %! y = [0, 0, 1/4, 1/9, 0]; %!assert (burrpdf (x, ones(1,5), ones (1,5), ones (1,5)), y) %!assert (burrpdf (x, 1, 1, 1), y) %!assert (burrpdf (x, [1, 1, NaN, 1, 1], 1, 1), [y(1:2), NaN, y(4:5)]) %!assert (burrpdf (x, 1, [1, 1, NaN, 1, 1], 1), [y(1:2), NaN, y(4:5)]) %!assert (burrpdf (x, 1, 1, [1, 1, NaN, 1, 1]), [y(1:2), NaN, y(4:5)]) %!assert (burrpdf ([x, NaN], 1, 1, 1), [y, NaN]) ## Test class of input preserved %!assert (burrpdf (single ([x, NaN]), 1, 1, 1), single ([y, NaN])) %!assert (burrpdf ([x, NaN], single (1), 1, 1), single ([y, NaN])) %!assert (burrpdf ([x, NaN], 1, single (1), 1), single ([y, NaN])) %!assert (burrpdf ([x, NaN], 1, 1, single (1)), single ([y, NaN])) ## Test input validation %!error burrpdf () %!error burrpdf (1) %!error burrpdf (1,2) %!error burrpdf (1,2,3) %!error burrpdf (1,2,3,4,5) %!error burrpdf (ones (3), ones (2), ones(2), ones(2)) %!error burrpdf (ones (2), ones (3), ones(2), ones(2)) %!error burrpdf (ones (2), ones (2), ones(3), ones(2)) %!error burrpdf (ones (2), ones (2), ones(2), ones(3)) %!error burrpdf (i, 2, 2, 2) %!error burrpdf (2, i, 2, 2) %!error burrpdf (2, 2, i, 2) %!error burrpdf (2, 2, 2, i) statistics-1.4.3/inst/burrrnd.m0000644000000000000000000001203014153320774014712 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} burrrnd (@var{alpha}, @var{c}, @var{k}) ## @deftypefnx {} {} burrrnd (@var{alpha}, @var{c}, @var{k}, @var{r}) ## @deftypefnx {} {} burrrnd (@var{alpha}, @var{c}, @var{k}, @var{r}, @var{c}, @dots{}) ## @deftypefnx {} {} burrrnd (@var{alpha}, @var{c}, @var{k}, [@var{sz}]) ## Return a matrix of random samples from the generalized Pareto distribution ## with scale parameter @var{alpha} and shape parameters @var{c} and @var{k}. ## ## When called with a single size argument, return a square matrix with ## the dimension specified. When called with more than one scalar argument the ## first two arguments are taken as the number of rows and columns and any ## further arguments specify additional matrix dimensions. The size may also ## be specified with a vector of dimensions @var{sz}. ## ## If no size arguments are given then the result matrix is the common size of ## @var{alpha}, @var{c} and @var{k}. ## @end deftypefn ## Author: Dag Lyberg ## Description: Random deviates from the generalized extreme value (GEV) distribution function rnd = burrrnd (alpha, c, k, varargin) if (nargin < 3) print_usage (); endif if (! isscalar (alpha) || ! isscalar (c) || ! isscalar (k)) [retval, alpha, c, k] = common_size (alpha, c, k); if (retval > 0) error ("burrrnd: ALPHA, C and K must be of common size or scalars"); endif endif if (iscomplex (alpha) || iscomplex (c) || iscomplex (k)) error ("burrrnd: ALPHA, C and K must not be complex"); endif if (nargin == 3) sz = size (alpha); elseif (nargin == 4) if (isscalar (varargin{1}) && varargin{1} >= 0) sz = [varargin{1}, varargin{1}]; elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) sz = varargin{1}; else error ("burrrnd: dimension vector must be row vector of non-negative integers"); endif elseif (nargin > 4) if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) error ("burrrnd: dimensions must be non-negative integers"); endif sz = [varargin{:}]; endif if (! isscalar (alpha) && ! isequal (size (c), sz) && ! isequal (size (k), sz)) error ("burrrnd: ALPHA, C and K must be scalar or of size SZ"); endif if (isa (alpha, "single") || isa (c, "single") || isa (k, "single")) cls = "single"; else cls = "double"; endif if (isscalar (alpha) && isscalar (c) && isscalar(k)) if ((0 < alpha) && (alpha < Inf) && (0 < c) && (c < Inf) ... && (0 < k) && (k < Inf)) rnd = rand (sz, cls); rnd(:) = ((1 - rnd(:) / alpha).^(-1 / k) - 1).^(1 / c); else rnd = NaN (sz, cls); endif else rnd = NaN (sz, cls); j = (0 < alpha) && (alpha < Inf) && (0 < c) && (c < Inf) ... && (0 < k) && (k < Inf); rnd(k) = rand(sum(j(:)),1); rnd(k) = ((1 - rnd(j) / alpha(j)).^(-1 ./ k(j)) - 1).^(1 ./ c(j)); endif endfunction %!assert (size (burrrnd (1, 1, 1)), [1 1]) %!assert (size (burrrnd (ones (2,1), 1, 1)), [2, 1]) %!assert (size (burrrnd (ones (2,2), 1, 1)), [2, 2]) %!assert (size (burrrnd (1, ones (2,1), 1)), [2, 1]) %!assert (size (burrrnd (1, ones (2,2), 1)), [2, 2]) %!assert (size (burrrnd (1, 1, ones (2,1))), [2, 1]) %!assert (size (burrrnd (1, 1, ones (2,2))), [2, 2]) %!assert (size (burrrnd (1, 1, 1, 3)), [3, 3]) %!assert (size (burrrnd (1, 1, 1, [4 1])), [4, 1]) %!assert (size (burrrnd (1, 1, 1, 4, 1)), [4, 1]) ## Test class of input preserved %!assert (class (burrrnd (1,1,1)), "double") %!assert (class (burrrnd (single (1),1,1)), "single") %!assert (class (burrrnd (single ([1 1]),1,1)), "single") %!assert (class (burrrnd (1,single (1),1)), "single") %!assert (class (burrrnd (1,single ([1 1]),1)), "single") %!assert (class (burrrnd (1,1,single (1))), "single") %!assert (class (burrrnd (1,1,single ([1 1]))), "single") ## Test input validation %!error burrrnd () %!error burrrnd (1) %!error burrrnd (1,2) %!error burrrnd (ones (3), ones (2), ones (2), 2) %!error burrrnd (ones (2), ones (3), ones (2), 2) %!error burrrnd (ones (2), ones (2), ones (3), 2) %!error burrrnd (i, 2, 2) %!error burrrnd (2, i, 2) %!error burrrnd (2, 2, i) %!error burrrnd (4,2,2, -1) %!error burrrnd (4,2,2, ones (2)) %!error burrrnd (4,2,2, [2 -1 2]) %!error burrrnd (4*ones (2),2,2, 3) %!error burrrnd (4*ones (2),2,2, [3, 2]) %!error burrrnd (4*ones (2),2,2, 3, 2) statistics-1.4.3/inst/canoncorr.m0000644000000000000000000000666014153320774015234 0ustar0000000000000000function [A,B,r,U,V,stats] = canoncorr (X,Y) ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{A} @var{B} @var{r} @var{U} @var{V}] =} canoncorr (@var{X}, @var{Y}) ## Canonical correlation analysis ## ## Given @var{X} (size @var{k}*@var{m}) and @var{Y} (@var{k}*@var{n}), returns projection matrices of canonical coefficients @var{A} (size @var{m}*@var{d}, where @var{d} is the smallest of @var{m}, @var{n}, @var{d}) and @var{B} (size @var{m}*@var{d}); the canonical correlations @var{r} (1*@var{d}, arranged in decreasing order); the canonical variables @var{U}, @var{V} (both @var{k}*@var{d}, with orthonormal columns); and @var{stats}, a structure containing results from Bartlett's chi-square and Rao's F tests of significance. ## ## References: @* ## William H. Press (2011), Canonical Correlation Clarified by Singular Value Decomposition, http://numerical.recipes/whp/notes/CanonCorrBySVD.pdf @* ## Philip B. Ender, Multivariate Analysis: Canonical Correlation Analysis, http://www.philender.com/courses/multivariate/notes2/can1.html ## ## @seealso{princomp} ## @end deftypefn # Copyright (C) 2016-2019 by Nir Krakauer # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program; If not, see . k = size (X, 1); #should also be size (Y, 1) m = size (X, 2); n = size (Y, 2); d = min ([k m n]); X = center (X); Y = center (Y); [Qx Rx] = qr (X, 0); [Qy Ry] = qr (Y, 0); [U S V] = svd (Qx' * Qy, "econ"); A = Rx \ U(:, 1:d); B = Ry \ V(:, 1:d); #A, B are scaled to make the covariance matrices of the outputs U, V identity matrices f = sqrt (k-1); A .*= f; B .*= f; if isargout(3) || isargout(6) r = max(0, min(diag(S), 1))'; endif if isargout (4) U = X * A; endif if isargout (5) V = Y * B; endif if isargout (6) Wilks = fliplr(cumprod(fliplr((1 - r .^ 2)))); chisq = - (k - 1 - (m + n + 1)/2) * log(Wilks); df1 = (m - (1:d) + 1) .* (n - (1:d) + 1); pChisq = 1 - chi2cdf (chisq, df1); s = sqrt((df1.^2 - 4) ./ ((m - (1:d) + 1).^2 + (n - (1:d) + 1).^2 - 5)); df2 = (k - 1 - (m + n + 1)/2) * s - df1/2 + 1; ls = Wilks .^ (1 ./ s); F = (1 ./ ls - 1) .* (df2 ./ df1); pF = 1 - fcdf (F, df1, df2); stats.Wilks = Wilks; stats.df1 = df1; stats.df2 = df2; stats.F = F; stats.pF = pF; stats.chisq = chisq; stats.pChisq = pChisq; endif %!shared X,Y,A,B,r,U,V,k %! k = 10; %! X = [1:k; sin(1:k); cos(1:k)]'; Y = [tan(1:k); tanh((1:k)/k)]'; %! [A,B,r,U,V,stats] = canoncorr (X,Y); %!assert (A, [-0.329229 0.072908; 0.074870 1.389318; -0.069302 -0.024109], 1E-6); %!assert (B, [-0.017086 -0.398402; -4.475049 -0.824538], 1E-6); %!assert (r, [0.99590 0.26754], 1E-5); %!assert (U, center(X) * A, 10*eps); %!assert (V, center(Y) * B, 10*eps); %!assert (cov(U), eye(size(U, 2)), 10*eps); %!assert (cov(V), eye(size(V, 2)), 10*eps); %! rand ("state", 1); [A,B,r] = canoncorr (rand(5, 10),rand(5, 20)); %!assert (r, ones(1, 5), 10*eps); statistics-1.4.3/inst/carbig.mat0000644000000000000000000003327414153320774015025 0ustar0000000000000000MATLAB 5.0 MAT-file, written by Octave 6.1.0, 2021-03-16 12:38:41 UTC IM̀xœuVKnÔ@u ûÙÏø7vw{’,Í>—@QFBB€đ ØĂ)æpœ;U¯¬zƒ-JU]]ưêƠ'y™eÙïYöt’Ï2‘Óï‰ê?.DŸ“[ö₫îî₫Óư·ß?~ù<©Ùóé÷u>xüvƒÈ­Ê|đöw*ߪ|£̣5ÙY¥̣’́{•-ÉNe#ŕU²C/(^Mz¥₫Ñß·÷àŸT–+¸X2_Ưß’ßüđpWíå˜èzô:x2|ÊÏxíăŒàw ăÏé²XÑ¿#ø£ÇcyÀŸê ~ 7ă+É¿ óƯ_₫iï.³CT"?¼[’ú‚®÷'⡈wéïŸơ/ôœ́•·̀3ëŒï@ç‘ü¸Îxç-ù·̃ß́Üïœ'ï ® á6¾Đk8áOsu6§đG_­điqPßµ₫®É¾_ñCØÛá8Ưđ÷Ïü5C¿S~ưœ?Ä)M_¥ç…êË₫{0ù/]‰¾¹’÷µÊ`ï?ñ ~à z§~•êDZÔ|–ŸÄ‡?ï+Ú÷ß‚yD‹#xÀ?æ2黕ñ|àƠç—G®₫9å×nàZö²Üo‰¥/Q_÷ƒ̃ÿẸ́Dןˆ#ñÓÔ_́Á$Îÿ§¨ç{‹/÷µnÇÜø¼ơKCù5ư†:€îq:Ê#~(ßÅÏă†ÜS\̃7˜£ü?™“̃æCÎolĐgá?K»úz êçûûxÙ;ÈKú?X~®N:ç§kơKêwĐø•ñ/q£í#̀ æưäù´:ÂQx^:ó“|yÿ$ÂCû2¡¿{ëWßgµíô­ÄĂÜơjO†s±seNf^JjQ1€Ä x ú̉PZ-@" ÓG¬½„̀!D“ëotÿQêorijÅ#‘ê›» Å!X÷W4>!ó‰ \ù‚X‘?HÍ÷Ô¦)ͯäæ{\î Ö½¤ê£v~¡Uz Ơ?„êj¥+JĂƒÖé=ÜĐËrưG(~ˆMÿ¸Êj‡ƒwJ‡ä¦#JăW‡zRĂ…ÚíZ•/"$ª‡¹ƒÔtMkĐ«₫¨ö¥₫¡^ø©F‹·xœ…UímQ|ù ¡”àRÂư àø”=Ûa)†đùă* —®Jp )3of¤³á¤ÓhßçÎî́¾ç)¥ûg)=îñI*x̉ÿ`ÿ:)ö₫ï—¥ëÛæf¾\mVï?ơfzÚÿÍ~bÿƯVq÷;qücÁßß æŸÛØùkÁ‡/+œ—¾ÅuƠ¬`÷çÓó—ÛWX?Å:`u÷·wUäcÙă7ç»ỵ̈›ă°™oéÂöµçqư™é…ç2OÄD¤œ¿Œó­ñØ™̣Ëî£ßÇ̣ăº¥n<ï̀7mêU~Z~yüÜÄờC‚?̣ÏKØΗ÷0̃ĐG‹|«,̃í2ÓY ø£?Ô›ë•:f¼‹3Ç™/̣â=#́îëêˆä+Ư°Œ£^OÊ#uîuJÛöøsy ̣º‰v—#<̣Êøa_7‹<½nXçêƒÔë›ơrUđôH$ï̃]“x®xÔ‡÷{üÔÇ'Ñ–²ùgºMˆ“÷¯wéÊt¡¾‚ûª‰û•OøÏ|âc:̣₫¢>µ8̀Wq´¾&ä>êÜëûY?à¥₫„ù(¿ëèyê}³ơœg^¥+¯Ị̈KƯWÓ8®₫´ˆë2æó́»6Ûâá₫z=̉ÿS‹‹¿ ̀+Çïù^ßÙ½Vê¿oă9[êœơ05´ü1ÛUDë>×ĂÄÖÍ£-[^XoŒ»̃%̣[F?½/«?-"¯wúËzöwOưqÙ±/üP<¨+Ö9ï»°{9n}‹ñÔ#ûêUôGï½C̀ïhù1ªö «§4û7â`yU=ư‡Ỵ̈́|êø…ù̃©£ùñO}p¨³?»YµƒÅxœu–[nAE; 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ŸœÎ×uœưZe÷ëÓIùêà qïé?ï{̀óctͨ³Å¾fŸ¸‡—èë„üÚñÈḶï6¯bïồĐ[G^àKÎ{ío;ÜOçø£ùWª³ ï?ø¥ơû~&Ùúß‚ÿoø7ÊwH–·„¹çqÿnËWbIyâû¢̀ó4»¾§ï-đ~6ÿüukô«/̃Kú–ô7̃ĂÈ7̣è5ÿM}Ÿ}Oü9~ẹ,˳ß~‹x à³®·âï†yeƯ‡z₫Ç<¿¿#¬÷ë̃â®ÈS¥?Ăn:ô£™~ç]ü^…¿Ă?a£:)sŒ÷¸—]ŒßÁø>Ă»‚ß¿üơ'9‘ï·w$ß®Í?oÀ»Z_ÖñNĂIư®¼œŸI\©₫§Øø½¦ç±?wànqkúç #Ρ NÚßvơ÷ơñ€́>|—'̣ëÇ}ʪsBưf|‡Ä÷8OK˜¹₫üÁ̃dï²g3tT̉÷³Ô|Wáf|Ó9¤Ï1/₫WÔ‘₫%¼ÏÓ¿KbĂ°Œî-ưºÊïªúçăûQMqmôŸƠ·cßÔ¯–7¾×‹vüîtÉ»6‘o7À—Ç–ÈJŸ7́aün[àÿ+û¼6Ä÷źÎ×Ơïp>LO'lÀg\|›ï¡#æĐÍßKqNE;îÛQuâ{ă¢|ñîeb7³ßÉäóªß…æ<uÀ¬¾Ç}ÛĐ¯§́É yFaüÚĂ₫^Zèn•w^¿èËĐ±È¿Ÿ×`=ưp.ỤÄßAXƒÏơo²Ïá÷`)̃SơîªÓóÿû́?M‹,úöxœEÍJC1…OAÅ>ƒË r«îê®T v£¸icúc 7)··…¾M¡è—”!93gÎü$×’=é¼äœqu^âèŸ ^q¬i¿ƯjêCḉ¢èg$Ÿµ“Ñnđ*n#¯9ø¢‰ÅÜ8åúzÔ½4Ôm?àkp‚̉êGÚñ+·¡̃'fó³QЦ[`?©é°4ÀbMî³G_– -~7ǨÑZ_iƒ}™›÷Ñ+næK—¶̀Œó¯‰C½ĂeÇü₫÷4;`ë?mM>ëTÚóÿKcâ†ưwäâ¬ÜÅá{0¾áë¶BËstatistics-1.4.3/inst/caseread.m0000644000000000000000000000352114153320774015010 0ustar0000000000000000## Copyright (C) 2008 Bill Denney ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{names} =} caseread (@var{filename}) ## Read case names from an ascii file. ## ## Essentially, this reads all lines from a file as text and returns ## them in a string matrix. ## @seealso{casewrite, tblread, tblwrite, csv2cell, cell2csv, fopen} ## @end deftypefn ## Author: Bill Denney ## Description: Read strings from a file function names = caseread (f="") ## Check arguments if nargin != 1 print_usage (); endif if isempty (f) ## FIXME: open a file dialog box in this case when a file dialog box ## becomes available error ("caseread: filename must be given") endif [fid msg] = fopen (f, "rt"); if fid < 0 || (! isempty (msg)) error ("caseread: cannot open %s: %s", f, msg); endif names = {}; t = fgetl (fid); while ischar (t) names{end+1} = t; t = fgetl (fid); endwhile if (fclose (fid) < 0) error ("caseread: error closing f") endif names = strvcat (names); endfunction ## Tests %!shared n, casereadfile %! n = ["a ";"bcd";"ef "]; %! casereadfile = file_in_loadpath("test/caseread.dat"); %!assert (caseread (casereadfile), n); statistics-1.4.3/inst/casewrite.m0000644000000000000000000000420114153320774015223 0ustar0000000000000000## Copyright (C) 2008 Bill Denney ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} casewrite (@var{strmat}, @var{filename}) ## Write case names to an ascii file. ## ## Essentially, this writes all lines from @var{strmat} to ## @var{filename} (after deblanking them). ## @seealso{caseread, tblread, tblwrite, csv2cell, cell2csv, fopen} ## @end deftypefn ## Author: Bill Denney ## Description: Write strings from a file function names = casewrite (s="", f="") ## Check arguments if nargin != 2 print_usage (); endif if isempty (f) ## FIXME: open a file dialog box in this case when a file dialog box ## becomes available error ("casewrite: filename must be given") endif if isempty (s) error ("casewrite: strmat must be given") elseif ! ischar (s) error ("casewrite: strmat must be a character matrix") elseif ndims (s) != 2 error ("casewrite: strmat must be two dimensional") endif [fid msg] = fopen (f, "wt"); if fid < 0 || (! isempty (msg)) error ("casewrite: cannot open %s for writing: %s", f, msg); endif for i = 1:rows (s) status = fputs (fid, sprintf ("%s\n", deblank (s(i,:)))); endfor if (fclose (fid) < 0) error ("casewrite: error closing f") endif endfunction %!test %! fname = [tempname() ".dat"]; %! unwind_protect %! s = ["a ";"bcd";"ef "]; %! casewrite (s, fname) %! names = caseread (fname); %! unwind_protect_cleanup %! unlink (fname); %! end_unwind_protect %! assert(names, s); statistics-1.4.3/inst/cdf.m0000644000000000000000000001012414153320774013772 0ustar0000000000000000## Copyright (C) 2013 Pantxo Diribarne ## ## This program is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} cdf (@var{name}, @var{X}, @dots{}) ## Return cumulative density function of @var{name} function for value ## @var{x}. ## This is a wrapper around various @var{name}cdf and @var{name}_cdf ## functions. See the individual functions help to learn the signification of ## the arguments after @var{x}. Supported functions and corresponding number of ## additional arguments are: ## ## @multitable @columnfractions 0.02 0.3 0.45 0.2 ## @headitem @tab function @tab alternative @tab args ## @item @tab "beta" @tab "beta" @tab 2 ## @item @tab "bino" @tab "binomial" @tab 2 ## @item @tab "cauchy" @tab @tab 2 ## @item @tab "chi2" @tab "chisquare" @tab 1 ## @item @tab "discrete" @tab @tab 2 ## @item @tab "exp" @tab "exponential" @tab 1 ## @item @tab "f" @tab @tab 2 ## @item @tab "gam" @tab "gamma" @tab 2 ## @item @tab "geo" @tab "geometric" @tab 1 ## @item @tab "gev" @tab "generalized extreme value" @tab 3 ## @item @tab "hyge" @tab "hypergeometric" @tab 3 ## @item @tab "kolmogorov_smirnov" @tab @tab 1 ## @item @tab "laplace" @tab @tab 0 ## @item @tab "logistic" @tab @tab 0 ## @item @tab "logn" @tab "lognormal" @tab 2 ## @item @tab "norm" @tab "normal" @tab 2 ## @item @tab "poiss" @tab "poisson" @tab 1 ## @item @tab "rayl" @tab "rayleigh" @tab 1 ## @item @tab "t" @tab @tab 1 ## @item @tab "unif" @tab "uniform" @tab 2 ## @item @tab "wbl" @tab "weibull" @tab 2 ## @end multitable ## ## @seealso{betacdf, binocdf, cauchy_cdf, chi2cdf, discrete_cdf, ## expcdf, fcdf, gamcdf, geocdf, gevcdf, hygecdf, ## kolmogorov_smirnov_cdf, laplace_cdf, logistic_cdf, logncdf, ## normcdf, poisscdf, raylcdf, tcdf, unifcdf, wblcdf} ## @end deftypefn function [retval] = cdf (varargin) ## implemented functions persistent allcdf = {{"beta", "beta"}, @betacdf, 2, ... {"bino", "binomial"}, @binocdf, 2, ... {"cauchy"}, @cauchy_cdf, 2, ... {"chi2", "chisquare"}, @chi2cdf, 1, ... {"discrete"}, @discrete_cdf, 2, ... {"exp", "exponential"}, @expcdf, 1, ... {"f"}, @fcdf, 2, ... {"gam", "gamma"}, @gamcdf, 2, ... {"geo", "geometric"}, @geocdf, 1, ... {"gev", "generalized extreme value"}, @gevcdf, 3, ... {"hyge", "hypergeometric"}, @hygecdf, 3, ... {"kolmogorov_smirnov"}, @kolmogorov_smirnov_cdf, 1, ... {"laplace"}, @laplace_cdf, 0, ... {"logistic"}, @logistic_cdf, 0, ... # ML has 2 args here {"logn", "lognormal"}, @logncdf, 2, ... {"norm", "normal"}, @normcdf, 2, ... {"poiss", "poisson"}, @poisscdf, 1, ... {"rayl", "rayleigh"}, @raylcdf, 1, ... {"t"}, @tcdf, 1, ... {"unif", "uniform"}, @unifcdf, 2, ... {"wbl", "weibull"}, @wblcdf, 2}; if (numel (varargin) < 2 || ! ischar (varargin{1})) print_usage (); endif name = varargin{1}; x = varargin{2}; varargin(1:2) = []; nargs = numel (varargin); cdfnames = allcdf(1:3:end); cdfhdl = allcdf(2:3:end); cdfargs = allcdf(3:3:end); idx = cellfun (@(x) any (strcmpi (name, x)), cdfnames); if (any (idx)) if (nargs == cdfargs{idx}) retval = feval (cdfhdl{idx}, x, varargin{:}); else error ("cdf: %s requires %d arguments", name, cdfargs{idx}) endif else error ("cdf: %s not implemented", name); endif endfunction %!test %! assert(cdf ('norm', 1, 0, 1), normcdf (1, 0, 1))statistics-1.4.3/inst/chi2stat.m0000644000000000000000000000445014153320774014764 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} chi2stat (@var{n}) ## Compute mean and variance of the chi-square distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{n} is the parameter of the chi-square distribution. The elements ## of @var{n} must be positive ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the chi-square distribution ## ## @item ## @var{v} is the variance of the chi-square distribution ## @end itemize ## ## @subheading Example ## ## @example ## @group ## n = 1:6; ## [m, v] = chi2stat (n) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the chi-square distribution function [m, v] = chi2stat (n) # Check arguments if (nargin != 1) print_usage (); endif if (! isempty (n) && ! ismatrix (n)) error ("chi2stat: n must be a numeric matrix"); endif # Calculate moments m = n; v = 2 .* n; # Continue argument check k = find (! (n > 0) | ! (n < Inf)); if (any (k)) m(k) = NaN; v(k) = NaN; endif endfunction %!test %! n = 1:6; %! [m, v] = chi2stat (n); %! assert (m, n); %! assert (v, [2, 4, 6, 8, 10, 12], 0.001); statistics-1.4.3/inst/cl_multinom.m0000644000000000000000000001201114153320774015555 0ustar0000000000000000## Copyright (C) 2009 Levente Torok ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## ## @deftypefn {Function File} {@var{CL} =} cl_multinom (@var{x}, @var{N}, @var{b}, @var{calculation_type} ) - Confidence level of multinomial portions ## Returns confidence level of multinomial parameters estimated @math{ p = x / sum(x) } with predefined confidence interval @var{b}. ## Finite population is also considered. ## ## This function calculates the level of confidence at which the samples represent the true distribution ## given that there is a predefined tolerance (confidence interval). ## This is the upside down case of the typical excercises at which we want to get the confidence interval ## given the confidence level (and the estimated parameters of the underlying distribution). ## But once we accept (lets say at elections) that we have a standard predefined ## maximal acceptable error rate (e.g. @var{b}=0.02 ) in the estimation and we just want to know that how sure we ## can be that the measured proportions are the same as in the ## entire population (ie. the expected value and mean of the samples are roghly the same) we need to use this function. ## ## @subheading Arguments ## @itemize @bullet ## @item @var{x} : int vector : sample frequencies bins ## @item @var{N} : int : Population size that was sampled by x. If N 4) print_usage; elseif (!ischar (calculation_type)) error ("Argument calculation_type must be a string"); endif k = rows(x); nn = sum(x); p = x / nn; if (isscalar( b )) if (b==0) b=0.02; endif b = ones( rows(x), 1 ) * b; if (b<0) b=1 ./ max( x, 1 ); endif endif bb = b .* b; if (N==nn) CL = 1; return; endif if (N ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{T} =} cluster (@var{Z},'Cutoff', @var{C}) ## @deftypefnx {Function File} @ ## {@var{T} =} cluster (@var{Z}, 'Cutoff', @var{C}, 'Depth', @var{D}) ## @deftypefnx {Function File} @ ## {@var{T} =} cluster (@var{Z}, 'Cutoff', @var{C}, 'Criterion', @var{criterion}) ## @deftypefnx {Function File} @ ## {@var{T} =} cluster (@var{Z}, 'MaxClust', @var{N}) ## ## Define clusters from an agglomerative hierarchical cluster tree. ## ## Given a hierarchical cluster tree @var{Z} generated by the @code{linkage} ## function, @code{cluster} defines clusters, using a threshold value @var{C} to ## identify new clusters ('Cutoff') or according to a maximum number of desired ## clusters @var{N} ('MaxClust'). ## ## @var{criterion} is used to choose the criterion for defining clusters, which ## can be either "inconsistent" (default) or "distance". When using ## "inconsistent", @code{cluster} compares the threshold value @var{C} to the ## inconsistency coefficient of each link; when using "distance", @code{cluster} ## compares the threshold value @var{C} to the height of each link. ## @var{D} is the depth used to evaluate the inconsistency coefficient, its ## default value is 2. ## ## @code{cluster} uses "distance" as a criterion for defining new clusters when ## it is used the 'MaxClust' method. ## ## @end deftypefn ## ## @seealso{clusterdata,dendrogram,inconsistent,kmeans,linkage,pdist} ## Author: Stefano Guidoni function T = cluster (Z, opt, varargin) switch (lower (opt)) ## check the input case "cutoff" if (nargin < 3) print_usage (); else C = varargin{1}; D = 2; criterion = "inconsistent"; if (nargin > 3) pair_index = 2; while (pair_index < (nargin - 2)) switch (lower (varargin{pair_index})) case "depth" D = varargin{pair_index + 1}; case "criterion" criterion = varargin{pair_index + 1}; otherwise error ("cluster: unknown property %s", varargin{pair_index}); endswitch pair_index += 2; endwhile endif endif if ((! (isscalar (C) || isvector (C))) || (C < 0)) error ... (["cluster: C must be a positive scalar or a vector of positive"... "numbers"]); endif case "maxclust" if (nargin != 3) print_usage (); else N = varargin{1}; C = []; endif if ((! (isscalar (N) || isvector (N))) || (N < 0)) error ... (["cluster: N must be a positive number or a vector of positive"... "numbers"]); endif otherwise error ("cluster: unknown option %s", opt); endswitch if ((columns (Z) != 3) || (! isnumeric (Z)) ... (! (max (Z(end, 1:2)) == rows (Z) * 2))) error ("cluster: Z must be a matrix generated by the linkage function"); endif ## number of observations n = rows (Z) + 1; ## vector of values used by the threshold check vThresholds = []; ## starting number of clusters nClusters = 1; ## the return value is the matrix T, constituted by one or more vector vT T = []; vT = zeros (1, n); ## main logic ## a few checks and computations before launching the recursive function switch (lower (opt)) case "cutoff" switch (lower (criterion)) case "inconsistent" vThresholds = inconsistent (Z, D)(:, 4); case "distance" vThresholds = Z(:, 3); otherwise error ("cluster: unkown criterion %s", criterion); endswitch case "maxclust" ## the MaxClust case can be regarded as a Cutoff case with distance ## criterion, where the threshold is set to the height of the highest node ## that allows us to have N different clusters vThresholds = Z(:, 3); ## let's build a vector with the apt threshold values for k = 1:length (N); if (N(k) > n) C(end+1) = 0; elseif (N(k) < 2) C(end+1) = Z(end, 3) + 1; else C(end+1) = Z((end + 2 - N(k)), 3); endif endfor endswitch for c_index = 1:length (C) cluster_cutoff_recursive (rows (Z), nClusters, c_index); T = [T; vT]; endfor T = T'; # return value ## recursive function ## for each link check if the cutoff criteria (a threshold value) are met, ## then call recursively this function for every node below that; ## when we find a leaf, we add the index of its cluster to the return value function cluster_cutoff_recursive (index, cluster_number, c_index) vClusterNumber = [cluster_number, cluster_number]; ## check the threshold value if (vThresholds(index) >= C(c_index)) ## create a new cluster nClusters++; vClusterNumber(2) = nClusters; endif; ## go on, down the tree for j = 1:2 if (Z(index,j) > n) new_index = Z(index,j) - n; cluster_cutoff_recursive (new_index, vClusterNumber(j), c_index); else ## if the next node is a leaf, add the index of its cluster to the ## result at the correct position, i.e. the leaf number; ## if leaf 14 belongs to cluster 3: ## vT(14) = 3; vT(Z(index,j)) = vClusterNumber(j); endif endfor endfunction endfunction ## Test input validation %!error cluster () %!error cluster ([1 1], "Cutoff", 1) %!error cluster ([1 2 1], "Bogus", 1) %!error cluster ([1 2 1], "Cutoff", -1) %!error cluster ([1 2 1], "Cutoff", 1, "Bogus", 1) ## Test output %!test % X = [(randn (10, 2) * 0.25) + 1; (randn (10, 2) * 0.25) - 1]; % Z = linkage(X, "ward"); % T = [ones (10, 1); 2 * ones (10, 1)]; % assert (cluster (Z, "MaxClust", 2), T); statistics-1.4.3/inst/clusterdata.m0000644000000000000000000001011214153320774015546 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{T} =} clusterdata (@var{X}, @var{cutoff}) ## @deftypefnx {Function File} @ ## {@var{T} =} clusterdata (@var{X}, @var{Name}, @var{Value}) ## ## Wrapper function for @code{linkage} and @code{cluster}. ## ## If @var{cutoff} is used, then @code{clusterdata} calls @code{linkage} and ## @code{cluster} with default value, using @var{cutoff} as a threshold value ## for @code{cluster}. If @var{cutoff} is an integer and greater or equal to 2, ## then @var{cutoff} is interpreted as the maximum number of cluster desired ## and the 'MaxClust' option is used for @code{cluster}. ## ## If @var{cutoff} is not used, then @code{clusterdata} expects a list of pair ## arguments. Then you must specify either the 'Cutoff' or 'MaxClust' option ## for @code{cluster}. The method and metric used by @code{linkage}, are ## defined through the 'linkage' and 'distance' arguments. ## ## @end deftypefn ## ## @seealso{cluster,dendrogram,inconsistent,kmeans,linkage,pdist} ## Author: Stefano Guidoni function T = clusterdata (X, varargin) if (nargin < 2) print_usage (); else linkage_criterion = "single"; distance_method = "euclidean"; savememory = "off"; clustering_method = []; criterion = "inconsistent"; D = 2; if (isnumeric (varargin{1})) # clusterdata (X, cutoff) if (isinteger (varargin{1}) && (varargin{1} >= 2)) clustering_method = "MaxClust"; else clustering_method = "Cutoff"; endif C = varargin{1}; else # clusterdata (Name, Value) pair_index = 1; while (pair_index < (nargin - 1)) switch (lower (varargin{pair_index})) case "criterion" criterion = varargin{pair_index + 1}; case "cutoff" clustering_method = "Cutoff"; C = varargin{pair_index + 1}; case "depth" D = varargin{pair_index + 1}; case "distance" distance_method = varargin{pair_index + 1}; case "linkage" linkage_criterion = varargin{pair_index + 1}; case "maxclust" clustering_method = "MaxClust"; C = varargin{pair_index + 1}; case "savememory" savememory = varargin{pair_index + 1}; otherwise error ("clusterdata: unknown property %s", varargin{pair_index}); endswitch pair_index += 2; endwhile endif endif if (isempty (clustering_method)) error ... (["clusterdata: you must specify either 'MaxClust' or 'Cutoff' when" ... "using name-value arguments"]); endif ## main body Z = linkage (X, linkage_criterion, distance_method, "savememory"); if (strcmp (lower (clustering_method), "cutoff")) T = cluster (Z, clustering_method, C, "Criterion", criterion, "Depth", D); else T = cluster (Z, clustering_method, C); endif endfunction ## Test input validation %!error clusterdata () %!error clusterdata (1) %!error clusterdata ([1 1], "Bogus", 1) %!error clusterdata ([1 1], "Depth", 1) ## Demonstration %!demo %! X = [(randn (10, 2) * 0.25) + 1; (randn (20, 2) * 0.5) - 1]; %! wnl = warning ("off", "Octave:linkage_savemem", "local"); %! T = clusterdata (X, "linkage", "ward", "MaxClust", 2); %! scatter (X(:,1), X(:,2), 36, T, "filled"); statistics-1.4.3/inst/cmdscale.m0000644000000000000000000001351014153320774015013 0ustar0000000000000000## Copyright (C) 2014 JD Walsh ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{Y} = cmdscale (@var{D}) ## @deftypefnx{Function File} [@var{Y}, @var{e} ] = cmdscale (@var{D}) ## Classical multidimensional scaling of a matrix. ## ## Takes an @var{n} by @var{n} distance (or difference, similarity, or ## dissimilarity) matrix @var{D}. Returns @var{Y}, a matrix of @var{n} points ## with coordinates in @var{p} dimensional space which approximate those ## distances (or differences, similarities, or dissimilarities). Also returns ## the eigenvalues @var{e} of ## @code{@var{B} = -1/2 * @var{J} * (@var{D}.^2) * @var{J}}, where ## @code{J = eye(@var{n}) - ones(@var{n},@var{n})/@var{n}}. @var{p}, the number ## of columns of @var{Y}, is equal to the number of positive real eigenvalues of ## @var{B}. ## ## @var{D} can be a full or sparse matrix or a vector of length ## @code{@var{n}*(@var{n}-1)/2} containing the upper triangular elements (like ## the output of the @code{pdist} function). It must be symmetric with ## non-negative entries whose values are further restricted by the type of ## matrix being represented: ## ## * If @var{D} is either a distance, dissimilarity, or difference matrix, then ## it must have zero entries along the main diagonal. In this case the points ## @var{Y} equal or approximate the distances given by @var{D}. ## ## * If @var{D} is a similarity matrix, the elements must all be less than or ## equal to one, with ones along the the main diagonal. In this case the points ## @var{Y} equal or approximate the distances given by ## @code{@var{D} = sqrt(ones(@var{n},@var{n})-@var{D})}. ## ## @var{D} is a Euclidean matrix if and only if @var{B} is positive ## semi-definite. When this is the case, then @var{Y} is an exact representation ## of the distances given in @var{D}. If @var{D} is non-Euclidean, @var{Y} only ## approximates the distance given in @var{D}. The approximation used by ## @code{cmdscale} minimizes the statistical loss function known as ## @var{strain}. ## ## The returned @var{Y} is an @var{n} by @var{p} matrix showing possible ## coordinates of the points in @var{p} dimensional space ## (@code{@var{p} < @var{n}}). The columns are correspond to the positive ## eigenvalues of @var{B} in descending order. A translation, rotation, or ## reflection of the coordinates given by @var{Y} will satisfy the same distance ## matrix up to the limits of machine precision. ## ## For any @code{@var{k} <= @var{p}}, if the largest @var{k} positive ## eigenvalues of @var{B} are significantly greater in absolute magnitude than ## its other eigenvalues, the first @var{k} columns of @var{Y} provide a ## @var{k}-dimensional reduction of @var{Y} which approximates the distances ## given by @var{D}. The optional return @var{e} can be used to consider various ## values of @var{k}, or to evaluate the accuracy of specific dimension ## reductions (e.g., @code{@var{k} = 2}). ## ## Reference: Ingwer Borg and Patrick J.F. Groenen (2005), Modern ## Multidimensional Scaling, Second Edition, Springer, ISBN: 978-0-387-25150-9 ## (Print) 978-0-387-28981-6 (Online) ## ## @seealso{pdist} ## @end deftypefn ## Author: JD Walsh ## Created: 2014-10-31 ## Description: Classical multidimensional scaling ## Keywords: multidimensional-scaling mds distance clustering ## TO DO: include missing functions `mdscale' and `procrustes' in @seealso function [Y, e] = cmdscale (D) % Check for matrix input if ((nargin ~= 1) || ... (~any(strcmp ({'matrix' 'scalar' 'range'}, typeinfo(D))))) usage ('cmdscale: input must be vector or matrix; see help'); endif % If vector, convert to matrix; otherwise, check for square symmetric input if (isvector (D)) D = squareform (D); elseif ((~issquare (D)) || (norm (D - D', 1) > 0)) usage ('cmdscale: matrix input must be square symmetric; see help'); endif n = size (D,1); % Check for valid format (see help above); If similarity matrix, convert if (any (any (D < 0))) usage ('cmdscale: entries must be nonnegative; see help'); elseif (trace (D) ~= 0) if ((~all (diag (D) == 1)) || (~all (D <= 1))) usage ('cmdscale: input must be distance vector or matrix; see help'); endif D = sqrt (ones (n,n) - D); endif % Build centering matrix, perform double centering, extract eigenpairs J = eye (n) - ones (n,n) / n; B = -1 / 2 * J * (D .^ 2) * J; [Q, e] = eig (B); e = diag (e); etmp = e; e = sort(e, 'descend'); % Remove complex eigenpairs (only possible due to machine approximation) if (iscomplex (etmp)) for i = 1 : size (etmp,1) cmp(i) = (isreal (etmp(i))); endfor etmp = etmp(cmp); Q = Q(:,cmp); endif % Order eigenpairs [etmp, ord] = sort (etmp, 'descend'); Q = Q(:,ord); % Remove negative eigenpairs cmp = (etmp > 0); etmp = etmp(cmp); Q = Q(:,cmp); % Test for n-dimensional results if (size(etmp,1) == n) etmp = etmp(1:n-1); Q = Q(:, 1:n-1); endif % Build output matrix Y Y = Q * diag (sqrt (etmp)); endfunction %!shared m, n, X, D %! m = randi(100) + 1; n = randi(100) + 1; X = rand(m, n); D = pdist(X); %!assert(norm(pdist(cmdscale(D))), norm(D), sqrt(eps)) %!assert(norm(pdist(cmdscale(squareform(D)))), norm(D), sqrt(eps)) statistics-1.4.3/inst/combnk.m0000644000000000000000000000466714153320774014526 0ustar0000000000000000## Copyright (C) 2010 Soren Hauberg ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{c} =} combnk (@var{data}, @var{k}) ## Return all combinations of @var{k} elements in @var{data}. ## @end deftypefn function retval = combnk (data, k) ## Check input if (nargin != 2) print_usage; elseif (! isvector (data)) error ("combnk: first input argument must be a vector"); elseif (!isreal (k) || k != round (k) || k < 0) error ("combnk: second input argument must be a non-negative integer"); endif ## Simple checks n = numel (data); if (k == 0 || k > n) retval = resize (data, 0, k); elseif (k == n) retval = data (:).'; else retval = __combnk__ (data, k); endif ## For some odd reason Matlab seems to treat strings differently compared to other data-types... if (ischar (data)) retval = flipud (retval); endif endfunction function retval = __combnk__ (data, k) ## Recursion stopping criteria if (k == 1) retval = data (:); else ## Process data n = numel (data); if iscell (data) retval = {}; else retval = []; endif for j = 1:n C = __combnk__ (data ((j+1):end), k-1); C = cat (2, repmat (data (j), rows (C), 1), C); if (!isempty (C)) if (isempty (retval)) retval = C; else retval = [retval; C]; endif endif endfor endif endfunction %!demo %! c = combnk (1:5, 2); %! disp ("All pairs of integers between 1 and 5:"); %! disp (c); %!test %! c = combnk (1:3, 2); %! assert (c, [1, 2; 1, 3; 2, 3]); %!test %! c = combnk (1:3, 6); %! assert (isempty (c)); %!test %! c = combnk ({1, 2, 3}, 2); %! assert (c, {1, 2; 1, 3; 2, 3}); %!test %! c = combnk ("hello", 2); %! assert (c, ["lo"; "lo"; "ll"; "eo"; "el"; "el"; "ho"; "hl"; "hl"; "he"]); statistics-1.4.3/inst/confusionchart.m0000644000000000000000000002427414153320774016276 0ustar0000000000000000## Copyright (C) 2020-2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {} {} confusionchart (@var{trueLabels}, @var{predictedLabels}) ## @deftypefnx {} {} confusionchart (@var{m}) ## @deftypefnx {} {} confusionchart (@var{m}, @var{classLabels}) ## @deftypefnx {} {} confusionchart (@var{parent}, @dots{}) ## @deftypefnx {} {} confusionchart (@dots{}, @var{prop}, @var{val}, @dots{}) ## @deftypefnx {} {@var{cm} =} confusionchart (@dots{}) ## ## Display a chart of a confusion matrix. ## ## The two vectors of values @var{trueLabels} and @var{predictedLabels}, which ## are used to compute the confusion matrix, must be defined with the same ## format as the inputs of @code{confusionmat}. ## Otherwise a confusion matrix @var{m} as computed by @code{confusionmat} can ## be given. ## ## @var{classLabels} is an array of labels, i.e. the list of the class names. ## ## If the first argument is a handle to a @code{figure} or to a @code{uipanel}, ## then the confusion matrix chart is displayed inside that object. ## ## Optional property/value pairs are passed directly to the underlying objects, ## e.g. @qcode{"xlabel"}, @qcode{"ylabel"}, @qcode{"title"}, @qcode{"fontname"}, ## @qcode{"fontsize"} etc. ## ## The optional return value @var{cm} is a @code{ConfusionMatrixChart} object. ## Specific properties of a @code{ConfusionMatrixChart} object are: ## @itemize @bullet ## @item @qcode{"DiagonalColor"} ## The color of the patches on the diagonal, default is [0.0, 0.4471, 0.7412]. ## ## @item @qcode{"OffDiagonalColor"} ## The color of the patches off the diagonal, default is [0.851, 0.3255, 0.098]. ## ## @item @qcode{"GridVisible"} ## Available values: @qcode{on} (default), @qcode{off}. ## ## @item @qcode{"Normalization"} ## Available values: @qcode{absolute} (default), @qcode{column-normalized}, ## @qcode{row-normalized}, @qcode{total-normalized}. ## ## @item @qcode{"ColumnSummary"} ## Available values: @qcode{off} (default), @qcode{absolute}, ## @qcode{column-normalized},@qcode{total-normalized}. ## ## @item @qcode{"RowSummary"} ## Available values: @qcode{off} (default), @qcode{absolute}, ## @qcode{row-normalized}, @qcode{total-normalized}. ## @end itemize ## ## Run @code{demo confusionchart} to see some examples. ## ## @end deftypefn ## ## @seealso{confusionmat, sortClasses} ## Author: Stefano Guidoni function cm = confusionchart (varargin) ## check the input parameters if (nargin < 1) print_usage (); endif p_i = 1; if (ishghandle (varargin{p_i})) ## parameter is a parent figure handle_type = get (varargin{p_i}, "type"); if (strcmp (handle_type, "figure")) h = figure (varargin{p_i}); hax = axes ("parent", h); elseif (strcmp (handle_type, "uipanel")) h = varargin{p_i}; hax = axes ("parent", varargin{p_i}); else ## MATLAB compatibility: on MATLAB are also available Tab objects, ## TiledChartLayout objects, GridLayout objects error ("confusionchart: invalid handle to parent object"); endif p_i++; else h = figure (); hax = axes ("parent", h); endif if (ismatrix (varargin{p_i}) && rows (varargin{p_i}) == ... columns (varargin{p_i})) ## parameter is a confusion matrix conmat = varargin{p_i}; p_i++; if (p_i <= nargin && ((isvector (varargin{p_i}) && ... length (varargin{p_i}) == rows (conmat)) || ... (ischar ( varargin{p_i}) && rows (varargin{p_i}) == rows (conmat)) ... || iscellstr (varargin{p_i}))) ## parameter is an array of labels labarr = varargin{p_i}; if (isrow (labarr)) labarr = vec (labarr); endif p_i++; else labarr = [1 : (rows (conmat))]'; endif elseif (isvector (varargin{p_i})) ## parameter must be a group for confusionmat [conmat, labarr] = confusionmat (varargin{p_i}, varargin{p_i + 1}); p_i = p_i + 2; else close (h); error ("confusionchart: invalid argument"); endif ## remaining parameters are stored i = p_i; args = {}; while (i <= nargin) args{end + 1} = varargin{i++}; endwhile ## prepare the labels if (!iscellstr (labarr)) if (!ischar (labarr)) labarr = num2str (labarr); endif labarr = cellstr (labarr); endif ## MATLAB compatibility: labels are sorted [labarr, I] = sort (labarr); conmat = conmat(I, :); conmat = conmat(:, I); cm = ConfusionMatrixChart (hax, conmat, labarr, args); endfunction ## Test input validation ## Get current figure visibility so it can be restored after tests %!shared visibility_setting %! visibility_setting = get (0, "DefaultFigureVisible"); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ()", "Invalid call"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 1; 2 2; 3 3])", "invalid argument"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'xxx', 1)", "invalid property"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'XLabel', 1)", "XLabel .* string"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'YLabel', [1 0])", ".* YLabel .* string"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'Title', .5)", ".* Title .* string"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'FontName', [])", ".* FontName .* string"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'FontSize', 'b')", ".* FontSize .* numeric"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'DiagonalColor', 'h')", ".* DiagonalColor .* color"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'OffDiagonalColor', [])", ".* OffDiagonalColor .* color"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'Normalization', '')", ".* invalid .* Normalization"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'ColumnSummary', [])", ".* invalid .* ColumnSummary"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'RowSummary', 1)", ".* invalid .* RowSummary"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'GridVisible', .1)", ".* invalid .* GridVisible"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'HandleVisibility', .1)", ".* invalid .* HandleVisibility"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'OuterPosition', .1)", ".* invalid .* OuterPosition"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'Position', .1)", ".* invalid .* Position"); %! set (0, "DefaultFigureVisible", visibility_setting); %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ("confusionchart ([1 2], [0 1], 'Units', .1)", ".* invalid .* Units"); %! set (0, "DefaultFigureVisible", visibility_setting); ## Demonstration using the confusion matrix example from ## R.Bonnin, "Machine Learning for Developers", pp. 55-56 %!demo "Setting the chart properties" %! Yt = [8 5 6 8 5 3 1 6 4 2 5 3 1 4]'; %! Yp = [8 5 6 8 5 2 3 4 4 5 5 7 2 6]'; %! confusionchart (Yt, Yp, "Title", ... %! "Demonstration with summaries","Normalization",... %! "absolute","ColumnSummary", "column-normalized","RowSummary",... %! "row-normalized") ## example: confusion matrix and class labels %!demo "Cellstr as inputs" %! Yt = {'Positive', 'Positive', 'Positive', 'Negative', 'Negative' }; %! Yp = {'Positive', 'Positive', 'Negative', 'Negative', 'Negative' }; %! m = confusionmat ( Yt, Yp ); %! confusionchart ( m, { 'Positive', 'Negative' } ); ## example: editing the properties of an existing ConfusionMatrixChart object %!demo "Editing the object properties" %! Yt = {'Positive', 'Positive', 'Positive', 'Negative', 'Negative' }; %! Yp = {'Positive', 'Positive', 'Negative', 'Negative', 'Negative' }; %! cm = confusionchart ( Yt, Yp ); %! cm.Title = "This is an example with a green diagonal"; %! cm.DiagonalColor = [0.4660, 0.6740, 0.1880]; ## example: drawing the chart inside a uipanel %!demo "Confusion chart in a uipanel" %! h = uipanel (); %! Yt = {'Positive', 'Positive', 'Positive', 'Negative', 'Negative' }; %! Yp = {'Positive', 'Positive', 'Negative', 'Negative', 'Negative' }; %! cm = confusionchart ( h, Yt, Yp ); ## example: sortClasses %!demo "Sorting classes" %! Yt = [8 5 6 8 5 3 1 6 4 2 5 3 1 4]'; %! Yp = [8 5 6 8 5 2 3 4 4 5 5 7 2 6]'; %! cm = confusionchart (Yt, Yp, "Title", ... %! "Classes are sorted according to clusters"); %! sortClasses (cm, "cluster"); statistics-1.4.3/inst/confusionmat.m0000644000000000000000000001512114153320774015745 0ustar0000000000000000## Copyright (C) 2020 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @ ## {@var{C} =} confusionmat (@var{group}, @var{grouphat}) ## @deftypefnx {Function File} @ ## {@var{C} =} confusionmat (@var{group}, @var{grouphat}, 'Order', @var{grouporder}) ## @deftypefnx {Function File} @ ## {[@var{C}, @var{order}] =} confusionmat (@var{group}, @var{grouphat}) ## ## Compute a confusion matrix for classification problems ## ## @code{confusionmat} returns the confusion matrix @var{C} for the group of ## actual values @var{group} and the group of predicted values @var{grouphat}. ## The row indices of the confusion matrix represent actual values, while the ## column indices represent predicted values. The indices are the same for both ## actual and predicted values, so the confusion matrix is a square matrix. ## Each element of the matrix represents the number of matches between a given ## actual value (row index) and a given predicted value (column index), hence ## correct matches lie on the main diagonal of the matrix. ## The order of the rows and columns is returned in @var{order}. ## ## @var{group} and @var{grouphat} must have the same number of observations ## and the same data type. ## Valid data types are numeric vectors, logical vectors, character arrays, ## string arrays (not implemented yet), cell arrays of strings. ## ## The order of the rows and columns can be specified by setting the ## @var{grouporder} variable. The data type of @var{grouporder} must be the ## same of @var{group} and @var{grouphat}. ## ## @end deftypefn ## ## @seealso{crosstab} ## Author: Stefano Guidoni ## MATLAB compatibility: Octave misses string arrays, categorical vectors and ## undefined values. function [C, order] = confusionmat ( group, grouphat, opt = 'Order', grouporder ) ## check the input parameters if ( nargin < 2 ) || ( nargin > 4 ) print_usage(); endif y_true = group; y_pred = grouphat; if class( y_true ) != class( y_pred ) error( "confusionmat: group and grouphat must be of the same data type" ); endif if length( y_true ) != length( y_pred ) error( "confusionmat: group and grouphat must be of the same length" ); endif if ( nargin > 3 ) && strcmp( opt, 'Order' ) unique_tokens = grouporder; if class( y_true ) != class( unique_tokens ) error( "confusionmat: group and grouporder must be of the same data type" ); endif endif if isvector( y_true ) if isrow( y_true ) y_true = vec( y_true ); endif else error( "confusionmat: group must be a vector or array" ); endif if isvector( y_pred ) if isrow( y_pred ) y_pred = vec( y_pred ); endif else error( "confusionmat: grouphat must be a vector or array" ); endif if exist( "unique_tokens", "var" ) if isvector( unique_tokens ) if isrow( unique_tokens ) unique_tokens = vec( unique_tokens ); endif else error( "confusionmat: grouporder must be a vector or array" ); endif endif ## compute the confusion matrix if isa( y_true, "numeric" ) || isa( y_true, "logical" ) ## numeric or boolean vector ## MATLAB compatibility: ## remove NaN values from grouphat nan_indices = find( isnan( y_pred ) ); y_pred(nan_indices) = []; ## MATLAB compatibility: ## numeric and boolean values ## are sorted in ascending order if !exist( "unique_tokens", "var" ) unique_tokens = union ( y_true, y_pred ); endif y_true(nan_indices) = []; C_size = length ( unique_tokens ); C = zeros ( C_size ); for i = 1:length( y_true) row_index = find( unique_tokens == y_true(i) ); col_index = find( unique_tokens == y_pred(i) ); C(row_index, col_index)++; endfor elseif iscellstr( y_true ) ## string cells ## MATLAB compatibility: ## remove empty values from grouphat empty_indices = []; for i = 1:length( y_pred ) if isempty( y_pred{i} ) empty_indices = [empty_indices; i]; endif endfor y_pred(empty_indices) = []; ## MATLAB compatibility: ## string values are sorted according to their ## first appearance in group and grouphat if !exist( "unique_tokens", "var" ) all_tokens = vertcat ( y_true, y_pred ); unique_tokens = [all_tokens(1)]; for i = 2:length( all_tokens ) if !any( strcmp( all_tokens(i), unique_tokens ) ) unique_tokens = [unique_tokens; all_tokens(i)]; endif endfor endif y_true(empty_indices) = []; C_size = length ( unique_tokens ); C = zeros ( C_size ); for i = 1:length( y_true) row_index = find( strcmp( y_true{i}, unique_tokens ) ); col_index = find( strcmp( y_pred{i}, unique_tokens ) ); C(row_index, col_index)++; endfor elseif ischar( y_true ) ## character array ## MATLAB compatibility: ## character values are sorted according to their ## first appearance in group and grouphat if !exist( "unique_tokens", "var" ) all_tokens = vertcat ( y_true, y_pred ); unique_tokens = [all_tokens(1)]; for i = 2:length( all_tokens ) if !any( find( unique_tokens == all_tokens(i) ) ) unique_tokens = [unique_tokens; all_tokens(i)]; endif endfor endif C_size = length ( unique_tokens ); C = zeros ( C_size ); for i = 1:length( y_true) row_index = find( unique_tokens == y_true(i) ); col_index = find( unique_tokens == y_pred(i) ); C(row_index, col_index)++; endfor elseif isstring( y_true ) ## string array ## FIXME: not implemented yet error( "confusionmat: string array not implemented yet" ); else error( "confusionmat: invalid data type" ); endif order = unique_tokens; endfunction ## Test the confusion matrix example from ## R.Bonnin, "Machine Learning for Developers", pp. 55-56 %!test %! Yt = [8 5 6 8 5 3 1 6 4 2 5 3 1 4]'; %! Yp = [8 5 6 8 5 2 3 4 4 5 5 7 2 6]'; %! C = [0 1 1 0 0 0 0 0; 0 0 0 0 1 0 0 0; 0 1 0 0 0 0 1 0; 0 0 0 1 0 1 0 0; ... %! 0 0 0 0 3 0 0 0; 0 0 0 1 0 1 0 0; 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 2]; %! assert (confusionmat (Yt, Yp), C) statistics-1.4.3/inst/cophenet.m0000644000000000000000000001035714153320774015053 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{c}, @var{d}] =} cophenet (@var{Z}, @var{y}) ## ## Compute the cophenetic correlation coefficient. ## ## The cophenetic correlation coefficient @var{C} of a hierarchical cluster tree ## @var{Z} is the linear correlation coefficient between the cophenetic ## distances @var{d} and the euclidean distances @var{y}. ## @tex ## \def\frac#1#2{{\begingroup#1\endgroup\over#2}} ## $$ c = \frac {\sum _{i n) l_v = nonzeros (N(l_n - n, :)); # the list of leaves from the left branch else l_v = l_n; endif if (r_n > n) r_v = nonzeros (N(r_n - n, :)); # the list of leaves from the right branch else r_v = r_n; endif j_max = length (l_v); k_max = length (r_v); ## keep track of the leaves in each sub-branch, i.e. node; ## this does not matter for the last node, which includes all leaves if (i < m) N(i, 1 : (j_max + k_max)) = [l_v' r_v']; endif for j = 1 : j_max for k = 1: k_max ## d is in the same format as y if (l_v(j) < r_v(k)) index = (l_v(j) - 1) * m - sum (1 : (l_v(j) - 2)) + (r_v(k) - l_v(j)); else index = (r_v(k) - 1) * m - sum (1 : (r_v(k) - 2)) + (l_v(j) - r_v(k)); endif d(index) = Z(i, 3); endfor endfor endfor ## compute the cophenetic correlation c y_mean = mean (y); z_mean = mean (d); Y_sigma = y - y_mean; Z_sigma = d - z_mean; c = sum (Z_sigma .* Y_sigma) / sqrt (sum (Y_sigma .^ 2) * sum (Z_sigma .^ 2)); endfunction ## Test input validation %!error cophenet () %!error cophenet (ones (2,2), 1) %!error cophenet ([1 2 1], "a") %!error cophenet ([1 2 1], [1 2]) ## Demonstration %!demo "usage"; %! X = randn (10,2); %! y = pdist (X); %! Z = linkage (y, "average"); %! cophenet (Z, y) statistics-1.4.3/inst/copulacdf.m0000644000000000000000000002174014153320774015204 0ustar0000000000000000## Copyright (C) 2008 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} =} copulacdf (@var{family}, @var{x}, @var{theta}) ## @deftypefnx {Function File} {} copulacdf ('t', @var{x}, @var{theta}, @var{nu}) ## Compute the cumulative distribution function of a copula family. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{family} is the copula family name. Currently, @var{family} can ## be @code{'Gaussian'} for the Gaussian family, @code{'t'} for the ## Student's t family, @code{'Clayton'} for the Clayton family, ## @code{'Gumbel'} for the Gumbel-Hougaard family, @code{'Frank'} for ## the Frank family, @code{'AMH'} for the Ali-Mikhail-Haq family, or ## @code{'FGM'} for the Farlie-Gumbel-Morgenstern family. ## ## @item ## @var{x} is the support where each row corresponds to an observation. ## ## @item ## @var{theta} is the parameter of the copula. For the Gaussian and ## Student's t copula, @var{theta} must be a correlation matrix. For ## bivariate copulas @var{theta} can also be a correlation coefficient. ## For the Clayton family, the Gumbel-Hougaard family, the Frank family, ## and the Ali-Mikhail-Haq family, @var{theta} must be a vector with the ## same number of elements as observations in @var{x} or be scalar. For ## the Farlie-Gumbel-Morgenstern family, @var{theta} must be a matrix of ## coefficients for the Farlie-Gumbel-Morgenstern polynomial where each ## row corresponds to one set of coefficients for an observation in ## @var{x}. A single row is expanded. The coefficients are in binary ## order. ## ## @item ## @var{nu} is the degrees of freedom for the Student's t family. ## @var{nu} must be a vector with the same number of elements as ## observations in @var{x} or be scalar. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{p} is the cumulative distribution of the copula at each row of ## @var{x} and corresponding parameter @var{theta}. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## x = [0.2:0.2:0.6; 0.2:0.2:0.6]; ## theta = [1; 2]; ## p = copulacdf ("Clayton", x, theta) ## @end group ## ## @group ## x = [0.2:0.2:0.6; 0.2:0.1:0.4]; ## theta = [0.2, 0.1, 0.1, 0.05]; ## p = copulacdf ("FGM", x, theta) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Roger B. Nelsen. @cite{An Introduction to Copulas}. Springer, ## New York, second edition, 2006. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: CDF of a copula family function p = copulacdf (family, x, theta, nu) # Check arguments if (nargin != 3 && (nargin != 4 || ! strcmpi (family, "t"))) print_usage (); endif if (! ischar (family)) error ("copulacdf: family must be one of 'Gaussian', 't', 'Clayton', 'Gumbel', 'Frank', 'AMH', and 'FGM'"); endif if (! isempty (x) && ! ismatrix (x)) error ("copulacdf: x must be a numeric matrix"); endif [n, d] = size (x); lower_family = lower (family); # Check family and copula parameters switch (lower_family) case {"gaussian", "t"} # Family with a covariance matrix if (d == 2 && isscalar (theta)) # Expand a scalar to a correlation matrix theta = [1, theta; theta, 1]; endif if (any (size (theta) != [d, d]) || any (diag (theta) != 1) || any (any (theta != theta')) || min (eig (theta)) <= 0) error ("copulacdf: theta must be a correlation matrix"); endif if (nargin == 4) # Student's t family if (! isscalar (nu) && (! isvector (nu) || length (nu) != n)) error ("copulacdf: nu must be a vector with the same number of rows as x or be scalar"); endif nu = nu(:); endif case {"clayton", "gumbel", "frank", "amh"} # Archimedian one parameter family if (! isvector (theta) || (! isscalar (theta) && length (theta) != n)) error ("copulacdf: theta must be a vector with the same number of rows as x or be scalar"); endif theta = theta(:); if (n > 1 && isscalar (theta)) theta = repmat (theta, n, 1); endif case {"fgm"} # Exponential number of parameters if (! ismatrix (theta) || size (theta, 2) != (2 .^ d - d - 1) || (size (theta, 1) != 1 && size (theta, 1) != n)) error ("copulacdf: theta must be a row vector of length 2^d-d-1 or a matrix of size n x (2^d-d-1)"); endif if (n > 1 && size (theta, 1) == 1) theta = repmat (theta, n, 1); endif otherwise error ("copulacdf: unknown copula family '%s'", family); endswitch if (n == 0) # Input is empty p = zeros (0, 1); else # Truncate input to unit hypercube x(x < 0) = 0; x(x > 1) = 1; # Compute the cumulative distribution function according to family switch (lower_family) case {"gaussian"} # The Gaussian family p = mvncdf (norminv (x), zeros (1, d), theta); # No parameter bounds check k = []; case {"t"} # The Student's t family p = mvtcdf (tinv (x, nu), theta, nu); # No parameter bounds check k = []; case {"clayton"} # The Clayton family p = exp (-log (max (sum (x .^ (repmat (-theta, 1, d)), 2) - d + 1, 0)) ./ theta); # Product copula at columns where theta == 0 k = find (theta == 0); if (any (k)) p(k) = prod (x(k, :), 2); endif # Check bounds if (d > 2) k = find (! (theta >= 0) | ! (theta < inf)); else k = find (! (theta >= -1) | ! (theta < inf)); endif case {"gumbel"} # The Gumbel-Hougaard family p = exp (-(sum ((-log (x)) .^ repmat (theta, 1, d), 2)) .^ (1 ./ theta)); # Check bounds k = find (! (theta >= 1) | ! (theta < inf)); case {"frank"} # The Frank family p = -log (1 + (prod (expm1 (repmat (-theta, 1, d) .* x), 2)) ./ (expm1 (-theta) .^ (d - 1))) ./ theta; # Product copula at columns where theta == 0 k = find (theta == 0); if (any (k)) p(k) = prod (x(k, :), 2); endif # Check bounds if (d > 2) k = find (! (theta > 0) | ! (theta < inf)); else k = find (! (theta > -inf) | ! (theta < inf)); endif case {"amh"} # The Ali-Mikhail-Haq family p = (theta - 1) ./ (theta - prod ((1 + repmat (theta, 1, d) .* (x - 1)) ./ x, 2)); # Check bounds if (d > 2) k = find (! (theta >= 0) | ! (theta < 1)); else k = find (! (theta >= -1) | ! (theta < 1)); endif case {"fgm"} # The Farlie-Gumbel-Morgenstern family # All binary combinations bcomb = logical (floor (mod (((0:(2 .^ d - 1))' * 2 .^ ((1 - d):0)), 2))); ecomb = ones (size (bcomb)); ecomb(bcomb) = -1; # Summation over all combinations of order >= 2 bcomb = bcomb(sum (bcomb, 2) >= 2, end:-1:1); # Linear constraints matrix ac = zeros (size (ecomb, 1), size (bcomb, 1)); # Matrix to compute p ap = zeros (size (x, 1), size (bcomb, 1)); for i = 1:size (bcomb, 1) ac(:, i) = -prod (ecomb(:, bcomb(i, :)), 2); ap(:, i) = prod (1 - x(:, bcomb(i, :)), 2); endfor p = prod (x, 2) .* (1 + sum (ap .* theta, 2)); # Check linear constraints k = false (n, 1); for i = 1:n k(i) = any (ac * theta(i, :)' > 1); endfor endswitch # Out of bounds parameters if (any (k)) p(k) = NaN; endif endif endfunction %!test %! x = [0.2:0.2:0.6; 0.2:0.2:0.6]; %! theta = [1; 2]; %! p = copulacdf ("Clayton", x, theta); %! expected_p = [0.1395; 0.1767]; %! assert (p, expected_p, 0.001); %!test %! x = [0.2:0.2:0.6; 0.2:0.2:0.6]; %! p = copulacdf ("Gumbel", x, 2); %! expected_p = [0.1464; 0.1464]; %! assert (p, expected_p, 0.001); %!test %! x = [0.2:0.2:0.6; 0.2:0.2:0.6]; %! theta = [1; 2]; %! p = copulacdf ("Frank", x, theta); %! expected_p = [0.0699; 0.0930]; %! assert (p, expected_p, 0.001); %!test %! x = [0.2:0.2:0.6; 0.2:0.2:0.6]; %! theta = [0.3; 0.7]; %! p = copulacdf ("AMH", x, theta); %! expected_p = [0.0629; 0.0959]; %! assert (p, expected_p, 0.001); %!test %! x = [0.2:0.2:0.6; 0.2:0.1:0.4]; %! theta = [0.2, 0.1, 0.1, 0.05]; %! p = copulacdf ("FGM", x, theta); %! expected_p = [0.0558; 0.0293]; %! assert (p, expected_p, 0.001); statistics-1.4.3/inst/copulapdf.m0000644000000000000000000001372514153320774015225 0ustar0000000000000000## Copyright (C) 2008 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} =} copulapdf (@var{family}, @var{x}, @var{theta}) ## Compute the probability density function of a copula family. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{family} is the copula family name. Currently, @var{family} can ## be @code{'Clayton'} for the Clayton family, @code{'Gumbel'} for the ## Gumbel-Hougaard family, @code{'Frank'} for the Frank family, or ## @code{'AMH'} for the Ali-Mikhail-Haq family. ## ## @item ## @var{x} is the support where each row corresponds to an observation. ## ## @item ## @var{theta} is the parameter of the copula. The elements of ## @var{theta} must be greater than or equal to @code{-1} for the ## Clayton family, greater than or equal to @code{1} for the ## Gumbel-Hougaard family, arbitrary for the Frank family, and greater ## than or equal to @code{-1} and lower than @code{1} for the ## Ali-Mikhail-Haq family. Moreover, @var{theta} must be non-negative ## for dimensions greater than @code{2}. @var{theta} must be a column ## vector with the same number of rows as @var{x} or be scalar. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{p} is the probability density of the copula at each row of ## @var{x} and corresponding parameter @var{theta}. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## x = [0.2:0.2:0.6; 0.2:0.2:0.6]; ## theta = [1; 2]; ## p = copulapdf ("Clayton", x, theta) ## @end group ## ## @group ## p = copulapdf ("Gumbel", x, 2) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Roger B. Nelsen. @cite{An Introduction to Copulas}. Springer, ## New York, second edition, 2006. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: PDF of a copula family function p = copulapdf (family, x, theta) # Check arguments if (nargin != 3) print_usage (); endif if (! ischar (family)) error ("copulapdf: family must be one of 'Clayton', 'Gumbel', 'Frank', and 'AMH'"); endif if (! isempty (x) && ! ismatrix (x)) error ("copulapdf: x must be a numeric matrix"); endif [n, d] = size (x); if (! isvector (theta) || (! isscalar (theta) && size (theta, 1) != n)) error ("copulapdf: theta must be a column vector with the same number of rows as x or be scalar"); endif if (n == 0) # Input is empty p = zeros (0, 1); else if (n > 1 && isscalar (theta)) theta = repmat (theta, n, 1); endif # Truncate input to unit hypercube x(x < 0) = 0; x(x > 1) = 1; # Compute the cumulative distribution function according to family lowerarg = lower (family); if (strcmp (lowerarg, "clayton")) # The Clayton family log_cdf = -log (max (sum (x .^ (repmat (-theta, 1, d)), 2) - d + 1, 0)) ./ theta; p = prod (repmat (theta, 1, d) .* repmat (0:(d - 1), n, 1) + 1, 2) .* exp ((1 + theta .* d) .* log_cdf - (theta + 1) .* sum (log (x), 2)); # Product copula at columns where theta == 0 k = find (theta == 0); if (any (k)) p(k) = 1; endif # Check theta if (d > 2) k = find (! (theta >= 0) | ! (theta < inf)); else k = find (! (theta >= -1) | ! (theta < inf)); endif elseif (strcmp (lowerarg, "gumbel")) # The Gumbel-Hougaard family g = sum ((-log (x)) .^ repmat (theta, 1, d), 2); c = exp (-g .^ (1 ./ theta)); p = ((prod (-log (x), 2)) .^ (theta - 1)) ./ prod (x, 2) .* c .* (g .^ (2 ./ theta - 2) + (theta - 1) .* g .^ (1 ./ theta - 2)); # Check theta k = find (! (theta >= 1) | ! (theta < inf)); elseif (strcmp (lowerarg, "frank")) # The Frank family if (d != 2) error ("copulapdf: Frank copula PDF implemented as bivariate only"); endif p = (theta .* exp (theta .* (1 + sum (x, 2))) .* (exp (theta) - 1))./ (exp (theta) - exp (theta + theta .* x(:, 1)) + exp (theta .* sum (x, 2)) - exp (theta + theta .* x(:, 2))) .^ 2; # Product copula at columns where theta == 0 k = find (theta == 0); if (any (k)) p(k) = 1; endif # Check theta k = find (! (theta > -inf) | ! (theta < inf)); elseif (strcmp (lowerarg, "amh")) # The Ali-Mikhail-Haq family if (d != 2) error ("copulapdf: Ali-Mikhail-Haq copula PDF implemented as bivariate only"); endif z = theta .* prod (x - 1, 2) - 1; p = (theta .* (1 - sum (x, 2) - prod (x, 2) - z) - 1) ./ (z .^ 3); # Check theta k = find (! (theta >= -1) | ! (theta < 1)); else error ("copulapdf: unknown copula family '%s'", family); endif if (any (k)) p(k) = NaN; endif endif endfunction %!test %! x = [0.2:0.2:0.6; 0.2:0.2:0.6]; %! theta = [1; 2]; %! p = copulapdf ("Clayton", x, theta); %! expected_p = [0.9872; 0.7295]; %! assert (p, expected_p, 0.001); %!test %! x = [0.2:0.2:0.6; 0.2:0.2:0.6]; %! p = copulapdf ("Gumbel", x, 2); %! expected_p = [0.9468; 0.9468]; %! assert (p, expected_p, 0.001); %!test %! x = [0.2, 0.6; 0.2, 0.6]; %! theta = [1; 2]; %! p = copulapdf ("Frank", x, theta); %! expected_p = [0.9378; 0.8678]; %! assert (p, expected_p, 0.001); %!test %! x = [0.2, 0.6; 0.2, 0.6]; %! theta = [0.3; 0.7]; %! p = copulapdf ("AMH", x, theta); %! expected_p = [0.9540; 0.8577]; %! assert (p, expected_p, 0.001); statistics-1.4.3/inst/copularnd.m0000644000000000000000000001762414153320774015241 0ustar0000000000000000## Copyright (C) 2012 Arno Onken ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{x} =} copularnd (@var{family}, @var{theta}, @var{n}) ## @deftypefnx {Function File} {} copularnd (@var{family}, @var{theta}, @var{n}, @var{d}) ## @deftypefnx {Function File} {} copularnd ('t', @var{theta}, @var{nu}, @var{n}) ## Generate random samples from a copula family. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{family} is the copula family name. Currently, @var{family} can be ## @code{'Gaussian'} for the Gaussian family, @code{'t'} for the Student's t ## family, or @code{'Clayton'} for the Clayton family. ## ## @item ## @var{theta} is the parameter of the copula. For the Gaussian and Student's t ## copula, @var{theta} must be a correlation matrix. For bivariate copulas ## @var{theta} can also be a correlation coefficient. For the Clayton family, ## @var{theta} must be a vector with the same number of elements as samples to ## be generated or be scalar. ## ## @item ## @var{nu} is the degrees of freedom for the Student's t family. @var{nu} must ## be a vector with the same number of elements as samples to be generated or ## be scalar. ## ## @item ## @var{n} is the number of rows of the matrix to be generated. @var{n} must be ## a non-negative integer and corresponds to the number of samples to be ## generated. ## ## @item ## @var{d} is the number of columns of the matrix to be generated. @var{d} must ## be a positive integer and corresponds to the dimension of the copula. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{x} is a matrix of random samples from the copula with @var{n} samples ## of distribution dimension @var{d}. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## theta = 0.5; ## x = copularnd ("Gaussian", theta); ## @end group ## ## @group ## theta = 0.5; ## nu = 2; ## x = copularnd ("t", theta, nu); ## @end group ## ## @group ## theta = 0.5; ## n = 2; ## x = copularnd ("Clayton", theta, n); ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Roger B. Nelsen. @cite{An Introduction to Copulas}. Springer, New York, ## second edition, 2006. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Random samples from a copula family function x = copularnd (family, theta, nu, n) # Check arguments if (nargin < 2) print_usage (); endif if (! ischar (family)) error ("copularnd: family must be one of 'Gaussian', 't', and 'Clayton'"); endif lower_family = lower (family); # Check family and copula parameters switch (lower_family) case {"gaussian"} # Gaussian family if (isscalar (theta)) # Expand a scalar to a correlation matrix theta = [1, theta; theta, 1]; endif if (! ismatrix (theta) || any (diag (theta) != 1) || any (any (theta != theta')) || min (eig (theta)) <= 0) error ("copularnd: theta must be a correlation matrix"); endif if (nargin > 3) d = n; if (! isscalar (d) || d != size (theta, 1)) error ("copularnd: d must correspond to dimension of theta"); endif else d = size (theta, 1); endif if (nargin < 3) n = 1; else n = nu; if (! isscalar (n) || (n < 0) || round (n) != n) error ("copularnd: n must be a non-negative integer"); endif endif case {"t"} # Student's t family if (nargin < 3) print_usage (); endif if (isscalar (theta)) # Expand a scalar to a correlation matrix theta = [1, theta; theta, 1]; endif if (! ismatrix (theta) || any (diag (theta) != 1) || any (any (theta != theta')) || min (eig (theta)) <= 0) error ("copularnd: theta must be a correlation matrix"); endif if (! isscalar (nu) && (! isvector (nu) || length (nu) != n)) error ("copularnd: nu must be a vector with the same number of rows as x or be scalar"); endif nu = nu(:); if (nargin < 4) n = 1; else if (! isscalar (n) || (n < 0) || round (n) != n) error ("copularnd: n must be a non-negative integer"); endif endif case {"clayton"} # Archimedian one parameter family if (nargin < 4) # Default is bivariate d = 2; else d = n; if (! isscalar (d) || (d < 2) || round (d) != d) error ("copularnd: d must be an integer greater than 1"); endif endif if (nargin < 3) # Default is one sample n = 1; else n = nu; if (! isscalar (n) || (n < 0) || round (n) != n) error ("copularnd: n must be a non-negative integer"); endif endif if (! isvector (theta) || (! isscalar (theta) && size (theta, 1) != n)) error ("copularnd: theta must be a column vector with the number of rows equal to n or be scalar"); endif if (n > 1 && isscalar (theta)) theta = repmat (theta, n, 1); endif otherwise error ("copularnd: unknown copula family '%s'", family); endswitch if (n == 0) # Input is empty x = zeros (0, d); else # Draw random samples according to family switch (lower_family) case {"gaussian"} # The Gaussian family x = normcdf (mvnrnd (zeros (1, d), theta, n), 0, 1); # No parameter bounds check k = []; case {"t"} # The Student's t family x = tcdf (mvtrnd (theta, nu, n), nu); # No parameter bounds check k = []; case {"clayton"} # The Clayton family u = rand (n, d); if (d == 2) x = zeros (n, 2); # Conditional distribution method for the bivariate case which also # works for theta < 0 x(:, 1) = u(:, 1); x(:, 2) = (1 + u(:, 1) .^ (-theta) .* (u(:, 2) .^ (-theta ./ (1 + theta)) - 1)) .^ (-1 ./ theta); else # Apply the algorithm by Marshall and Olkin: # Frailty distribution for Clayton copula is gamma y = randg (1 ./ theta, n, 1); x = (1 - log (u) ./ repmat (y, 1, d)) .^ (-1 ./ repmat (theta, 1, d)); endif k = find (theta == 0); if (any (k)) # Produkt copula at columns k x(k, :) = u(k, :); endif # Continue argument check if (d == 2) k = find (! (theta >= -1) | ! (theta < inf)); else k = find (! (theta >= 0) | ! (theta < inf)); endif endswitch # Out of bounds parameters if (any (k)) x(k, :) = NaN; endif endif endfunction %!test %! theta = 0.5; %! x = copularnd ("Gaussian", theta); %! assert (size (x), [1, 2]); %! assert (all ((x >= 0) & (x <= 1))); %!test %! theta = 0.5; %! nu = 2; %! x = copularnd ("t", theta, nu); %! assert (size (x), [1, 2]); %! assert (all ((x >= 0) & (x <= 1))); %!test %! theta = 0.5; %! x = copularnd ("Clayton", theta); %! assert (size (x), [1, 2]); %! assert (all ((x >= 0) & (x <= 1))); %!test %! theta = 0.5; %! n = 2; %! x = copularnd ("Clayton", theta, n); %! assert (size (x), [n, 2]); %! assert (all ((x >= 0) & (x <= 1))); %!test %! theta = [1; 2]; %! n = 2; %! d = 3; %! x = copularnd ("Clayton", theta, n, d); %! assert (size (x), [n, d]); %! assert (all ((x >= 0) & (x <= 1))); statistics-1.4.3/inst/crossval.m0000644000000000000000000001365614153320774015107 0ustar0000000000000000## Copyright (C) 2014 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{results} =} crossval (@var{f}, @var{X}, @var{y}[, @var{params}]) ## Perform cross validation on given data. ## ## @var{f} should be a function that takes 4 inputs @var{xtrain}, @var{ytrain}, ## @var{xtest}, @var{ytest}, fits a model based on @var{xtrain}, @var{ytrain}, ## applies the fitted model to @var{xtest}, and returns a goodness of fit ## measure based on comparing the predicted and actual @var{ytest}. ## @code{crossval} returns an array containing the values returned by @var{f} ## for every cross-validation fold or resampling applied to the given data. ## ## @var{X} should be an @var{n} by @var{m} matrix of predictor values ## ## @var{y} should be an @var{n} by @var{1} vector of predicand values ## ## @var{params} may include parameter-value pairs as follows: ## ## @table @asis ## @item @qcode{"KFold"} ## Divide set into @var{k} equal-size subsets, using each one successively ## for validation. ## ## @item @qcode{"HoldOut"} ## Divide set into two subsets, training and validation. If the value ## @var{k} is a fraction, that is the fraction of values put in the ## validation subset (by default @var{k}=0.1); if it is a positive integer, ## that is the number of values in the validation subset. ## ## @item @qcode{"LeaveOut"} ## Leave-one-out partition (each element is placed in its own subset). ## The value is ignored. ## ## @item @qcode{"Partition"} ## The value should be a @var{cvpartition} object. ## ## @item @qcode{"Given"} ## The value should be an @var{n} by @var{1} vector specifying in which ## partition to put each element. ## ## @item @qcode{"stratify"} ## The value should be an @var{n} by @var{1} vector containing class ## designations for the elements, in which case the @qcode{"KFold"} and ## @qcode{"HoldOut"} partitionings attempt to ensure each partition ## represents the classes proportionately. ## ## @item @qcode{"mcreps"} ## The value should be a positive integer specifying the number of times ## to resample based on different partitionings. Currently only works with ## the partition type @qcode{"HoldOut"}. ## ## @end table ## ## Only one of @qcode{"KFold"}, @qcode{"HoldOut"}, @qcode{"LeaveOut"}, ## @qcode{"Given"}, @qcode{"Partition"} should be specified. If none is ## specified, the default is @qcode{"KFold"} with @var{k} = 10. ## ## @seealso{cvpartition} ## @end deftypefn ## Author: Nir Krakauer function results = crossval (f, X, y, varargin) [n m] = size (X); if numel(y) != n error('X, y sizes incompatible') endif #extract optional parameter-value argument pairs if numel(varargin) > 1 vargs = varargin; nargs = numel (vargs); values = vargs(2:2:nargs); names = vargs(1:2:nargs)(1:numel(values)); validnames = {'KFold', 'HoldOut', 'LeaveOut', 'Partition', 'Given', 'stratify', 'mcreps'}; for i = 1:numel(names) names(i) = validatestring (names(i){:}, validnames); end for i = 1:numel(validnames) name = validnames(i){:}; name_pos = strmatch (name, names); if !isempty(name_pos) eval([name ' = values(name_pos){:};']) endif endfor endif #construct CV partition if exist ("Partition", "var") P = Partition; elseif exist ("Given", "var") P = cvpartition (Given, "Given"); elseif exist ("KFold", "var") if !exist ("stratify", "var") stratify = n; endif P = cvpartition (stratify, "KFold", KFold); elseif exist ("HoldOut", "var") if !exist ("stratify", "var") stratify = n; endif P = cvpartition (stratify, "HoldOut", HoldOut); if !exist ("mcreps", "var") || isempty (mcreps) mcreps = 1; endif elseif exist ("LeaveOut", "var") P = cvpartition (n, "LeaveOut"); else #KFold if !exist ("stratify", "var") stratify = n; endif P = cvpartition (stratify, "KFold"); endif nr = get(P, "NumTestSets"); #number of test sets to do cross validation on nreps = 1; if strcmp(get(P, "Type"), 'holdout') && exist("mcreps", "var") && mcreps > 1 nreps = mcreps; endif results = nan (nreps, nr); for rep = 1:nreps if rep > 1 P = repartition (P); endif for i = 1:nr inds_train = training (P, i); inds_test = test (P, i); result = f (X(inds_train, :), y(inds_train), X(inds_test, :), y(inds_test)); results(rep, i) = result; endfor endfor endfunction %!test %! load fisheriris.txt %! y = fisheriris(:, 2); %! X = [ones(size(y)) fisheriris(:, 3:5)]; %! f = @(X1, y1, X2, y2) meansq (y2 - X2*regress(y1, X1)); %! results0 = crossval (f, X, y); %! results1 = crossval (f, X, y, 'KFold', 10); %! folds = 5; %! results2 = crossval (f, X, y, 'KFold', folds); %! results3 = crossval (f, X, y, 'Partition', cvpartition (numel (y), 'KFold', folds)); %! results4 = crossval (f, X, y, 'LeaveOut', 1); %! mcreps = 2; n_holdout = 20; %! results5 = crossval (f, X, y, 'HoldOut', n_holdout, 'mcreps', mcreps); %! %! ## ensure equal representation of iris species in the training set -- tends %! ## to slightly reduce cross-validation mean square error %! results6 = crossval (f, X, y, 'KFold', 5, 'stratify', fisheriris(:, 1)); %! %! assert (results0, results1); %! assert (results2, results3); %! assert (size(results4), [1 numel(y)]); %! assert (mean(results4), 4.5304, 1E-4); %! assert (size(results5), [mcreps 1]); statistics-1.4.3/inst/datasample.m0000644000000000000000000001654314153320774015364 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} datasample (@var{data}, @var{k}) ## @deftypefnx {Function File} @ ## {@var{y} =} datasample (@var{data}, @var{k}, @var{dim}) ## @deftypefnx {Function File} @ ## {@var{y} =} datasample (@dots{}, Name, Value) ## @deftypefnx {Function File} @ ## {[@var{y} @var{idcs}] =} datasample (@dots{}) ## ## Randomly sample data. ## ## Return @var{k} observations randomly sampled from @var{data}. @var{data} can ## be a vector or a matrix of any data. When @var{data} is a matrix or a ## n-dimensional array, the samples are the subarrays of size n - 1, taken along ## the dimension @var{dim}. The default value for @var{dim} is 1, that is the ## row vectors when sampling a matrix. ## ## Output @var{y} is the returned sampled data. Optional output @var{idcs} is ## the vector of the indices to build @var{y} from @var{data}. ## ## Additional options are set through pairs of parameter name and value. The ## known parameters are: ## ## @table @code ## @item @qcode{Replace} ## a logical value that can be @code{true} (default) or @code{false}: when set ## to @code{true}, @code{datasample} returns data sampled with replacement. ## ## @item @qcode{Weigths} ## a vector of positive numbers that sets the probability of each element. It ## must have the same size as @var{data} along dimension @var{dim}. ## ## @end table ## ## ## @end deftypefn ## ## @seealso{rand, randi, randperm, randsample} ## MATLAB compatibility: there are no random number streams in Octave ## Author: Stefano Guidoni function [y, idcs] = datasample (data, k, varargin) ## check input if ( nargin < 2 ) print_usage (); endif ## data: some data, any type, any format but cell ## MATLAB compatibility: there are no "table" or "dataset array" types in ## Octave if (iscell (data)) error ("datasample: data must be a vector or matrix"); endif ## k, a positive integer if ((! isnumeric (k) || ! isscalar (k)) || (! (floor (k) == k)) || (k <= 0)) error ("datasample: k must be a positive integer scalar"); endif dim = 1; replace = true; weights = []; if ( nargin > 2 ) pair_index = 1; if (! ischar (varargin{1})) ## it must be dim dim = varargin{1}; ## the (Name, Value) pairs start further pair_index += 1; ## dim, another positive integer if ((! isscalar (dim)) || (! (floor (dim) == dim)) || (dim <= 0)) error ("datasample: DIM must be a positive integer scalar"); endif endif ## (Name, Value) pairs while (pair_index < (nargin - 2)) switch (lower (varargin{pair_index})) case "replace" if (! islogical (varargin{pair_index + 1})) error ("datasample: expected a logical value for 'Replace'"); endif replace = varargin{pair_index + 1}; case "weights" if ((! isnumeric (varargin{pair_index + 1})) || (! isvector (varargin{pair_index + 1})) || (any (varargin{pair_index + 1} < 0))) error (["datasample: the sampling weights must be defined as a " ... "vector of positive values"]); endif weights = varargin{pair_index + 1}; otherwise error ("datasample: unknown property %s", varargin{pair_index}); endswitch pair_index += 2; endwhile endif ## get the size of the population to sample if (isvector (data)) imax = length (data); else imax = size (data, dim); endif if (isempty (weights)) ## all elements have the same probability of being chosen ## this is easy ## with or without replacement if (replace) idcs = randi (imax, k, 1); else idcs = randperm (imax, k); endif else ## first check if the weights vector is right if (imax != length (weights)) error (["datasample: the size of the vector of sampling weights must"... " be equal to the size of the sampled data"]); endif if (replace) ## easy case: ## normalize the weights, weights_n = cumsum (weights ./ sum (weights)); weights_n(end) = 1; # just to be sure ## then choose k numbers uniformly between 0 and 1 samples = rand (k, 1); ## we have subdivided the space between 0 and 1 accordingly to the ## weights vector: we have just to map back the random numbers to the ## indices of the orginal dataset for iter = 1 : k idcs(iter) = find (weights_n >= samples(iter), 1); endfor else ## complex case ## choose k numbers uniformly between 0 and 1 samples = rand (k, 1); for iter = 1 : k ## normalize the weights weights_n = cumsum (weights ./ sum (weights)); weights_n(end) = 1; # just to be sure idcs(iter) = find (weights_n >= samples(iter), 1); ## remove the element from the set, i. e. set its probability to zero weights(idcs(iter)) = 0; endfor endif endif ## let's get the actual data from the original set if (isvector (data)) ## data is a vector y = data(idcs); else vS = size (data); if (length (vS) == 2) ## data is a 2-dimensional matrix if (dim == 1) y = data(idcs, :); else y = data(:, idcs); endif else ## data is an n-dimensional matrix s = "y = data("; for iter = 1 : length (vS) if (iter == dim) s = [s "idcs,"]; else s = [s ":,"]; endif endfor s = [s ":);"]; eval (s); endif endif endfunction ## some tests %!error datasample(); %!error datasample(1); %!error datasample({1, 2, 3}, 1); %!error datasample([1 2], -1); %!error datasample([1 2], 1.5); %!error datasample([1 2], [1 1]); %!error datasample([1 2], 'g', [1 1]); %!error datasample([1 2], 1, -1); %!error datasample([1 2], 1, 1.5); %!error datasample([1 2], 1, [1 1]); %!error datasample([1 2], 1, 1, "Replace", -2); %!error datasample([1 2], 1, 1, "Weights", "abc"); %!error datasample([1 2], 1, 1, "Weights", [1 -2 3]); %!error datasample([1 2], 1, 1, "Weights", ones (2)); %!error datasample([1 2], 1, 1, "Weights", [1 2 3]); %!test %! dat = randn (10, 4); %! assert (size (datasample (dat, 3, 1)), [3 4]); %!test %! dat = randn (10, 4); %! assert (size (datasample (dat, 3, 2)), [10 3]); statistics-1.4.3/inst/dcov.m0000644000000000000000000001035114153320774014173 0ustar0000000000000000## Copyright (C) 2014 - Maria L. Rizzo and Gabor J. Szekely ## Copyright (C) 2014 Juan Pablo Carbajal ## This work is derived from the R energy package. It was adapted ## for Octave by Juan Pablo Carbajal. ## ## This progrm is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## Author: Juan Pablo Carbajal ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{dCor}, @var{dCov}, @var{dVarX}, @var{dVarY}] =} dcov (@var{x}, @var{y}, @var{index}=1) ## Distance correlation, covariance and correlation statistics. ## ## It returns distace correlation (@var{dCor}), ## distance covariance (@var{dCov}), diatance variace on x (@var{dVarX}) and ## distance variance on y (@var{dVarY}). ## ## Reference: https://en.wikipedia.org/wiki/Distance_correlation ## ## @seealso{corr, cov} ## @end deftypefn function [dCor, dCov, dVarX, dVarY] = dcov (x,y,index=1.0) %x = abs(x - x.'); %y = abs(y - y.'); x = abs (bsxfun (@minus, x, x.')); y = abs (bsxfun (@minus, y, y.')); [n nc] = size (x); [m mc] = size (y); if (n != m) error ("Octave:invalid-input-arg", "Sample sizes must agree."); endif if any (isnan (x) | isnan (y)) error ("Octave:invalid-input-arg","Data contains missing or infinite values."); endif if index < 0 || index > 2 warning ("Octave:invalid-input-arg","index must be in [0,2), using default index=1"); index = 1.0; endif A = Akl (x, index); B = Akl (y, index); dCov = sqrt (mean (A(:) .* B(:))); dVarX = sqrt (mean (A(:).^2) ); dVarY = sqrt (mean (B(:).^2) ); V = sqrt (dVarX .* dVarY); if V > 0 dCor = dCov / V; else dCor = 0; end endfunction function c = Akl (x, index) # Double centered distance d = x .^ index; rm = mean (d, 2); # row mean gm = mean (d(:)); # grand mean c = d - bsxfun (@plus, rm, rm.') + gm; endfunction %!demo %! base=@(x) (x- min(x))./(max(x)-min(x)); %! N = 5e2; %! x = randn (N,1); x = base (x); %! z = randn (N,1); z = base (z); %! # Linear relations %! cy = [1 0.55 0.3 0 -0.3 -0.55 -1]; %! ly = x .* cy; %! ly(:,[1:3 5:end]) = base (ly(:,[1:3 5:end])); %! # Correlated Gaussian %! cz = 1 - abs (cy); %! gy = base ( ly + cz.*z); %! # Shapes %! sx = repmat (x,1,7); %! sy = zeros (size (ly)); %! v = 2 * rand (size(x,1),2) - 1; %! sx(:,1) = v(:,1); sy(:,1) = cos(2*pi*sx(:,1)) + 0.5*v(:,2).*exp(-sx(:,1).^2/0.5); %! R =@(d) [cosd(d) sind(d); -sind(d) cosd(d)]; %! tmp = R(35) * v.'; %! sx(:,2) = tmp(1,:); sy(:,2) = tmp(2,:); %! tmp = R(45) * v.'; %! sx(:,3) = tmp(1,:); sy(:,3) = tmp(2,:); %! sx(:,4) = v(:,1); sy(:,4) = sx(:,4).^2 + 0.5*v(:,2); %! sx(:,5) = v(:,1); sy(:,5) = 3*sign(v(:,2)).*(sx(:,5)).^2 + v(:,2); %! sx(:,6) = cos (2*pi*v(:,1)) + 0.5*(x-0.5); %! sy(:,6) = sin (2*pi*v(:,1)) + 0.5*(z-0.5); %! sx(:,7) = x + sign(v(:,1)); sy(:,7) = z + sign(v(:,2)); %! sy = base (sy); %! sx = base (sx); %! # scaled shape %! sc = 1/3; %! ssy = (sy-0.5) * sc + 0.5; %! n = size (ly,2); %! ym = 1.2; %! xm = 0.5; %! fmt={'horizontalalignment','center'}; %! ff = "% .2f"; %! figure (1) %! for i=1:n %! subplot(4,n,i); %! plot (x, gy(:,i), '.b'); %! axis tight %! axis off %! text (xm,ym,sprintf (ff, dcov (x,gy(:,i))),fmt{:}) %! %! subplot(4,n,i+n); %! plot (x, ly(:,i), '.b'); %! axis tight %! axis off %! text (xm,ym,sprintf (ff, dcov (x,ly(:,i))),fmt{:}) %! %! subplot(4,n,i+2*n); %! plot (sx(:,i), sy(:,i), '.b'); %! axis tight %! axis off %! text (xm,ym,sprintf (ff, dcov (sx(:,i),sy(:,i))),fmt{:}) %! v = axis (); %! %! subplot(4,n,i+3*n); %! plot (sx(:,i), ssy(:,i), '.b'); %! axis (v) %! axis off %! text (xm,ym,sprintf (ff, dcov (sx(:,i),ssy(:,i))),fmt{:}) %! endfor statistics-1.4.3/inst/dendrogram.m0000644000000000000000000003155114153320774015367 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## Copyright (c) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} dendrogram (@var{tree}) ## @deftypefnx {Function File} {} dendrogram (@var{tree}, @var{p}) ## @deftypefnx {Function File} {} dendrogram (@var{tree}, @var{prop}, @var{val}) ## @deftypefnx {Function File} @ ## {} dendrogram (@var{tree}, @var{p}, @var{prop}, @var{val} ) ## @deftypefnx {Function File} {@var{h} = } dendrogram (@dots{}) ## @deftypefnx {Function File} @ ## {[@var{h}, @var{t}, @var{perm}] = } dendrogram (@dots{}) ## ## Plot a dendrogram of a hierarchical binary cluster tree. ## ## Given @var{tree}, a hierarchical binary cluster tree as the output of ## @code{linkage}, plot a dendrogram of the tree. The number of leaves shown by ## the dendrogram plot is limited to @var{p}. The default value for @var{p} is ## 30. Set @var{p} to 0 to plot all leaves. ## ## The optional outputs are @var{h}, @var{t} and @var{perm}: ## @itemize @bullet ## @item @var{h} is a handle to the lines of the plot. ## ## @item @var{t} is the vector with the numbers assigned to each leaf. ## Each element of @var{t} is a leaf of @var{tree} and its value is the number ## shown in the plot. ## When the dendrogram plot is collapsed, that is when the number of shown ## leaves @var{p} is inferior to the total number of leaves, a single leaf of ## the plot can represent more than one leaf of @var{tree}: in that case ## multiple elements of @var{t} share the same value, that is the same leaf of ## the plot. ## When the dendrogram plot is not collapsed, each leaf of the plot is the leaf ## of @var{tree} with the same number. ## ## @item @var{perm} is the vector list of the leaves as ordered as in the plot. ## @end itemize ## ## Additional input properties can be specified by pairs of properties and ## values. Known properties are: ## @itemize @bullet ## @item @qcode{"Reorder"} ## Reorder the leaves of the dendrogram plot using a numerical vector of size n, ## the number of leaves. When @var{p} is smaller than @var{n}, the reordering ## cannot break the @var{p} groups of leaves. ## ## @item @qcode{"Orientation"} ## Change the orientation of the plot. Available values: @qcode{top} (default), ## @qcode{bottom}, @qcode{left}, @qcode{right}. ## ## @item @qcode{"CheckCrossing"} ## Check if the lines of a reordered dendrogram cross each other. Available ## values: @qcode{true} (default), @qcode{false}. ## ## @item @qcode{"ColorThreshold"} ## Not implemented. ## ## @item @qcode{"Labels"} ## Use a char, string or cellstr array of size @var{n} to set the label for each ## leaf; the label is dispayed only for nodes with just one leaf. ## @end itemize ## ## @end deftypefn ## ## @seealso{cluster, clusterdata, cophenet, inconsistent, linkage, pdist} function [H, T, perm] = dendrogram (tree, varargin) [m d] = size (tree); if ((d != 3) || (! isnumeric (tree)) || ... (! (max (tree(end, 1:2)) == m * 2))) error (["dendrogram: tree must be a matrix as generated by the " ... "linkage function"]); end pair_index = 1; ## node count n = m + 1; P = 30; # default value vReorder = []; csLabels = {}; checkCrossing = 1; orientation = "top"; if (nargin > 1) if (isnumeric (varargin{1}) && isscalar (varargin{1})) ## dendrogram (tree, P) P = varargin{1}; pair_index++; endif ## dendrogram (..., Name, Value) while (pair_index < (nargin - 1)) switch (lower (varargin{pair_index})) case "reorder" if (isvector (varargin{pair_index + 1}) && ... isnumeric (varargin{pair_index + 1}) && ... length (varargin{pair_index + 1}) == n ) vReorder = varargin{pair_index + 1}; else error (["dendrogram: 'reorder' must be a numeric vector of size" ... "n, the number of leaves"]); endif case "checkcrossing" if (ischar (varargin{pair_index + 1})) switch (lower (varargin{pair_index + 1})) case "true" checkCrossing = 1; case "false" checkCrossing = 0; otherwise error ("dendrogram: unknown value '%s' for CheckCrossing", ... varargin{pair_index + 1}); endswitch elseif error (["dendrogram: the value of property CheckCrossing must ", ... "be either 'true' or 'false'"]); endif case "colorthreshold" warning ("dendrogram: property '%s' not implemented",... varargin{pair_index}); case "orientation" orientation = varargin{pair_index + 1}; # validity check below case "labels" if (ischar (varargin{pair_index + 1}) && ... (isvector (varargin{pair_index + 1}) && ... length (varargin{pair_index + 1}) == n) || ... (ismatrix (varargin{pair_index + 1}) && ... rows (varargin{pair_index + 1}) == n)) csLabels = cellstr (varargin{pair_index + 1}); elseif (iscellstr (varargin{pair_index + 1}) && length (varargin{pair_index + 1}) == n) csLabels = varargin{pair_index + 1}; else error (["dendrogram: labels must be a char or string or" ... "cellstr array of size n"]); endif otherwise error ("dendrogram: unknown property '%s'", varargin{pair_index}); endswitch pair_index += 2; endwhile endif ## MATLAB compatibility: ## P <= 0 to plot all leaves if (P < 1) P = n; endif if (n > P) level_0 = tree((n - P), 3); else P = n; level_0 = 0; endif vLeafPosition = zeros((n + m), 1); T = (1:n)'; nodecnt = 1; ## main dendrogram_recursive (m, 0); ## T reordering ## MATLAB compatibility: when n > P, each node group is renamed with a number ## between 1 and P, according to the smallest node index of each group; ## the group with the node 1 is always group 1, while group 2 is the group ## with the smallest node index outside of group 1, and group 3 is the group ## with the smallest node index outside of groups 1 and 2... newT = 1 : (length (T)); if (n > P) uniqueT = unique (T); minT = zeros (uniqueT, 1); counter = 1; for i = 1 : length (uniqueT) # it should be exactly equal to P idcs = find (T == uniqueT(i)); minT(i) = min (idcs); endfor minT = minT(find (minT > 0)); # to prevent a strange bug [minT, minTidcs] = sort (minT); uniqueT = uniqueT(minTidcs); for i = 1 : length (uniqueT) idcs = find (T == uniqueT(i)); newT(idcs) = counter++; endfor endif ## leaf reordering if (! isempty(vReorder)) if (P < n) checkT = newT(vReorder(:)); for i = 1 : P idcs = find (checkT == i); if (length (idcs) > 1) if (max (idcs) - min (idcs) >= length (idcs)) error (["dendrogram: invalid reordering that redefines the 'P'"... "groups of leaves"]); endif endif endfor checkT = unique (checkT, "stable"); vNewLeafPosition = zeros (n, 1); uT = unique (T, "stable"); for i = 1 : P vNewLeafPosition(uT(checkT(i))) = i; endfor vLeafPosition = vNewLeafPosition; else for i = 1 : length (vReorder) vLeafPosition(vReorder(i)) = i; endfor endif endif ## figure x = []; hd = figure (gcf); ## ticks and tricks xticks = 1:P; perm = zeros (P, 1); for i = 1 : length (vLeafPosition) if (vLeafPosition(i) != 0) idcs = find (T == i); perm(vLeafPosition(i)) = newT(idcs(1)); endif endfor T = newT; # this should be unnecessary for n <= P ## lines for i = (n - P + 1) : m vLeafPosition(n + i) = mean (vLeafPosition(tree(i, 1:2), 1)); x(end + 1,1:4) = [vLeafPosition(tree(i, 1:2))' tree(i, [3 3])]; for j = 1 : 2 x0 = 0; if (tree(i,j) > (2 * n - P)) x0 = tree(tree(i, j) - n, 3); endif x(end + 1, 1:4) = [vLeafPosition(tree(i, [j j]))' x0 tree(i, 3)]; endfor endfor ## plot stuff if (strcmp (orientation, "top")) H = line (x(:, 1:2)', x(:, 3:4)', "color", "blue"); set (gca, "xticklabel", perm, "xtick", xticks); elseif (strcmp (orientation, "bottom")) H = line (x(:, 1:2)', x(:, 3:4)', "color", "blue"); set (gca, "xticklabel", perm, "xtick", xticks, "xaxislocation", "top"); axis ("ij"); elseif (strcmp (orientation, "left")) H = line (x(:, 3:4)', x(:, 1:2)', "color", "blue"); set (gca, "yticklabel", perm, "ytick", xticks, "xdir", "reverse",... "yaxislocation", "right"); elseif (strcmp (orientation, "right")) H = line (x(:, 3:4)', x(:, 1:2)', "color", "blue"); set (gca, "yticklabel", perm, "ytick", xticks); else close (hd); error ("dendrogram: invalid orientation '%s'", orientation); endif ## labels if (! isempty (csLabels)) csCurrent = cellstr (num2str (perm)); for i = 1 : n ## when there is just one leaf, use the named label for that leaf if (1 == length (find (T == i))) csCurrent(find (perm == i)) = csLabels(find (T == i)); endif endfor switch (orientation) case {"top", "bottom"} xticklabels (csCurrent); case {"left", "right"} yticklabels (csCurrent); endswitch endif ## check crossings if (checkCrossing && ! isempty(vReorder)) for j = 1 : rows (x) if (x(j, 3) == x(j, 4)) # an horizontal line for i = 1 : rows (x) if (x(i, 1) == x(i, 2) && ... # orthogonal lines (x(i, 1) > x(j, 1) && x(i, 1) < x(j, 2)) && ... (x(j, 3) > x(i, 3) && x(j, 3) < x(i, 4))) warning ("dendrogram: line intersection detected"); endif endfor endif endfor endif ## dendrogram_recursive function dendrogram_recursive (k, cn) if (tree(k, 3) > level_0) for j = 1:2 if (tree(k, j) > n) dendrogram_recursive (tree(k, j) - n, 0) else vLeafPosition(tree(k, j)) = nodecnt++; T(tree(k, j)) = tree(k, j); endif endfor else for j = 1:2 if (cn == 0) cn = n + k; vLeafPosition(cn) = nodecnt++; endif if (tree(k, j) > n) dendrogram_recursive (tree(k, j) - n, cn) else T(tree(k, j)) = cn; endif endfor endif endfunction endfunction ## Get current figure visibility so it can be restored after tests %!shared visibility_setting %! visibility_setting = get (0, "DefaultFigureVisible"); ## Test input validation %!error dendrogram () %!error dendrogram (ones (2, 2), 1) %!error dendrogram ([1 2 1], 1, "xxx", "xxx") %!error dendrogram ([1 2 1], "Reorder", "xxx") %!error dendrogram ([1 2 1], "Reorder", [1 2 3 4]) %!test %! set (0, "DefaultFigureVisible", "off"); %! fail ('dendrogram ([1 2 1], "Orientation", "north")', "invalid orientation .*") %! set (0, "DefaultFigureVisible", visibility_setting); ## Demonstrations ## 1. %!demo 1 %! y = [4 5; 2 6; 3 7; 8 9; 1 10]; %! y(:,3) = 1:5; %! figure (gcf); clf; %! dendrogram (y); ## 2. %!demo 2 %! v = 2 * rand (30, 1) - 1; %! d = abs (bsxfun (@minus, v(:, 1), v(:, 1)')); %! y = linkage (squareform (d, "tovector")); %! figure (gcf); clf; %! dendrogram (y); ## 3. collapsed tree %!demo "collapsed tree, find all the leaves of node 5" %! X = randn (60, 2); %! D = pdist (X); %! y = linkage (D, "average"); %! figure (gcf); clf; %! subplot (2, 1, 1); %! title ("original tree"); %! dendrogram (y, 0); %! subplot (2, 1, 2); %! title ("collapsed tree"); %! [~, t] = dendrogram (y, 20); %! find(t == 5) ## 4. optimal leaf order %!demo "optimal leaf order" %! X = randn (30, 2); %! D = pdist (X); %! y = linkage (D, "average"); %! order = optimalleaforder (y, D); %! figure (gcf); clf; %! subplot (2, 1, 1); %! title ("original leaf order"); %! dendrogram (y); %! subplot (2, 1, 2); %! title ("optimal leaf order"); %! dendrogram (y, "Reorder", order); ## 5. orientation %!demo "horizontal orientation and labels" %! X = randn (8, 2); %! D = pdist (X); %! L = ["Snow White"; "Doc"; "Grumpy"; "Happy"; "Sleepy"; "Bashful"; ... %! "Sneezy"; "Dopey"]; %! y = linkage (D, "average"); %! dendrogram (y, "Orientation", "left", "Labels", L); statistics-1.4.3/inst/evalclusters.m0000644000000000000000000003547714153320774015774 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{eva} =} evalclusters (@var{x}, @var{clust}, @var{criterion}) ## @deftypefnx {Function File} {@var{eva} =} evalclusters (@dots{}, @qcode{Name}, @qcode{Value}) ## ## Create a clustering evaluation object to find the optimal number of clusters. ## ## @code{evalclusters} creates a clustering evaluation object to evaluate the ## optimal number of clusters for data @var{x}, using criterion @var{criterion}. ## The input data @var{x} is a matrix with @code{n} observations of @code{p} ## variables. ## The evaluation criterion @var{criterion} is one of the following: ## @table @code ## @item @qcode{CalinskiHarabasz} ## to create a @code{CalinskiHarabaszEvaluation} object. ## ## @item @qcode{DaviesBouldin} ## to create a @code{DaviesBouldinEvaluation} object. ## ## @item @qcode{gap} ## to create a @code{GapEvaluation} object. ## ## @item @qcode{silhouette} ## to create a @code{SilhouetteEvaluation} object. ## ## @end table ## The clustering algorithm @var{clust} is one of the following: ## @table @code ## @item @qcode{kmeans} ## to cluster the data using @code{kmeans} with @code{EmptyAction} set to ## @code{singleton} and @code{Replicates} set to 5. ## ## @item @qcode{linkage} ## to cluster the data using @code{clusterdata} with @code{linkage} set to ## @code{Ward}. ## ## @item @qcode{gmdistribution} ## to cluster the data using @code{fitgmdist} with @code{SharedCov} set to ## @code{true} and @code{Replicates} set to 5. ## ## @end table ## If the @var{criterion} is @code{CalinskiHarabasz}, @code{DaviesBouldin}, or ## @code{silhouette}, @var{clust} can also be a function handle to a function ## of the form @code{c = clust(x, k)}, where @var{x} is the input data, ## @var{k} the number of clusters to evaluate and @var{c} the clustering result. ## The clustering result can be either an array of size @code{n} with @code{k} ## different integer values, or a matrix of size @code{n} by @code{k} with a ## likelihood value assigned to each one of the @code{n} observations for each ## one of the @var{k} clusters. In the latter case, each observation is assigned ## to the cluster with the higher value. ## If the @var{criterion} is @code{CalinskiHarabasz}, @code{DaviesBouldin}, or ## @code{silhouette}, @var{clust} can also be a matrix of size @code{n} by ## @code{k}, where @code{k} is the number of proposed clustering solutions, so ## that each column of @var{clust} is a clustering solution. ## ## In addition to the obligatory @var{x}, @var{clust} and @var{criterion} inputs ## there is a number of optional arguments, specified as pairs of @code{Name} ## and @code{Value} options. The known @code{Name} arguments are: ## @table @code ## @item @qcode{KList} ## a vector of positive integer numbers, that is the cluster sizes to evaluate. ## This option is necessary, unless @var{clust} is a matrix of proposed ## clustering solutions. ## ## @item @qcode{Distance} ## a distance metric as accepted by the chosen @var{clust}. It can be the ## name of the distance metric as a string or a function handle. When ## @var{criterion} is @code{silhouette}, it can be a vector as created by ## function @code{pdist}. Valid distance metric strings are: @code{sqEuclidean} ## (default), @code{Euclidean}, @code{cityblock}, @code{cosine}, ## @code{correlation}, @code{Hamming}, @code{Jaccard}. ## Only used by @code{silhouette} and @code{gap} evaluation. ## ## @item @qcode{ClusterPriors} ## the prior probabilities of each cluster, which can be either @code{empirical} ## (default), or @code{equal}. When @code{empirical} the silhouette value is ## the average of the silhouette values of all points; when @code{equal} the ## silhouette value is the average of the average silhouette value of each ## cluster. Only used by @code{silhouette} evaluation. ## ## @item @qcode{B} ## the number of reference datasets generated from the reference distribution. ## Only used by @code{gap} evaluation. ## ## @item @qcode{ReferenceDistribution} ## the reference distribution used to create the reference data. It can be ## @code{PCA} (default) for a distribution based on the principal components of ## @var{X}, or @code{uniform} for a uniform distribution based on the range of ## the observed data. @code{PCA} is currently not implemented. ## Only used by @code{gap} evaluation. ## ## @item @qcode{SearchMethod} ## the method for selecting the optimal value with a @code{gap} evaluation. It ## can be either @code{globalMaxSE} (default) for selecting the smallest number ## of clusters which is inside the standard error of the maximum gap value, or ## @code{firstMaxSE} for selecting the first number of clusters which is inside ## the standard error of the following cluster number. ## Only used by @code{gap} evaluation. ## ## @end table ## ## Output @var{eva} is a clustering evaluation object. ## ## @end deftypefn ## ## @seealso{CalinskiHarabaszEvaluation, DaviesBouldinEvaluation, GapEvaluation, ## SilhouetteEvaluation} function cc = evalclusters (x, clust, criterion, varargin) ## input check if (nargin < 3) print_usage (); endif ## parsing input data if ((! ismatrix (x)) || (! isnumeric (x))) error ("evalclusters: 'x' must be a numeric matrix"); endif ## useful values for input check n = rows (x); p = columns (x); ## parsing the clustering algorithm if (ischar (clust)) clust = lower (clust); if (! any (strcmpi (clust, {"kmeans", "linkage", "gmdistribution"}))) error ("evalclusters: unknown clustering algorithm '%s'", clust); endif elseif (! isscalar (clust)) if ((! isnumeric (clust)) || (length (size (clust)) != 2) || ... (rows (clust) != n)) error ("evalclusters: invalid matrix of clustering solutions"); endif elseif (! isa (clust, "function_handle")) error ("evalclusters: invalid argument for 'clust'"); endif ## parsing the criterion parameter ## we check the rest later, as the check depends on the chosen criterion if (! ischar (criterion)) error ("evalclusters: invalid criterion, it must be a string"); else criterion = lower (criterion); if (! any (strcmpi (criterion, {"calinskiharabasz", "daviesbouldin", ... "silhouette", "gap"}))) error ("evalclusters: unknown criterion '%s'", criterion); endif endif ## some default value klist = []; distance = "sqeuclidean"; clusterpriors = "empirical"; b = 100; referencedistribution = "pca"; searchmethod = "globalmaxse"; ## parse the name/value pairs pair_index = 1; while (pair_index < (nargin - 3)) ## type check if (! ischar (varargin{pair_index})) error ("evalclusters: invalid property, string expected"); endif ## now parse the parameter switch (lower (varargin{pair_index})) case "klist" ## klist must be an array of positive interger numbers; ## there is a special case when it can be empty, but that is not the ## suggested way to use it (it is better to omit it instead) if (isempty (varargin{pair_index + 1})) if (ischar (clust) || isa (clust, "function_handle")) error (["evalclusters: 'KList' can be empty only when 'clust' "... "is a matrix"]); endif elseif ((! isnumeric (varargin{pair_index + 1})) || ... (! isvector (varargin{pair_index + 1})) || ... any (find (varargin{pair_index + 1} < 1)) || ... any (floor (varargin{pair_index + 1}) != varargin{pair_index + 1})) error ("evalclusters: 'KList' must be an array of positive integers"); endif klist = varargin{pair_index + 1}; case "distance" ## used by silhouette and gap if (! (strcmpi (criterion, "silhouette") || strcmpi (criterion, "gap"))) error (["evalclusters: distance metric cannot be used with '%s'"... " criterion"], criterion); endif if (ischar (varargin{pair_index + 1})) if (! any (strcmpi (varargin{pair_index + 1}, ... {"sqeuclidean", "euclidean", "cityblock", "cosine", ... "correlation", "hamming", "jaccard"}))) error ("evalclusters: unknown distance criterion '%s'", ... varargin{pair_index + 1}); endif elseif (! isa (varargin{pair_index + 1}, "function_handle") || ! ((isvector (varargin{pair_index + 1}) && ... isnumeric (varargin{pair_index + 1})))) error ("evalclusters: invalid distance metric"); endif distance = varargin{pair_index + 1}; case "clusterpriors" ## used by silhouette evaluation if (! strcmpi (criterion, "silhouette")) error (["evalclusters: cluster prior probabilities cannot be used "... "with '%s' criterion"], criterion); endif if (any (strcmpi (varargin{pair_index + 1}, {"empirical", "equal"}))) clusterpriors = lower (varargin{pair_index + 1}); else error ("evalclusters: invalid cluster prior probabilities value"); endif case "b" ## used by gap evaluation if (! isnumeric (varargin{pair_index + 1}) || ... ! isscalar (varargin{pair_index + 1}) || ... varargin{pair_index + 1} != floor (varargin{pair_index + 1}) || ... varargin{pair_index + 1} < 1) error ("evalclusters: b must a be positive integer number"); endif b = varargin{pair_index + 1}; case "referencedistribution" ## used by gap evaluation if (! ischar (varargin{pair_index + 1}) || any (strcmpi ... (varargin{pair_index + 1}, {"pca", "uniform"}))) error (["evalclusters: the reference distribution must be either" ... "'PCA' or 'uniform'"]); endif referencedistribution = lower (varargin{pair_index + 1}); case "searchmethod" ## used by gap evaluation if (! ischar (varargin{pair_index + 1}) || any (strcmpi ... (varargin{pair_index + 1}, {"globalmaxse", "uniform"}))) error (["evalclusters: the search method must be either" ... "'globalMaxSE' or 'firstmaxse'"]); endif searchmethod = lower (varargin{pair_index + 1}); otherwise error ("evalclusters: unknown property %s", varargin{pair_index}); endswitch pair_index += 2; endwhile ## check if there are parameters without a value or a name left if (nargin - 2 - pair_index) if (ischar (varargin{pair_index})) error ("evalclusters: invalid parameter '%s'", varargin{pair_index}); else error ("evalclusters: invalid parameter '%d'", varargin{pair_index}); endif endif ## another check on klist if (isempty (klist) && (ischar (clust) || isa (clust, "function_handle"))) error (["evalclusters: 'KList' can be empty only when 'clust' ", ... "is a matrix"]); endif ## main switch (lower (criterion)) case "calinskiharabasz" ## further compatibility checks between the chosen parameters are ## delegated to the class constructor if (isempty (klist)) klist = 1 : columns (clust); endif cc = CalinskiHarabaszEvaluation (x, clust, klist); case "daviesbouldin" ## further compatibility checks between the chosen parameters are ## delegated to the class constructor if (isempty (klist)) klist = 1 : columns (clust); endif cc = DaviesBouldinEvaluation (x, clust, klist); case "silhouette" ## further compatibility checks between the chosen parameters are ## delegated to the class constructor if (isempty (klist)) klist = 1 : columns (clust); endif cc = SilhouetteEvaluation (x, clust, klist, distance, clusterpriors); case "gap" ## gap cannot be used with a pre-computed solution, i.e. a matrix for ## 'clust', and klist must be specified if (isnumeric (clust)) error (["evalclusters: 'clust' must be a clustering algorithm when "... "using the gap criterion"]); endif if (isempty (klist)) error (["evalclusters: 'klist' cannot be empty when using the gap " ... "criterion"]); endif cc = GapEvaluation (x, clust, klist, b, distance, ... referencedistribution, searchmethod); otherwise error ("evalclusters: invalid criterion '%s'", criterion); endswitch endfunction ## input tests %!error evalclusters () %!error evalclusters ([1 1;0 1]) %!error evalclusters ([1 1;0 1], "kmeans") %!error <'x' must be a numeric*> evalclusters ("abc", "kmeans", "gap") %!error evalclusters ([1 1;0 1], "xxx", "gap") %!error evalclusters ([1 1;0 1], [1 2], "gap") %!error evalclusters ([1 1;0 1], 1.2, "gap") %!error evalclusters ([1 1;0 1], [1; 2], 123) %!error evalclusters ([1 1;0 1], [1; 2], "xxx") %!error <'KList' can be empty*> evalclusters ([1 1;0 1], "kmeans", "gap") %!error evalclusters ([1 1;0 1], [1; 2], "gap", 1) %!error evalclusters ([1 1;0 1], [1; 2], "gap", 1, 1) %!error evalclusters ([1 1;0 1], [1; 2], "gap", "xxx", 1) %!error <'KList'*> evalclusters ([1 1;0 1], [1; 2], "gap", "KList", [-1 0]) %!error <'KList'*> evalclusters ([1 1;0 1], [1; 2], "gap", "KList", [1 .5]) %!error <'KList'*> evalclusters ([1 1;0 1], [1; 2], "gap", "KList", [1 1; 1 1]) %!error evalclusters ([1 1;0 1], [1; 2], "gap", ... %! "distance", "a") %!error evalclusters ([1 1;0 1], [1; 2], "daviesbouldin", ... %! "distance", "a") %!error evalclusters ([1 1;0 1], [1; 2], "gap", ... %! "clusterpriors", "equal") %!error evalclusters ([1 1;0 1], [1; 2], ... %! "silhouette", "clusterpriors", "xxx") %!error <'clust' must be a clustering*> evalclusters ([1 1;0 1], [1; 2], "gap") ## demonstration %!demo %! load fisheriris; %! eva = evalclusters(meas, "kmeans", "calinskiharabasz", "KList", [1:6]) statistics-1.4.3/inst/expfit.m0000644000000000000000000002375114153320774014547 0ustar0000000000000000## Copyright (C) 2021 Nicholas R. Jankowski ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{mu} =} expfit (@var{s}) ## @deftypefnx {Function File} {[@var{mu}, @var{ci}] =} expfit (@var{s}) ## @deftypefnx {Function File} {[@var{mu}, @var{ci}] =} expfit (@var{s}, @var{alpha}) ## @deftypefnx {Function File} {@dots{} =} expfit (@var{s}, @var{alpha}, @var{c}) ## @deftypefnx {Function File} {@dots{} =} expfit (@var{s}, @var{alpha}, @var{c}, @var{f}) ## ## Estimate the mean of the exponential probability distribution function from ## which sample data @var{s} has been taken. @var{s} is expected to be a ## non-negative vector. If @var{s} is an array, the mean will be computed for ## each column of @var{s}. If any elements of @var{s} are NaN, that vector's ## mean will be returned as NaN. ## ## If the optional output variable @var{ci} is requested, @code{expfit} will ## also return the confidence interval bounds for the estimate as a two element ## column vector. If @var{s} is an array, each column of data will have a ## confidence interval returned as a two row array. ## ## The optional scalar input @var{alpha} can be used to define the ## (1-@var{alpha}) confidence interval to be applied to all estimates as a ## value between 0 and 1. The default is 0.05, resulting in a 0.95 or 95% CI. ## Any invalid values for alpha will return NaN for both CI bounds. ## ## The optional input @var{c} is a logical or numeric array of zeros and ones ## the same size as @var{s}, used to right-censor individual elements of ## @var{s}. A value of 1 indicates the data should be censored from ## the mean estimation. Any nonzero values in @var{c} are treated as a 1. ## ## The optional input @var{f} is a numeric array the same size as @var{s}, used ## to specify occurrence frequencies for the elements in @var{s}. Values of ## @var{f} need not be integers. Any NaN elements in the frequency array will ## produce a NaN output for @var{mu}. ## ## Options can be skipped by using [] to revert to the default. ## ## Matlab incompatibility: Matlab's @code{expfit} produces unpredictable results ## for some cases with higher dimensions (specifically 1 x m x n x ... arrays). ## Octave's implementation allows for n-D arrays, consistently performing ## calculations on individual column vectors. Additionally, @var{c} and @var{f} ## can be used with arrays of any size, whereas Matlab only allows their use ## when @var{s} is a vector. ## ## @end deftypefn ## ## @seealso{expcdf, expinv, explike, exppdf, exprnd, expstat} ## @seealso{expstat, exprnd, expcdf, expinv} function [m, v] = expfit (s, alpha = 0.05, c = [], f = []) ## Check arguments if (nargin ==0 || nargin > 4 || nargout > 2) print_usage (); endif if ! (isnumeric (s) || islogical (s)) s = double(s); endif ## guarantee working with column vectors if isvector (s) s = s(:); endif if any (s(:) < 0) error("expfit: input data S cannot be negative"); endif sz_s = size (s); if (isempty (alpha)) alpha = 0.05; elseif !(isscalar (alpha)) error ("expfit: ALPHA must be a scalar quantity"); endif if (isempty (c) && isempty (f)) ##simple case without f or c, shortcut other validations m = mean (s, 1); if (nargout == 2) S = sum (s, 1); v = [2*S ./ chi2inv(1 - alpha/2, 2*sz_s(1));... 2*S ./ chi2inv(alpha/2, 2*sz_s(1))]; endif else ## input validation for c and f if (isempty (c)) ##expand to full c with values that don't affect results c = zeros (sz_s); elseif (! (isnumeric(c) || islogical (c))) #check for incorrect f type error ("expfit: C must be a numeric or logical array") elseif (isvector (c)) ## guarantee working with a column vector c = c(:); endif if (isempty (f)) ##expand to full c with values that don't affect results f = ones (sz_s); elseif (! (isnumeric(f) || islogical (f))) #check for incorrect f type error ("expfit: F must be a numeric or logical array") elseif (isvector (f)) ## guarantee working with a column vector f = f(:); endif #check that size of c and f match s if !(isequal(size (c), sz_s)) error("expfit: C must be the same size as S"); elseif (! isequal(size (f), sz_s)) error("expfit: F must be the same size as S"); endif ## trivial case where c and f have no effect if (all (c(:) == 0 & f(:) == 1)) m = mean (s, 1); if (nargout == 2) S = sum (s, 1); v = [2*S ./ chi2inv(1 - alpha/2, 2*sz_s(1));... 2*S ./ chi2inv(alpha/2, 2*sz_s(1))]; endif ## no censoring, just adjust sample counts for f elseif (all (c(:) == 0)) S = sum (s.*f, 1); n = sum (f, 1); m = S ./ n; if (nargout == 2) v = [2*S ./ chi2inv(1 - alpha/2, 2*n);... 2*S ./ chi2inv(alpha/2, 2*n)]; endif ## censoring, but no sample counts adjustment elseif (all (f(:) == 1)) c = logical(c); ##convert any numeric c's to 0s and 1s S = sum (s, 1); r = sz_s(1) - sum (c, 1); m = S ./ r; if (nargout == 2) v = [2*S ./ chi2inv(1 - alpha/2, 2*r);... 2*S ./ chi2inv(alpha/2, 2*r)]; endif ## both censoring and sample count adjustment else c = logical(c); ##convert any numeric c's to 0s and 1s S = sum (s.*f , 1); r = sum (f.*(!c), 1); m = S ./ r; if (nargout == 2) v = [2*S ./ chi2inv(1 - alpha/2, 2*r);... 2*S ./ chi2inv(alpha/2, 2*r)]; endif endif ## compatibility check, NaN for columns where all c's or f's remove all samples null_columns = all (c) | ! all (f); m(null_columns) = NaN; if (nargout == 2) v(:,null_columns) = NaN; endif endif endfunction ##tests for mean %!assert (expfit (1), 1) %!assert (expfit (1:3), 2) %!assert (expfit ([1:3]'), 2) %!assert (expfit (1:3, []), 2) %!assert (expfit (1:3, [], [], []), 2) %!assert (expfit (magic (3)), [5 5 5]) %!assert (expfit (cat (3, magic (3), 2*magic (3))), cat (3,[5 5 5], [10 10 10])) %!assert (expfit (1:3, 0.1, [0 0 0], [1 1 1]), 2) %!assert (expfit ([1:3]', 0.1, [0 0 0]', [1 1 1]'), 2) %!assert (expfit (1:3, 0.1, [0 0 0]', [1 1 1]'), 2) %!assert (expfit (1:3, 0.1, [1 0 0], [1 1 1]), 3) %!assert (expfit (1:3, 0.1, [0 0 0], [4 1 1]), 1.5) %!assert (expfit (1:3, 0.1, [1 0 0], [4 1 1]), 4.5) %!assert (expfit (1:3, 0.1, [1 0 1], [4 1 1]), 9) %!assert (expfit (1:3, 0.1, [], [-1 1 1]), 4) %!assert (expfit (1:3, 0.1, [], [0.5 1 1]), 2.2) %!assert (expfit (1:3, 0.1, [1 1 1]), NaN) %!assert (expfit (1:3, 0.1, [], [0 0 0]), NaN) %!assert (expfit (reshape (1:9, [3 3])), [2 5 8]) %!assert (expfit (reshape (1:9, [3 3]), [], eye(3)), [3 7.5 12]) %!assert (expfit (reshape (1:9, [3 3]), [], 2*eye(3)), [3 7.5 12]) %!assert (expfit (reshape (1:9, [3 3]), [], [], [2 2 2; 1 1 1; 1 1 1]), [1.75 4.75 7.75]) %!assert (expfit (reshape (1:9, [3 3]), [], [], [2 2 2; 1 1 1; 1 1 1]), [1.75 4.75 7.75]) %!assert (expfit (reshape (1:9, [3 3]), [], eye(3), [2 2 2; 1 1 1; 1 1 1]), [3.5 19/3 31/3]) ##tests for confidence intervals %!assert ([~,v] = expfit (1:3, 0), [0; Inf]) %!assert ([~,v] = expfit (1:3, 2), [Inf; 0]) %!assert ([~,v] = expfit (1:3, 0.1, [1 1 1]), [NaN; NaN]) %!assert ([~,v] = expfit (1:3, 0.1, [], [0 0 0]), [NaN; NaN]) %!assert ([~,v] = expfit (1:3, -1), [NaN; NaN]) %!assert ([~,v] = expfit (1:3, 5), [NaN; NaN]) #!assert ([~,v] = expfit ([1:3;1:3], -1), NaN(2, 3)] #!assert ([~,v] = expfit ([1:3;1:3], 5), NaN(2, 3)] %!assert ([~,v] = expfit (1:3), [0.830485728373393; 9.698190330474096], 1000*eps) %!assert ([~,v] = expfit (1:3, 0.1), [0.953017262058213; 7.337731146400207], 1000*eps) %!assert ([~,v] = expfit ([1:3;2:4]), ... %! [0.538440777613095, 0.897401296021825, 1.256361814430554; ... %! 12.385982973214016, 20.643304955356694, 28.900626937499371], 1000*eps) %!assert ([~,v] = expfit ([1:3;2:4], [], [1 1 1; 0 0 0]), ... %! 100*[0.008132550920455, 0.013554251534091, 0.018975952147727; ... %! 1.184936706156216, 1.974894510260360, 2.764852314364504], 1000*eps) %!assert ([~,v] = expfit ([1:3;2:4], [], [], [3 3 3; 1 1 1]), ... %! [0.570302756652583, 1.026544961974649, 1.482787167296715; ... %! 4.587722594914109, 8.257900670845396, 11.928078746776684], 1000*eps) %!assert ([~,v] = expfit ([1:3;2:4], [], [0 0 0; 1 1 1], [3 3 3; 1 1 1]), ... %! [0.692071440311161, 1.245728592560089, 1.799385744809018; ... %! 8.081825275395081, 14.547285495711145, 21.012745716027212], 1000*eps) %!test %! s = reshape (1:8, [4 2]); %! s(4) = NaN; %! [m,v] = expfit (s); %! assert ({m, v}, {[NaN, 6.5], [NaN, 2.965574334593430;NaN, 23.856157493553368]}, 1000*eps); %!test %! s = magic (3); %! c = [0 1 0; 0 1 0; 0 1 0]; %! f = [1 1 0; 1 1 0; 1 1 0]; %! [m,v] = expfit (s, [], c, f); %! assert ({m, v}, {[5 NaN NaN], [[2.076214320933482; 24.245475826185242],NaN(2)]}, 1000*eps); ## input validation %!error expfit () %!error expfit (1,2,3,4,5) %!error [a b c] = expfit (1) %!error expfit (1, [1 2]) %!error expfit ([-1 2 3 4 5]) %!error expfit ([1:5], [], "test") %!error expfit ([1:5], [], [], "test") %!error expfit ([1:5], [], [0 0 0 0]) %!error expfit ([1:5], [], [], [1 1 1 1]) statistics-1.4.3/inst/explike.m0000644000000000000000000000475514153320774014714 0ustar0000000000000000## Copyright (C) 2021 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{nlogL}, @var{avar} =} explike (@var{param}, @var{data}) ## Compute the negative log-likelihood of data under the exponential distribution with given parameter value. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{param} is a scalar containing the scale parameter of the exponential distribution (equal to its mean). ## @item ## @var{data} is the vector of given values. ## ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{nlogL} is the negative log-likelihood. ## @item ## @var{avar} is the inverse of the Fisher information matrix. ## (The Fisher information matrix is the second derivative of the negative log likelihood with respect to the parameter value.) ## ## @end itemize ## ## @seealso{expcdf, expfit, expinv, explike, exppdf, exprnd} ## @end deftypefn ## Author: Nir Krakauer ## Description: Negative log-likelihood for the exponential distribution function [nlogL, avar] = explike (param, data) # Check arguments if (nargin != 2) print_usage; endif beta = param(1); n = numel (data); sx = sum (data(:)); sxb = sx/beta; #calculate negative log likelihood nlogL = sxb + n*log(beta); #optionally calculate the inverse (reciprocal) of the second derivative of the negative log likelihood with respect to parameter if nargout > 1 avar = (beta^2) ./ (2*sxb - n); endif endfunction %!test %! x = 12; %! beta = 5; %! [L, V] = explike (beta, x); %! expected_L = 4.0094; %! expected_V = 6.5789; %! assert (L, expected_L, 0.001); %! assert (V, expected_V, 0.001); %!test %! x = 1:5; %! beta = 2; %! [L, V] = explike (beta, x); %! expected_L = 10.9657; %! expected_V = 0.4; %! assert (L, expected_L, 0.001); %! assert (V, expected_V, 0.001); statistics-1.4.3/inst/expstat.m0000644000000000000000000000457614153320774014744 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} expstat (@var{l}) ## Compute mean and variance of the exponential distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{l} is the parameter of the exponential distribution. The ## elements of @var{l} must be positive ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the exponential distribution ## ## @item ## @var{v} is the variance of the exponential distribution ## @end itemize ## ## @subheading Example ## ## @example ## @group ## l = 1:6; ## [m, v] = expstat (l) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @seealso{expcdf, expfit, expinv, explike, exppdf, exprnd} ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the exponential distribution function [m, v] = expstat (l) # Check arguments if (nargin != 1) print_usage (); endif if (! isempty (l) && ! ismatrix (l)) error ("expstat: l must be a numeric matrix"); endif # Calculate moments m = l; v = m .^ 2; # Continue argument check k = find (! (l > 0) | ! (l < Inf)); if (any (k)) m(k) = NaN; v(k) = NaN; endif endfunction %!test %! l = 1:6; %! [m, v] = expstat (l); %! assert (m, [1, 2, 3, 4, 5, 6], 0.001); %! assert (v, [1, 4, 9, 16, 25, 36], 0.001); statistics-1.4.3/inst/ff2n.m0000644000000000000000000000047614153320774014102 0ustar0000000000000000## Author: Paul Kienzle ## This program is granted to the public domain. ## -*- texinfo -*- ## @deftypefn {Function File} ff2n (@var{n}) ## Full-factor design with n binary terms. ## ## @seealso {fullfact} ## @end deftypefn function A=ff2n(n) A = fullfact (2 * ones (1,n)) - 1; endfunction statistics-1.4.3/inst/fisheriris.mat0000644000000000000000000000231014153320774015730 0ustar0000000000000000MATLAB 5.0 MAT-file, written by Octave 4.2.1, 2021-01-16 21:04:21 UTC IM‰xœ—ÍNSQÇ/p -¼m¡@ùđ!|ú*.tçÊw1Ñ7qç–DW®Ø™ø%ƒ‘Kçüæd₫‡#Ü„ óq₫óŸ™û1Ưkf1nÍ¥́7&×–½¤X₫µ+[Û¼{óúư`ùÿ—eüÛƠµ?ÿôñá̀¿}}¸Æs³çÍêÂP±üwûs"u;?Íë̀óÂoúY’/…g³æ‰|3/̣£SŸ̃:×X÷‘Ü¿Ă$ûÉ>Hqư$‡ çE’;"·<̃ÎïºÜ(;®Á…‡ơcÏ%8àÂÇüÛE¨å|® »átÉ̃IÇ!o-á¬稃sèÄQơD{æ ¾ÉM‘ôaĂçaç{)o#ó]ó8_Œëy¼Ù[çE~́èàÅz7]ùZá½!y{rn§èG¼¯ZÇÅ磸[»-ú[;÷øưƯxÜ?q¾½âyă}”ïêa.:x¾WÜW:ŸĂŒ«ưƠ¹Ä¾—2Îwàü´ùư¾@î¯ óߺƯÎưu]ưèHăóÇư¦_'œ#ŸæÁ¯ºÉ…đ¹÷|HåWó×ꀧ̣Ó₫ «Œơß̉ßW¦_^¨y°Ó‡¨gœ˜_u•Í\¿¯àÄưúVæºî|k¸Zø‘w[øcŸr₫Ơ Óʯxœí̀= Â@ÅñđI!^Ă;XzY•D¬=…çÍ˲ l#¿x;³3̀¯–ôØI3×…SåLóÿù6›;ư5´1ôªƯïơº›wŨUy¿ïtÓŵIsœÿsœUál»ÎJTkíätxxxxxxxxxxxxxxx?ô–…·I^´pô{Nf“÷xxxxxxxxxxxxxxxß{̀`jöstatistics-1.4.3/inst/fisheriris.txt0000644000000000000000000000414214153320774015773 0ustar0000000000000000#Fisher iris data set #cf. https://en.wikipedia.org/wiki/Iris_flower_data_set #Type PW PL SW SL 0 2 14 33 50 1 24 56 31 67 1 23 51 31 69 0 2 10 36 46 1 20 52 30 65 1 19 51 27 58 2 13 45 28 57 2 16 47 33 63 1 17 45 25 49 2 14 47 32 70 0 2 16 31 48 1 19 50 25 63 0 1 14 36 49 0 2 13 32 44 2 12 40 26 58 1 18 49 27 63 2 10 33 23 50 0 2 16 38 51 0 2 16 30 50 1 21 56 28 64 0 4 19 38 51 0 2 14 30 49 2 10 41 27 58 2 15 45 29 60 0 2 14 36 50 1 19 51 27 58 0 4 15 34 54 1 18 55 31 64 2 10 33 24 49 0 2 14 42 55 1 15 50 22 60 2 14 39 27 52 0 2 14 29 44 2 12 39 27 58 1 23 57 32 69 2 15 42 30 59 1 20 49 28 56 1 18 58 25 67 2 13 44 23 63 2 15 49 25 63 2 11 30 25 51 1 21 54 31 69 1 25 61 36 72 2 13 36 29 56 1 21 55 30 68 0 1 14 30 48 0 3 17 38 57 2 14 44 30 66 0 4 15 37 51 2 17 50 30 67 1 22 56 28 64 1 15 51 28 63 2 15 45 22 62 2 14 46 30 61 2 11 39 25 56 1 23 59 32 68 1 23 54 34 62 1 25 57 33 67 0 2 13 35 55 2 15 45 32 64 1 18 51 30 59 1 23 53 32 64 2 15 45 30 54 1 21 57 33 67 0 2 13 30 44 0 2 16 32 47 1 18 60 32 72 1 18 49 30 61 0 2 12 32 50 0 1 11 30 43 2 14 44 31 67 0 2 14 35 51 0 4 16 34 50 2 10 35 26 57 1 23 61 30 77 2 13 42 26 57 0 1 15 41 52 1 18 48 30 60 2 13 42 27 56 0 2 15 31 49 0 4 17 39 54 2 16 45 34 60 2 10 35 20 50 0 2 13 32 47 2 13 54 29 62 0 2 15 34 51 2 10 50 22 60 0 1 15 31 49 0 2 15 37 54 2 12 47 28 61 2 13 41 28 57 0 4 13 39 54 1 20 51 32 65 2 15 49 31 69 2 13 40 25 55 0 3 13 23 45 0 3 15 38 51 2 14 48 28 68 0 2 15 35 52 1 25 60 33 63 2 15 46 28 65 0 3 14 34 46 2 18 48 32 59 2 16 51 27 60 1 18 55 30 65 0 5 17 33 51 1 22 67 38 77 1 21 66 30 76 1 13 52 30 67 2 13 40 28 61 2 11 38 24 55 0 2 14 34 52 1 20 64 38 79 0 6 16 35 50 1 20 67 28 77 2 12 44 26 55 0 3 14 30 48 0 2 19 34 48 1 14 56 26 61 0 2 12 40 58 1 18 48 28 62 2 15 45 30 56 0 2 14 32 46 0 4 15 44 57 1 24 56 34 63 1 16 58 30 72 1 21 59 30 71 1 18 56 29 63 2 12 42 30 57 1 23 69 26 77 2 13 56 29 66 0 2 15 34 52 2 10 37 24 55 0 2 15 31 46 1 19 61 28 74 0 3 13 35 50 1 18 63 29 73 2 15 47 31 67 2 13 41 30 56 2 13 43 29 64 1 22 58 30 65 0 3 14 35 51 2 14 47 29 61 1 19 53 27 64 0 2 16 34 48 1 20 50 25 57 2 13 40 23 55 0 2 17 34 54 1 24 51 28 58 0 2 15 37 53 statistics-1.4.3/inst/fitgmdist.m0000644000000000000000000004360014153320774015235 0ustar0000000000000000## Copyright (C) 2018 John Donoghue ## Copyright (C) 2015 Lachlan Andrew ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{GMdist} =} fitgmdist (@var{data}, @var{k}, @var{param1}, @var{value1}, @dots{}) ## Fit a Gaussian mixture model with @var{k} components to @var{data}. ## Each row of @var{data} is a data sample. Each column is a variable. ## ## Optional parameters are: ## @itemize ## @item 'start': initialization conditions. Possible values are: ## @itemize ## @item 'randSample' (default) takes means uniformly from rows of data ## @item 'plus' use k-means++ to initialize means ## @item 'cluster' Performs an initial clustering with 10% of the data ## @item vector A vector whose length is the number of rows in data, ## and whose values are 1 to k specify the components ## each row is initially allocated to. The mean, variance ## and weight of each component is calculated from that ## @item structure with elements mu, Sigma ComponentProportion ## @end itemize ## For 'randSample', 'plus' and 'cluster', the initial variance of each ## component is the variance of the entire data sample. ## ## @item 'Replicates' Number of random restarts to perform ## ## @item 'RegularizationValue' ## @item 'Regularize' A small number added to the diagonal entries ## of the covariance to prevent singular covariances ## ## @item 'SharedCovariance' ## @item 'SharedCov' (logical) True if all components must share the ## same variance, to reduce the number of free parameters ## ## @item 'CovarianceType' ## @item 'CovType' (string). Possible values are: ## @itemize ## @item 'full' (default) Allow arbitrary covariance matrices ## @item 'diagonal' Force covariances to be diagonal, to reduce the ## number of free parameters. ## @end itemize ## ## @item 'Option' A structure with all of the following fields: ## @itemize ## @item 'MaxIter' Maximum number of EM iterations (default 100) ## @item 'TolFun' Threshold increase in likelihood to terminate EM ## (default 1e-6) ## @item 'Display' ## @itemize ## @item 'off' (default): display nothing ## @item 'final': display the number of iterations and likelihood ## once execution completes ## @item 'iter': display the above after each iteration ## @end itemize ## @end itemize ## @item 'Weight' A column vector or n-by-2 matrix. The first column ## consists of non-negative weights given to the ## samples. ## If these are all integers, this is equivalent ## to specifying @var{weight}(i) copies of row i of ## @var{data}, but potentially faster. ## ## If a row of @var{data} is used to represent samples ## that are similar but not identical, then the second ## column of @var{weight} indicates the variance of ## those original samples. Specifically, in the EM ## algorithm, the contribution of row i towards the ## variance is set to at least @var{weight}(i,2), to ## prevent spurious components with zero variance. ## @end itemize ## ## @seealso{gmdistribution, kmeans} ## @end deftypefn function obj = fitgmdist(data, k, varargin) if nargin < 2 || mod (nargin, 2) == 1 print_usage; endif [~, prop] = parseparams (varargin); ## defaults for options diagonalCovar = false; # "full". (true is "diagonal") sharedCovar = false; start = "randSample"; replicates = 1; option.MaxIter= 100; option.TolFun = 1e-6; option.Display= "off"; # "off" (1 is "final", 2 is "iter") Regularizer = 0; weights = []; # Each row i counts as "weights(i,1)" rows # Remove rows containing NaN / NA data = data(!any (isnan (data), 2),:); # used for getting the number of samples nRows = rows (data); nCols = columns (data); # Parse options while (!isempty (prop)) try switch (lower (prop{1})) case {"sharedcovariance",... "sharedcov"}, sharedCovar = prop{2}; case {"covariancetype",... "covartype"}, diagonalCovar = prop{2}; case {"regularizationvalue",... "regularize"}, Regularizer = prop{2}; case "replicates", replicates = prop{2}; case "start", start = prop{2}; case "weights", weights = prop{2}; case "option" option.MaxIter = prop{2}.MaxIter; option.TolFun = prop{2}.TolFun; option.Display = prop{2}.Display; otherwise error ("fitgmdist: Unknown option %s", prop{1}); endswitch catch ME if (length (prop) < 2) error ("fitgmdist: Option '%s' has no argument", prop{1}); else rethrow (ME) endif end_try_catch prop = prop(3:end); endwhile # Process options # check for the "replicates" property try if isempty (1:replicates) error ("fitgmdist: replicates must be positive"); endif catch error ("fitgmdist: invalid number of replicates"); end_try_catch # check for the "option" property MaxIter = option.MaxIter; TolFun = option.TolFun; switch (lower (option.Display)) case "off", Display = 0; case "final", Display = 1; case "iter", Display = 2; case "notify", Display = 0; otherwise, error ("fitgmdist: Unknown Display option %s", option.Display); endswitch try p = ones(1, k) / k; # Default is uniform component proportions catch ME if (!isscalar (k) || !isnumeric (k)) error ("fitgmdist: The second argument must be a numeric scalar"); else rethrow (ME) endif end_try_catch # check for the "start" property if (ischar (start)) start = lower (start); switch (start) case {"randsample", "plus", "cluster", "randsamplep", "plusp", "clusterp"} otherwise error ("fitgmdist: Unknown Start value %s\n", start); endswitch component_order_free = true; else component_order_free = false; if (!ismatrix (start) || !isnumeric (start)) try mu = start.mu; Sigma = start.Sigma; if (isfield (start, 'ComponentProportion')) p = start.ComponentProportion(:)'; end if (any (size (data, 2) ~= [size(mu,2), size(Sigma)]) || ... any (k ~= [size(mu,1), size(p,2)])) error ('fitgmdist: Start parameter has mismatched dimensions'); endif catch error ("fitgmdist: invalid start parameter"); end_try_catch else validIndices = 0; mu = zeros (k, nRows); Sigma = zeros (nRows, nRows, k); for i = 1:k idx = (start == i); validIndices = validIndices + sum (idx); mu(i,:) = mean (data(idx,:)); Sigma(:,:,i) = cov (data(idx,:)) + Regularizer*eye (nCols); endfor if (validIndices < nRows) error ("fitgmdist: Start is numeric, but is not integers between 1 and k"); endif endif start = []; # so that variance isn't recalculated later replicates = 1; # Will be the same each time anyway endif # check for the "SharedCovariance" property if (!islogical (sharedCovar)) error ("fitgmdist: SharedCoveriance must be logical true or false"); endif # check for the "CovarianceType" property if (!islogical (diagonalCovar)) try if (strcmpi (diagonalCovar, "diagonal")) diagonalCovar = true; elseif (strcmpi (diagonalCovar, "full")) diagonalCovar = false; else error ("fitgmdist: CovarianceType must be Full or Diagonal"); endif catch error ("fitgmdist: CovarianceType must be 'Full' or 'Diagonal'"); end_try_catch endif # check for the "Regularizer" property try if (Regularizer < 0) error ("fitgmdist: Regularizer must be non-negative"); endif catch ME if (!isscalar (Regularizer) || !isnumeric (Regularizer)) error ("fitgmdist: Regularizer must be a numeric scalar"); else rethrow (ME) endif end_try_catch # check for the "Weights" property and the matrix try if (!isempty (weights)) if (columns (weights) > 2 || any (weights(:) < 0)) error ("fitgmdist: weights must be a nonnegative numeric dx1 or dx2 matrix"); endif if (rows (weights) != nRows) error ("fitgmdist: number of weights %d must match number of samples %d",... rows (weights), nRows) endif non_zero = (weights(:,1) > 0); weights = weights(non_zero,:); data = data (non_zero,:); nRows = rows (data); raw_samples = sum (weights(:,1)); else raw_samples = nRows; endif # Validate the matrix if (!isreal (data(k,1))) error ("fitgmdist: first input argument must be a DxN real data matrix"); endif catch ME if (!isnumeric (data) || !ismatrix (data) || !isreal (data)) error ("fitgmdist: first input argument must be a DxN real data matrix"); elseif (k > nRows || k < 0) if (exists("non_zero", "var") && k <= length(non_zero)) error ("fitgmdist: The number of non-zero weights (%d) must be at least the number of components (%d)", nRows, k); else error ("fitgmdist: The number of components (%d) must be a positive number less than the number of data rows (%d)", k, nRows); endif elseif (!ismatrix (weights) || !isnumeric (weights)) error ("fitgmdist: weights must be a nonnegative numeric dx1 or dx2 matrix"); else rethrow (ME) endif end_try_catch #if k == 1 # replicates = 1; #endif # Done processing options ####################################### # used to hold the probability of each class, given each data vector try p_x_l = zeros (nRows, k); # probability of observation x given class l best = -realmax; best_params = []; diag_slice = 1:(nCols+1):(nCols)^2; # Create index slices to calculate symmetric completion of upper triangular Mx lower_half = zeros(nCols*(nCols-1)/2,1); upper_half = zeros(nCols*(nCols-1)/2,1); i = 1; for rw = 1:nCols for cl = rw+1:nCols upper_half(i) = sub2ind([nCols, nCols], rw, cl); lower_half(i) = sub2ind([nCols, nCols], cl, rw); i = i + 1; endfor endfor for rep = 1:replicates if (!isempty (start)) # Initialize the means switch (start) case {"randsample"} if (isempty (weights)) idx = randperm (nRows, k); else idx = randsample (nRows, k, false, weights); endif mu = data(idx, :); case {"plus"} # k-means++, by Arthur and Vassilios mu(1,:) = data(randi (nRows),:); d = inf (nRows, 1); # Distance to nearest centroid so far for i = 2:k d = min (d, sum (bsxfun (@minus, data, mu(i-1, :)).^2, 2)); # pick next sample with prob. prop to dist.*weights if (isempty (weights)) cs = cumsum (d); else cs = cumsum (d .* weights(:,1)); endif mu(i,:) = data(find (cs > rand * cs(end), 1), :); endfor case {"cluster"} subsamp = max (k, ceil (nRows/10)); if (isempty (weights)) idx = randperm (nRows, subsamp); else idx = randsample (nRows, subsamp, false, weights); endif [~, mu] = kmeans (data(idx), k, "start", "sample"); endswitch # Initialize the variance, unless set explicitly # Sigma = var (data) + Regularizer; if (!diagonalCovar) Sigma = diag (Sigma); endif if (!sharedCovar) Sigma = repmat (Sigma, [1, 1, k]); endif endif # Run the algorithm iter = 1; log_likeli = -inf; incr = 1; while (incr > TolFun && iter <= MaxIter) iter = iter + 1; ####################################### # "E step" # Calculate probability of class l given observations for i = 1:k if (sharedCovar) sig = Sigma; else sig = Sigma(:,:,i); endif if (diagonalCovar) sig = diag(sig); endif try p_x_l (:, i) = mvnpdf (data, mu(i, :), sig); catch ME if (strfind (ME.message, "positive definite")) error ("fitgmdist: Covariance is not positive definite. Increase RegularizationValue"); else rethrow (ME) endif end_try_catch endfor # Bayes' rule p_x_l = bsxfun (@times, p_x_l, p); # weight by priors p_l_x = bsxfun (@rdivide, p_x_l, sum (p_x_l, 2)); # Normalize ####################################### # "M step" # Calculate new parameters if (!isempty (weights)) p_l_x = bsxfun (@times, p_l_x, weights(:,1)); endif sum_p_l_x = sum(p_l_x); # row vec of \sum_{data} p(class|data,params) p = sum_p_l_x / raw_samples; # new proportions mu = bsxfun(@rdivide, p_l_x' * data, sum_p_l_x'); # new means if (sharedCovar) sumSigma = zeros (size (Sigma(:,:,1))); # diagonalCovar gives size endif for i = 1:k # Sigma deviation = bsxfun(@minus, data, mu(i,:)); lhs = bsxfun(@times, p_l_x(:,i), deviation); # Calculate covariance # Iterate either over elements of the covariance matrix, since # there should be fewer of those than rows of data. for rw = 1:nCols for cl = rw:nCols sig(rw,cl) = lhs(:,rw)' * deviation(:,cl); endfor endfor sig(lower_half) = sig(upper_half); sig = sig/sum_p_l_x(i) + Regularizer*eye (nCols); if (columns (weights) > 1) # don't give "singleton" clusters low var sig(diag_slice) = max (sig(diag_slice), weights(i,2)); endif if (diagonalCovar) sig = diag(sig)'; endif if (sharedCovar) sumSigma = sumSigma + sig * p(i); # Heuristic. Should it use else # old p? Something else? Sigma(:,:,i) = sig; endif endfor if (sharedCovar) Sigma = sumSigma; endif ####################################### # calculate the new (and relative change in) log-likelihood if (isempty (weights)) new_log_likeli = sum (log (sum (p_x_l, 2))); else new_log_likeli = sum (weights(:,1) .* log (sum (p_x_l, 2))); endif incr = (new_log_likeli - log_likeli)/max(1,abs(new_log_likeli)); if Display == 2 fprintf("iter %d log-likelihood %g\n", iter-1, new_log_likeli); %disp(mu); endif log_likeli = new_log_likeli; endwhile if (log_likeli > best) best = log_likeli; best_params.mu = mu; best_params.Sigma = Sigma; best_params.p = p; endif endfor catch ME try if (1 < MaxIter), end catch error ("fitgmdist: invalid MaxIter"); end_try_catch rethrow (ME) end_try_catch # List components in descending order of proportion, # unless the order was implicitly specified by "start" if (component_order_free) [~, idx] = sort (-best_params.p); best_params.p = best_params.p (idx); best_params.mu = best_params.mu(idx,:); if (!sharedCovar) best_params.Sigma = best_params.Sigma(:,:,idx); endif endif # Calculate number of parameters if (diagonalCovar) params = nCols; else params = nCols * (nCols+1) / 2; endif params = params*size (Sigma, 3) + 2*rows (mu) - 1; # This works in Octave, but not in Matlab #obj = gmdistribution (best_params.mu, best_params.Sigma, best_params.p', extra); obj = gmdistribution (best_params.mu, best_params.Sigma, best_params.p'); obj.NegativeLogLikelihood = -best; obj.AIC = -2*(best - params); obj.BIC = -2*best + params * log (raw_samples); obj.Converged = (incr <= TolFun); obj.NumIterations = iter-1; obj.RegularizationValue = Regularizer; if (Display == 1) fprintf (" %d iterations log-likelihood = %g\n", ... obj.NumIterations, -obj.NegativeLogLikelihood); endif endfunction %!xdemo <50286> %! ## Generate a two-cluster problem %! C1 = randn (100, 2) + 1; %! C2 = randn (100, 2) - 1; %! data = [C1; C2]; %! %! ## Perform clustering %! GMModel = fitgmdist (data, 2); %! %! ## Plot the result %! figure %! [heights, bins] = hist3([C1; C2]); %! [xx, yy] = meshgrid(bins{1}, bins{2}); %! bbins = [xx(:), yy(:)]; %! contour (reshape (GMModel.pdf (bbins), heights)); %! hold on %! plot (centers (:, 1), centers (:, 2), "kv", "markersize", 10); %! hold off statistics-1.4.3/inst/fstat.m0000644000000000000000000000672414153320774014372 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mn}, @var{v}] =} fstat (@var{m}, @var{n}) ## Compute mean and variance of the F distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{m} is the first parameter of the F distribution. The elements ## of @var{m} must be positive ## ## @item ## @var{n} is the second parameter of the F distribution. The ## elements of @var{n} must be positive ## @end itemize ## @var{m} and @var{n} must be of common size or one of them must be scalar ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{mn} is the mean of the F distribution. The mean is undefined for ## @var{n} not greater than 2 ## ## @item ## @var{v} is the variance of the F distribution. The variance is undefined ## for @var{n} not greater than 4 ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## m = 1:6; ## n = 5:10; ## [mn, v] = fstat (m, n) ## @end group ## ## @group ## [mn, v] = fstat (m, 5) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the F distribution function [mn, v] = fstat (m, n) # Check arguments if (nargin != 2) print_usage (); endif if (! isempty (m) && ! ismatrix (m)) error ("fstat: m must be a numeric matrix"); endif if (! isempty (n) && ! ismatrix (n)) error ("fstat: n must be a numeric matrix"); endif if (! isscalar (m) || ! isscalar (n)) [retval, m, n] = common_size (m, n); if (retval > 0) error ("fstat: m and n must be of common size or scalar"); endif endif # Calculate moments mn = n ./ (n - 2); v = (2 .* (n .^ 2) .* (m + n - 2)) ./ (m .* ((n - 2) .^ 2) .* (n - 4)); # Continue argument check k = find (! (m > 0) | ! (m < Inf) | ! (n > 2) | ! (n < Inf)); if (any (k)) mn(k) = NaN; v(k) = NaN; endif k = find (! (n > 4)); if (any (k)) v(k) = NaN; endif endfunction %!test %! m = 1:6; %! n = 5:10; %! [mn, v] = fstat (m, n); %! expected_mn = [1.6667, 1.5000, 1.4000, 1.3333, 1.2857, 1.2500]; %! expected_v = [22.2222, 6.7500, 3.4844, 2.2222, 1.5869, 1.2153]; %! assert (mn, expected_mn, 0.001); %! assert (v, expected_v, 0.001); %!test %! m = 1:6; %! [mn, v] = fstat (m, 5); %! expected_mn = [1.6667, 1.6667, 1.6667, 1.6667, 1.6667, 1.6667]; %! expected_v = [22.2222, 13.8889, 11.1111, 9.7222, 8.8889, 8.3333]; %! assert (mn, expected_mn, 0.001); %! assert (v, expected_v, 0.001); statistics-1.4.3/inst/fullfact.m0000644000000000000000000000140414153320774015037 0ustar0000000000000000## Author: Paul Kienzle ## This program is granted to the public domain. ## -*- texinfo -*- ## @deftypefn {Function File} fullfact (@var{N}) ## Full factorial design. ## ## If @var{N} is a scalar, return the full factorial design with @var{N} binary ## choices, 0 and 1. ## ## If @var{N} is a vector, return the full factorial design with choices 1 ## through @var{n_i} for each factor @var{i}. ## ## @end deftypefn function A = fullfact(n) if length(n) == 1 % combinatorial design with n either/or choices A = fullfact(2*ones(1,n))-1; else % combinatorial design with n(i) choices per level A = [1:n(end)]'; for i=length(n)-1:-1:1 A = [kron([1:n(i)]',ones(rows(A),1)), repmat(A,n(i),1)]; end end endfunction statistics-1.4.3/inst/gamfit.m0000644000000000000000000000453514153320774014516 0ustar0000000000000000 ## -*- texinfo -*- ## @deftypefn {Function File} {@var{MLE} =} gamfit (@var{data}) ## Calculate gamma distribution parameters. ## ## Find the maximum likelihood estimate parameters of the Gamma distribution ## of @var{data}. @var{MLE} is a two element vector with shape parameter ## @var{A} and scale @var{B}. ## ## @seealso{gampdf, gaminv, gamrnd, gamlike} ## @end deftypefn ## This function works by minimizing the value of gamlike for the vector R. ## Just about any minimization function will work, all it has to do is ## minimize for one variable. Although the gamma distribution has two ## parameters, their product is the mean of the data. so a helper function ## for the search takes one parameter, calculates the other and then returns ## the value of gamlike. ## Author: Martijn van Oosterhout ## This program is granted to the public domain. # Revisions copyright (C) 2019 by Nir Krakauer under GPL (below). # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program; If not, see . function res = gamfit(R) if (nargin != 1) print_usage; endif avg = mean(R); # Optimize with respect to log(a), since both a and b must be positive x = fminsearch( @(x) gamfit_search(x, avg, R), 0 ); a = exp(x); b = avg/a; res = [a b]; endfunction # Helper function so we only have to minimize for one variable. function res = gamfit_search( x, avg, R ) a = exp(x); b = avg/a; res = gamlike([a b], R); endfunction #example data from https://www.real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-gamma-parameters-mle/ %!shared v, res %! v = [1.2 1.6 1.7 1.8 1.9 2.0 2.2 2.6 3.0 3.5 4.0 4.8 5.6 6.6 7.6]; %! res = gamfit(v); %!assert (res(1), 3.425, 1E-3); %!assert (res(2), 0.975, 1E-3); statistics-1.4.3/inst/gamlike.m0000644000000000000000000000106114153320774014647 0ustar0000000000000000## Author: Martijn van Oosterhout ## This program is granted to the public domain. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{X} =} gamlike ([@var{A} @var{B}], @var{R}) ## Calculates the negative log-likelihood function for the Gamma ## distribution over vector @var{R}, with the given parameters @var{A} and @var{B}. ## @seealso{gampdf, gaminv, gamrnd, gamfit} ## @end deftypefn function res = gamlike(P,K) if (nargin != 2) print_usage; endif a=P(1); b=P(2); res = -sum( log( gampdf(K, a, b) ) ); endfunction statistics-1.4.3/inst/gamstat.m0000644000000000000000000000627614153320774014713 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} gamstat (@var{a}, @var{b}) ## Compute mean and variance of the gamma distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{a} is the first parameter of the gamma distribution. @var{a} must be ## positive ## ## @item ## @var{b} is the second parameter of the gamma distribution. @var{b} must be ## positive ## @end itemize ## @var{a} and @var{b} must be of common size or one of them must be scalar ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the gamma distribution ## ## @item ## @var{v} is the variance of the gamma distribution ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## a = 1:6; ## b = 1:0.2:2; ## [m, v] = gamstat (a, b) ## @end group ## ## @group ## [m, v] = gamstat (a, 1.5) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the gamma distribution function [m, v] = gamstat (a, b) # Check arguments if (nargin != 2) print_usage (); endif if (! isempty (a) && ! ismatrix (a)) error ("gamstat: a must be a numeric matrix"); endif if (! isempty (b) && ! ismatrix (b)) error ("gamstat: b must be a numeric matrix"); endif if (! isscalar (a) || ! isscalar (b)) [retval, a, b] = common_size (a, b); if (retval > 0) error ("gamstat: a and b must be of common size or scalar"); endif endif # Calculate moments m = a .* b; v = a .* (b .^ 2); # Continue argument check k = find (! (a > 0) | ! (a < Inf) | ! (b > 0) | ! (b < Inf)); if (any (k)) m(k) = NaN; v(k) = NaN; endif endfunction %!test %! a = 1:6; %! b = 1:0.2:2; %! [m, v] = gamstat (a, b); %! expected_m = [1.00, 2.40, 4.20, 6.40, 9.00, 12.00]; %! expected_v = [1.00, 2.88, 5.88, 10.24, 16.20, 24.00]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); %!test %! a = 1:6; %! [m, v] = gamstat (a, 1.5); %! expected_m = [1.50, 3.00, 4.50, 6.00, 7.50, 9.00]; %! expected_v = [2.25, 4.50, 6.75, 9.00, 11.25, 13.50]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); statistics-1.4.3/inst/geomean.m0000644000000000000000000000214714153320774014657 0ustar0000000000000000## Copyright (C) 2001 Paul Kienzle ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} geomean (@var{x}) ## @deftypefnx{Function File} geomean (@var{x}, @var{dim}) ## Compute the geometric mean. ## ## This function does the same as @code{mean (x, "g")}. ## ## @seealso{mean} ## @end deftypefn function a = geomean(x, dim) if (nargin == 1) a = mean(x, "g"); elseif (nargin == 2) a = mean(x, "g", dim); else print_usage; endif endfunction statistics-1.4.3/inst/geostat.m0000644000000000000000000000455014153320774014712 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} geostat (@var{p}) ## Compute mean and variance of the geometric distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{p} is the rate parameter of the geometric distribution. The ## elements of @var{p} must be probabilities ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the geometric distribution ## ## @item ## @var{v} is the variance of the geometric distribution ## @end itemize ## ## @subheading Example ## ## @example ## @group ## p = 1 ./ (1:6); ## [m, v] = geostat (p) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the geometric distribution function [m, v] = geostat (p) # Check arguments if (nargin != 1) print_usage (); endif if (! isempty (p) && ! ismatrix (p)) error ("geostat: p must be a numeric matrix"); endif # Calculate moments q = 1 - p; m = q ./ p; v = q ./ (p .^ 2); # Continue argument check k = find (! (p >= 0) | ! (p <= 1)); if (any (k)) m(k) = NaN; v(k) = NaN; endif endfunction %!test %! p = 1 ./ (1:6); %! [m, v] = geostat (p); %! assert (m, [0, 1, 2, 3, 4, 5], 0.001); %! assert (v, [0, 2, 6, 12, 20, 30], 0.001); statistics-1.4.3/inst/gevcdf.m0000644000000000000000000000730014153320774014476 0ustar0000000000000000## Copyright (C) 2012 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} =} gevcdf (@var{x}, @var{k}, @var{sigma}, @var{mu}) ## Compute the cumulative distribution function of the generalized extreme value (GEV) distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{x} is the support. ## ## @item ## @var{k} is the shape parameter of the GEV distribution. (Also denoted gamma or xi.) ## @item ## @var{sigma} is the scale parameter of the GEV distribution. The elements ## of @var{sigma} must be positive. ## @item ## @var{mu} is the location parameter of the GEV distribution. ## @end itemize ## The inputs must be of common size, or some of them must be scalar. ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{p} is the cumulative distribution of the GEV distribution at each ## element of @var{x} and corresponding parameter values. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## x = 0:0.5:2.5; ## sigma = 1:6; ## k = 1; ## mu = 0; ## y = gevcdf (x, k, sigma, mu) ## @end group ## ## @group ## y = gevcdf (x, k, 0.5, mu) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Rolf-Dieter Reiss and Michael Thomas. @cite{Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields}. Chapter 1, pages 16-17, Springer, 2007. ## ## @end enumerate ## @seealso{gevfit, gevinv, gevlike, gevpdf, gevrnd, gevstat} ## @end deftypefn ## Author: Nir Krakauer ## Description: CDF of the generalized extreme value distribution function p = gevcdf (x, k, sigma, mu) # Check arguments if (nargin != 4) print_usage (); endif if (isempty (x) || isempty (k) || isempty (sigma) || isempty (mu) || ~ismatrix (x) || ~ismatrix (k) || ~ismatrix (sigma) || ~ismatrix (mu)) error ("gevcdf: inputs must be a numeric matrices"); endif [retval, x, k, sigma, mu] = common_size (x, k, sigma, mu); if (retval > 0) error ("gevcdf: inputs must be of common size or scalars"); endif z = 1 + k .* (x - mu) ./ sigma; # Calculate pdf p = exp(-(z .^ (-1 ./ k))); p(z <= 0 & x < mu) = 0; p(z <= 0 & x > mu) = 1; inds = (abs (k) < (eps^0.7)); %use a different formula if k is very close to zero if any(inds) z = (mu(inds) - x(inds)) ./ sigma(inds); p(inds) = exp(-exp(z)); endif endfunction %!test %! x = 0:0.5:2.5; %! sigma = 1:6; %! k = 1; %! mu = 0; %! p = gevcdf (x, k, sigma, mu); %! expected_p = [0.36788 0.44933 0.47237 0.48323 0.48954 0.49367]; %! assert (p, expected_p, 0.001); %!test %! x = -0.5:0.5:2.5; %! sigma = 0.5; %! k = 1; %! mu = 0; %! p = gevcdf (x, k, sigma, mu); %! expected_p = [0 0.36788 0.60653 0.71653 0.77880 0.81873 0.84648]; %! assert (p, expected_p, 0.001); %!test #check for continuity for k near 0 %! x = 1; %! sigma = 0.5; %! k = -0.03:0.01:0.03; %! mu = 0; %! p = gevcdf (x, k, sigma, mu); %! expected_p = [0.88062 0.87820 0.87580 0.87342 0.87107 0.86874 0.86643]; %! assert (p, expected_p, 0.001); statistics-1.4.3/inst/gevfit.m0000644000000000000000000000703114153320774014525 0ustar0000000000000000## Copyright (C) 2012-2021 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{paramhat}, @var{paramci} =} gevfit (@var{data}, @var{parmguess}) ## Find the maximum likelihood estimator (@var{paramhat}) of the generalized extreme value (GEV) distribution to fit @var{data}. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{data} is the vector of given values. ## @item ## @var{parmguess} is an initial guess for the maximum likelihood parameter vector. If not given, this defaults to @var{k}=0 and @var{sigma}, @var{mu} determined by matching the data mean and standard deviation to their expected values. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{parmhat} is the 3-parameter maximum-likelihood parameter vector [@var{k} @var{sigma} @var{mu}], where @var{k} is the shape parameter of the GEV distribution, @var{sigma} is the scale parameter of the GEV distribution, and @var{mu} is the location parameter of the GEV distribution. ## @item ## @var{paramci} has the approximate 95% confidence intervals of the parameter values based on the Fisher information matrix at the maximum-likelihood position. ## ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## data = 1:50; ## [pfit, pci] = gevfit (data); ## p1 = gevcdf(data,pfit(1),pfit(2),pfit(3)); ## plot(data, p1) ## @end group ## @end example ## @seealso{gevcdf, gevinv, gevlike, gevpdf, gevrnd, gevstat} ## @end deftypefn ## Author: Nir Krakauer ## Description: Maximum likelihood parameter estimation for the generalized extreme value distribution function [paramhat, paramci] = gevfit (data, paramguess) # Check arguments if (nargin < 1) print_usage; endif if (nargin < 2) || isempty(paramguess) paramguess = zeros (3, 1); paramguess(2) = (sqrt(6)/pi) * std (data); paramguess(3) = mean(data) - 0.5772156649*paramguess(2); #expectation involves Euler–Mascheroni constant endif #cost function to minimize f = @(p) gevlike (p, data); [paramhat, ~, info] = fminunc(f, paramguess, optimset("GradObj", "on")); if info <= 0 warning ('gevfit: optimization did not converge, results may be unreliable') endif paramhat = paramhat(:)'; #return a row vector for Matlab compatibility if nargout > 1 [nlogL, ~, ACOV] = gevlike (paramhat, data); param_se = sqrt(diag(inv(ACOV)))'; if any(iscomplex(param_se)) warning ('gevfit: Fisher information matrix not positive definite; parameter optimization likely did not converge') paramci = nan (3, 2); else paramci(1, :) = paramhat - 1.96*param_se; paramci(2, :) = paramhat + 1.96*param_se; endif endif endfunction %!test %! data = 1:50; %! [pfit, pci] = gevfit (data); %! expected_p = [-0.44 15.19 21.53]; %! expected_pu = [-0.13 19.31 26.49]; %! assert (pfit, expected_p, 0.1); %! assert (pci(2, :), expected_pu, 0.1); statistics-1.4.3/inst/gevfit_lmom.m0000644000000000000000000000677314153320774015565 0ustar0000000000000000## Copyright (C) 2012 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{paramhat}, @var{paramci} =} gevfit_lmom (@var{data}) ## Find an estimator (@var{paramhat}) of the generalized extreme value (GEV) distribution fitting @var{data} using the method of L-moments. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{data} is the vector of given values. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{parmhat} is the 3-parameter maximum-likelihood parameter vector [@var{k}; @var{sigma}; @var{mu}], where @var{k} is the shape parameter of the GEV distribution, @var{sigma} is the scale parameter of the GEV distribution, and @var{mu} is the location parameter of the GEV distribution. ## @item ## @var{paramci} has the approximate 95% confidence intervals of the parameter values (currently not implemented). ## ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## data = gevrnd (0.1, 1, 0, 100, 1); ## [pfit, pci] = gevfit_lmom (data); ## p1 = gevcdf (data,pfit(1),pfit(2),pfit(3)); ## [f, x] = ecdf (data); ## plot(data, p1, 's', x, f) ## @end group ## @end example ## @seealso{gevfit} ## @subheading References ## ## @enumerate ## @item ## Ailliot, P.; Thompson, C. & Thomson, P. Mixed methods for fitting the GEV distribution, Water Resources Research, 2011, 47, W05551 ## ## @end enumerate ## @end deftypefn ## Author: Nir Krakauer ## Description: L-moments parameter estimation for the generalized extreme value distribution function [paramhat, paramci] = gevfit_lmom (data) # Check arguments if (nargin < 1) print_usage; endif # find the L-moments data = sort (data(:))'; n = numel(data); L1 = mean(data); L2 = sum(data .* (2*(1:n) - n - 1)) / (2*nchoosek(n, 2)); # or mean(triu(data' - data, 1, 'pack')) / 2; b = bincoeff((1:n) - 1, 2); L3 = sum(data .* (b - 2 * ((1:n) - 1) .* (n - (1:n)) + fliplr(b))) / (3*nchoosek(n, 3)); #match the moments to the GEV distribution #first find k based on L3/L2 f = @(k) (L3/L2 + 3)/2 - limdiv((1 - 3^(k)), (1 - 2^(k))); k = fzero(f, 0); #next find sigma and mu given k if abs(k) < 1E-8 sigma = L2 / log(2); eg = 0.57721566490153286; %Euler-Mascheroni constant mu = L1 - sigma * eg; else sigma = -k*L2 / (gamma(1 - k) * (1 - 2^(k))); mu = L1 - sigma * ((gamma(1 - k) - 1) / k); endif paramhat = [k; sigma; mu]; if nargout > 1 paramci = NaN; endif endfunction #internal function to accurately evaluate (1 - 3^k)/(1 - 2^k) in the limit as k --> 0 function c = limdiv(a, b) # c = ifelse (abs(b) < 1E-8, log(3)/log(2), a ./ b); if abs(b) < 1E-8 c = log(3)/log(2); else c = a / b; endif endfunction %!xtest <31070> %! data = 1:50; %! [pfit, pci] = gevfit_lmom (data); %! expected_p = [-0.28 15.01 20.22]'; %! assert (pfit, expected_p, 0.1); statistics-1.4.3/inst/gevinv.m0000644000000000000000000000621214153320774014537 0ustar0000000000000000## Copyright (C) 2012 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{X} =} gevinv (@var{P}, @var{k}, @var{sigma}, @var{mu}) ## Compute a desired quantile (inverse CDF) of the generalized extreme value (GEV) distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{P} is the desired quantile of the GEV distribution. (Between 0 and 1.) ## @item ## @var{k} is the shape parameter of the GEV distribution. (Also denoted gamma or xi.) ## @item ## @var{sigma} is the scale parameter of the GEV distribution. The elements ## of @var{sigma} must be positive. ## @item ## @var{mu} is the location parameter of the GEV distribution. ## @end itemize ## The inputs must be of common size, or some of them must be scalar. ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{X} is the value corresponding to each quantile of the GEV distribution ## @end itemize ## @subheading References ## ## @enumerate ## @item ## Rolf-Dieter Reiss and Michael Thomas. @cite{Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields}. Chapter 1, pages 16-17, Springer, 2007. ## @item ## J. R. M. Hosking (2012). @cite{L-moments}. R package, version 1.6. URL: http://CRAN.R-project.org/package=lmom. ## ## @end enumerate ## @seealso{gevcdf, gevfit, gevlike, gevpdf, gevrnd, gevstat} ## @end deftypefn ## Author: Nir Krakauer ## Description: Inverse CDF of the generalized extreme value distribution function [X] = gevinv (P, k = 0, sigma = 1, mu = 0) [retval, P, k, sigma, mu] = common_size (P, k, sigma, mu); if (retval > 0) error ("gevinv: inputs must be of common size or scalars"); endif X = P; llP = log(-log(P)); kllP = k .* llP; ii = (abs(kllP) < 1E-4); #use the Taylor series expansion of the exponential to avoid roundoff error or dividing by zero when k is small X(ii) = mu(ii) - sigma(ii) .* llP(ii) .* (1 - kllP(ii) .* (1 - kllP(ii))); X(~ii) = mu(~ii) + (sigma(~ii) ./ k(~ii)) .* (exp(-kllP(~ii)) - 1); endfunction %!test %! p = 0.1:0.1:0.9; %! k = 0; %! sigma = 1; %! mu = 0; %! x = gevinv (p, k, sigma, mu); %! c = gevcdf(x, k, sigma, mu); %! assert (c, p, 0.001); %!test %! p = 0.1:0.1:0.9; %! k = 1; %! sigma = 1; %! mu = 0; %! x = gevinv (p, k, sigma, mu); %! c = gevcdf(x, k, sigma, mu); %! assert (c, p, 0.001); %!test %! p = 0.1:0.1:0.9; %! k = 0.3; %! sigma = 1; %! mu = 0; %! x = gevinv (p, k, sigma, mu); %! c = gevcdf(x, k, sigma, mu); %! assert (c, p, 0.001); statistics-1.4.3/inst/gevlike.m0000644000000000000000000002722014153320774014671 0ustar0000000000000000## Copyright (C) 2012 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{nlogL}, @var{Grad}, @var{ACOV} =} gevlike (@var{params}, @var{data}) ## Compute the negative log-likelihood of data under the generalized extreme value (GEV) distribution with given parameter values. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{params} is the 3-parameter vector [@var{k}, @var{sigma}, @var{mu}], where @var{k} is the shape parameter of the GEV distribution, @var{sigma} is the scale parameter of the GEV distribution, and @var{mu} is the location parameter of the GEV distribution. ## @item ## @var{data} is the vector of given values. ## ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{nlogL} is the negative log-likelihood. ## @item ## @var{Grad} is the 3 by 1 gradient vector (first derivative of the negative log likelihood with respect to the parameter values) ## @item ## @var{ACOV} is the 3 by 3 Fisher information matrix (second derivative of the negative log likelihood with respect to the parameter values) ## ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## x = -5:-1; ## k = -0.2; ## sigma = 0.3; ## mu = 0.5; ## [L, ~, C] = gevlike ([k sigma mu], x); ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Rolf-Dieter Reiss and Michael Thomas. @cite{Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields}. Chapter 1, pages 16-17, Springer, 2007. ## ## @end enumerate ## @seealso{gevcdf, gevfit, gevinv, gevpdf, gevrnd, gevstat} ## @end deftypefn ## Author: Nir Krakauer ## Description: Negative log-likelihood for the generalized extreme value distribution function [nlogL, Grad, ACOV] = gevlike (params, data) # Check arguments if (nargin != 2) print_usage; endif k = params(1); sigma = params(2); mu = params(3); #calculate negative log likelihood [nll, k_terms] = gevnll (data, k, sigma, mu); nlogL = sum(nll(:)); #optionally calculate the first and second derivatives of the negative log likelihood with respect to parameters if nargout > 1 [Grad, kk_terms] = gevgrad (data, k, sigma, mu, k_terms); if nargout > 2 ACOV = gevfim (data, k, sigma, mu, k_terms, kk_terms); endif endif endfunction function [nlogL, k_terms] = gevnll (x, k, sigma, mu) #internal function to calculate negative log likelihood for gevlike #no input checking done k_terms = []; a = (x - mu) ./ sigma; if all(k == 0) nlogL = exp(-a) + a + log(sigma); else aa = k .* a; if min(abs(aa)) < 1E-3 && max(abs(aa)) < 0.5 #use a series expansion to find the log likelihood more accurately when k is small k_terms = 1; sgn = 1; i = 0; while 1 sgn = -sgn; i++; newterm = (sgn / (i + 1)) * (aa .^ i); k_terms = k_terms + newterm; if max(abs(newterm)) <= eps break endif endwhile nlogL = exp(-a .* k_terms) + a .* (k + 1) .* k_terms + log(sigma); else b = 1 + aa; nlogL = b .^ (-1 ./ k) + (1 + 1 ./ k) .* log(b) + log(sigma); nlogL(b <= 0) = Inf; endif endif endfunction function [G, kk_terms] = gevgrad (x, k, sigma, mu, k_terms) #calculate the gradient of the negative log likelihood of data x with respect to the parameters of the generalized extreme value distribution for gevlike #no input checking done kk_terms = []; G = ones(3, 1); if k == 0 ##use the expressions for first derivatives that are the limits as k --> 0 a = (x - mu) ./ sigma; f = exp(-a) - 1; #k #g = -(2 * x .* (mu .* (1 - f) - sigma .* f) + 2 .* sigma .* mu .* f + (x.^2 + mu.^2).*(f - 1)) ./ (2 * f .* sigma .^ 2); g = a .* (1 + a .* f / 2); G(1) = sum(g(:)); #sigma g = (a .* f + 1) ./ sigma; G(2) = sum(g(:)); #mu g = f ./ sigma; G(3) = sum(g(:)); return endif a = (x - mu) ./ sigma; b = 1 + k .* a; if any (b <= 0) G(:) = 0; #negative log likelihood is locally infinite return endif #k c = log(b); d = 1 ./ k + 1; if nargin > 4 && ~isempty(k_terms) #use a series expansion to find the gradient more accurately when k is small aa = k .* a; f = exp(-a .* k_terms); kk_terms = 0.5; sgn = 1; i = 0; while 1 sgn = -sgn; i++; newterm = (sgn * (i + 1) / (i + 2)) * (aa .^ i); kk_terms = kk_terms + newterm; if max(abs(newterm)) <= eps break endif endwhile g = a .* ((a .* kk_terms) .* (f - 1 - k) + k_terms); else g = (c ./ k - a ./ b) ./ (k .* b .^ (1/k)) - c ./ (k .^ 2) + a .* d ./ b; endif %keyboard G(1) = sum(g(:)); #sigma if nargin > 4 && ~isempty(k_terms) #use a series expansion to find the gradient more accurately when k is small g = (1 - a .* (a .* k .* kk_terms - k_terms) .* (f - k - 1)) ./ sigma; else #g = (a .* b .^ (-d) - d .* k .* a ./ b + 1) ./ sigma; g = (a .* b .^ (-d) - (k + 1) .* a ./ b + 1) ./ sigma; endif G(2) = sum(g(:)); #mu if nargin > 4 && ~isempty(k_terms) #use a series expansion to find the gradient more accurately when k is small g = -(a .* k .* kk_terms - k_terms) .* (f - k - 1) ./ sigma; else #g = (b .^ (-d) - d .* k ./ b) ./ sigma; g = (b .^ (-d) - (k + 1) ./ b) ./ sigma; end G(3) = sum(g(:)); endfunction function ACOV = gevfim (x, k, sigma, mu, k_terms, kk_terms) #internal function to calculate the Fisher information matrix for gevlike #no input checking done #find the various second derivatives (used Maxima to help find the expressions) ACOV = ones(3); if k == 0 ##use the expressions for second derivatives that are the limits as k --> 0 #k, k a = (x - mu) ./ sigma; f = exp(-a); #der = (x .* (24 * mu .^ 2 .* sigma .* (f - 1) + 24 * mu .* sigma .^ 2 .* f - 12 * mu .^ 3) + x .^ 3 .* (8 * sigma .* (f - 1) - 12*mu) + x .^ 2 .* (-12 * sigma .^ 2 .* f + 24 * mu .* sigma .* (1 - f) + 18 * mu .^ 2) - 12 * mu .^ 2 .* sigma .^ 2 .* f + 8 * mu .^ 3 .* sigma .* (1 - f) + 3 * (x .^ 4 + mu .^ 4)) ./ (12 .* f .* sigma .^ 4); der = (a .^ 2) .* (a .* (a/4 - 2/3) .* f + 2/3 * a - 1); ACOV(1, 1) = sum(der(:)); #sigma, sigma der = (sigma .^ -2) .* (a .* ((a - 2) .* f + 2) - 1); ACOV(2, 2) = sum(der(:)); #mu, mu der = (sigma .^ -2) .* f; ACOV(3, 3) = sum(der(:)); #k, sigma #der = (x .^2 .* (2*sigma .* (f - 1) - 3*mu) + x .* (-2 * sigma .^ 2 .* f + 4 * mu .* sigma .* (1 - f) + 3 .* mu .^ 2) + 2 * mu .^ 2 .* sigma .* (f - 1) + 2 * mu * sigma .^ 2 * f + x .^ 3 - mu .^ 3) ./ (2 .* f .* sigma .^ 4); der = (-a ./ sigma) .* (a .* (1 - a/2) .* f - a + 1); ACOV(1, 2) = ACOV(2, 1) = sum(der(:)); #k, mu #der = (x .* (2*sigma .* (f - 1) - 2*mu) - 2 * f .* sigma .^ 2 + 2 .* mu .* sigma .* (1 - f) + x .^ 2 + mu .^ 2)./ (2 .* f .* sigma .^ 3); der = (-1 ./ sigma) .* (a .* (1 - a/2) .* f - a + 1); ACOV(1, 3) = ACOV(3, 1) = sum(der(:)); #sigma, mu der = (1 + (a - 1) .* f) ./ (sigma .^ 2); ACOV(2, 3) = ACOV(3, 2) = sum(der(:)); return endif #general case z = 1 + k .* (x - mu) ./ sigma; #k, k a = (x - mu) ./ sigma; b = k .* a + 1; c = log(b); d = 1 ./ k + 1; if nargin > 5 && ~isempty(kk_terms) #use a series expansion to find the derivatives more accurately when k is small aa = k .* a; f = exp(-a .* k_terms); kkk_terms = 2/3; sgn = 1; i = 0; while 1 sgn = -sgn; i++; newterm = (sgn * (i + 1) * (i + 2) / (i + 3)) * (aa .^ i); kkk_terms = kkk_terms + newterm; if max(abs(newterm)) <= eps break endif endwhile der = (a .^ 2) .* (a .* (a .* kk_terms .^ 2 - kkk_terms) .* f + a .* (1 + k) .* kkk_terms - 2 * kk_terms); else der = ((((c ./ k.^2) - (a ./ (k .* b))) .^ 2) ./ (b .^ (1 ./ k))) + ... ((-2*c ./ k.^3) + (2*a ./ (k.^2 .* b)) + ((a ./ b) .^ 2 ./ k)) ./ (b .^ (1 ./ k)) + ... 2*c ./ k.^3 - ... (2*a ./ (k.^2 .* b)) - (d .* (a ./ b) .^ 2); endif der(z <= 0) = 0; %no probability mass in this region ACOV(1, 1) = sum(der(:)); #sigma, sigma if nargin > 5 && ~isempty(kk_terms) #use a series expansion to find the derivatives more accurately when k is small der = ((-2*a .* k_terms + 4 * a .^ 2 .* k .* kk_terms - a .^ 3 .* (k .^ 2) .* kkk_terms) .* (f - k - 1) + f .* ((a .* (k_terms - a .* k .* kk_terms)) .^ 2) - 1) ./ (sigma .^ 2); else der = (sigma .^ -2) .* (... -2*a .* b .^ (-d) + ... d .* k .* a .^ 2 .* (b .^ (-d-1)) + ... 2 .* d .* k .* a ./ b - ... d .* (k .* a ./ b) .^ 2 - 1); end der(z <= 0) = 0; %no probability mass in this region ACOV(2, 2) = sum(der(:)); #mu, mu if nargin > 5 && ~isempty(kk_terms) #use a series expansion to find the derivatives involving k more accurately when k is small der = (f .* (a .* k .* kk_terms - k_terms) .^ 2 - a .* k .^ 2 .* kkk_terms .* (f - k - 1)) ./ (sigma .^ 2); else der = (d .* (sigma .^ -2)) .* (... k .* (b .^ (-d-1)) - ... (k ./ b) .^ 2); endif der(z <= 0) = 0; %no probability mass in this region ACOV(3, 3) = sum(der(:)); #k, mu if nargin > 5 && ~isempty(kk_terms) #use a series expansion to find the derivatives involving k more accurately when k is small der = 2 * a .* kk_terms .* (f - 1 - k) - a .^ 2 .* k_terms .* kk_terms .* f + k_terms; #k, a second derivative der = -der ./ sigma; else der = ( (b .^ (-d)) .* (c ./ k - a ./ b) ./ k - ... a .* (b .^ (-d-1)) + ... ((1 ./ k) - d) ./ b + a .* k .* d ./ (b .^ 2)) ./ sigma; endif der(z <= 0) = 0; %no probability mass in this region ACOV(1, 3) = ACOV(3, 1) = sum(der(:)); #k, sigma der = a .* der; der(z <= 0) = 0; %no probability mass in this region ACOV(1, 2) = ACOV(2, 1) = sum(der(:)); #sigma, mu if nargin > 5 && ~isempty(kk_terms) #use a series expansion to find the derivatives involving k more accurately when k is small der = ((-k_terms + 3 * a .* k .* kk_terms - (a .* k) .^ 2 .* kkk_terms) .* (f - k - 1) + a .* (k_terms - a .* k .* kk_terms) .^ 2 .* f) ./ (sigma .^ 2); else der = ( -(b .^ (-d)) + ... a .* k .* d .* (b .^ (-d-1)) + ... (d .* k ./ b) - a .* (k./b).^2 .* d) ./ (sigma .^ 2); end der(z <= 0) = 0; %no probability mass in this region ACOV(2, 3) = ACOV(3, 2) = sum(der(:)); endfunction %!test %! x = 1; %! k = 0.2; %! sigma = 0.3; %! mu = 0.5; %! [L, D, C] = gevlike ([k sigma mu], x); %! expected_L = 0.75942; %! expected_D = [0.53150; -0.67790; -2.40674]; %! expected_C = [-0.12547 1.77884 1.06731; 1.77884 16.40761 8.48877; 1.06731 8.48877 0.27979]; %! assert (L, expected_L, 0.001); %! assert (D, expected_D, 0.001); %! assert (C, expected_C, 0.001); %!test %! x = 1; %! k = 0; %! sigma = 0.3; %! mu = 0.5; %! [L, D, C] = gevlike ([k sigma mu], x); %! expected_L = 0.65157; %! expected_D = [0.54011; -1.17291; -2.70375]; %! expected_C = [0.090036 3.41229 2.047337; 3.412229 24.760027 12.510190; 2.047337 12.510190 2.098618]; %! assert (L, expected_L, 0.001); %! assert (D, expected_D, 0.001); %! assert (C, expected_C, 0.001); %!test %! x = -5:-1; %! k = -0.2; %! sigma = 0.3; %! mu = 0.5; %! [L, D, C] = gevlike ([k sigma mu], x); %! expected_L = 3786.4; %! expected_D = [6.4511e+04; -4.8194e+04; 3.0633e+03]; %! expected_C = -[-1.4937e+06 1.0083e+06 -6.1837e+04; 1.0083e+06 -8.1138e+05 4.0917e+04; -6.1837e+04 4.0917e+04 -2.0422e+03]; %! assert (L, expected_L, -0.001); %! assert (D, expected_D, -0.001); %! assert (C, expected_C, -0.001); statistics-1.4.3/inst/gevpdf.m0000644000000000000000000000731414153320774014520 0ustar0000000000000000## Copyright (C) 2012 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} gevpdf (@var{x}, @var{k}, @var{sigma}, @var{mu}) ## Compute the probability density function of the generalized extreme value (GEV) distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{x} is the support. ## ## @item ## @var{k} is the shape parameter of the GEV distribution. (Also denoted gamma or xi.) ## @item ## @var{sigma} is the scale parameter of the GEV distribution. The elements ## of @var{sigma} must be positive. ## @item ## @var{mu} is the location parameter of the GEV distribution. ## @end itemize ## The inputs must be of common size, or some of them must be scalar. ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{y} is the probability density of the GEV distribution at each ## element of @var{x} and corresponding parameter values. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## x = 0:0.5:2.5; ## sigma = 1:6; ## k = 1; ## mu = 0; ## y = gevpdf (x, k, sigma, mu) ## @end group ## ## @group ## y = gevpdf (x, k, 0.5, mu) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Rolf-Dieter Reiss and Michael Thomas. @cite{Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields}. Chapter 1, pages 16-17, Springer, 2007. ## ## @end enumerate ## @seealso{gevcdf, gevfit, gevinv, gevlike, gevrnd, gevstat} ## @end deftypefn ## Author: Nir Krakauer ## Description: PDF of the generalized extreme value distribution function y = gevpdf (x, k, sigma, mu) # Check arguments if (nargin != 4) print_usage (); endif if (isempty (x) || isempty (k) || isempty (sigma) || isempty (mu) || ~ismatrix (x) || ~ismatrix (k) || ~ismatrix (sigma) || ~ismatrix (mu)) error ("gevpdf: inputs must be numeric matrices"); endif [retval, x, k, sigma, mu] = common_size (x, k, sigma, mu); if (retval > 0) error ("gevpdf: inputs must be of common size or scalars"); endif z = 1 + k .* (x - mu) ./ sigma; # Calculate pdf y = exp(-(z .^ (-1 ./ k))) .* (z .^ (-1 - 1 ./ k)) ./ sigma; y(z <= 0) = 0; inds = (abs (k) < (eps^0.7)); %use a different formula if k is very close to zero if any(inds) z = (mu(inds) - x(inds)) ./ sigma(inds); y(inds) = exp(z-exp(z)) ./ sigma(inds); endif endfunction %!test %! x = 0:0.5:2.5; %! sigma = 1:6; %! k = 1; %! mu = 0; %! y = gevpdf (x, k, sigma, mu); %! expected_y = [0.367879 0.143785 0.088569 0.063898 0.049953 0.040997]; %! assert (y, expected_y, 0.001); %!test %! x = -0.5:0.5:2.5; %! sigma = 0.5; %! k = 1; %! mu = 0; %! y = gevpdf (x, k, sigma, mu); %! expected_y = [0 0.735759 0.303265 0.159229 0.097350 0.065498 0.047027]; %! assert (y, expected_y, 0.001); %!test #check for continuity for k near 0 %! x = 1; %! sigma = 0.5; %! k = -0.03:0.01:0.03; %! mu = 0; %! y = gevpdf (x, k, sigma, mu); %! expected_y = [0.23820 0.23764 0.23704 0.23641 0.23576 0.23508 0.23438]; %! assert (y, expected_y, 0.001); statistics-1.4.3/inst/gevrnd.m0000644000000000000000000001021514153320774014524 0ustar0000000000000000## Copyright (C) 2012 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {Function File} {} gevrnd (@var{k}, @var{sigma}, @var{mu}) ## @deftypefnx {Function File} {} gevrnd (@var{k}, @var{sigma}, @var{mu}, @var{r}) ## @deftypefnx {Function File} {} gevrnd (@var{k}, @var{sigma}, @var{mu}, @var{r}, @var{c}, @dots{}) ## @deftypefnx {Function File} {} gevrnd (@var{k}, @var{sigma}, @var{mu}, [@var{sz}]) ## Return a matrix of random samples from the generalized extreme value (GEV) distribution with parameters ## @var{k}, @var{sigma}, @var{mu}. ## ## When called with a single size argument, returns a square matrix with ## the dimension specified. When called with more than one scalar argument the ## first two arguments are taken as the number of rows and columns and any ## further arguments specify additional matrix dimensions. The size may also ## be specified with a vector @var{sz} of dimensions. ## ## If no size arguments are given, then the result matrix is the common size of ## the input parameters. ## @seealso{gevcdf, gevfit, gevinv, gevlike, gevpdf, gevstat} ## @end deftypefn ## Author: Nir Krakauer ## Description: Random deviates from the generalized extreme value distribution function rnd = gevrnd (k, sigma, mu, varargin) if (nargin < 3) print_usage (); endif if any (sigma <= 0) error ("gevrnd: sigma must be positive"); endif if (!isscalar (k) || !isscalar (sigma) || !isscalar (mu)) [retval, k, sigma, mu] = common_size (k, sigma, mu); if (retval > 0) error ("gevrnd: k, sigma, mu must be of common size or scalars"); endif endif if (iscomplex (k) || iscomplex (sigma) || iscomplex (mu)) error ("gevrnd: k, sigma, mu must not be complex"); endif if (nargin == 3) sz = size (k); elseif (nargin == 4) if (isscalar (varargin{1}) && varargin{1} >= 0) sz = [varargin{1}, varargin{1}]; elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) sz = varargin{1}; else error ("gevrnd: dimension vector must be row vector of non-negative integers"); endif elseif (nargin > 4) if (any (cellfun (@(x) (!isscalar (x) || x < 0), varargin))) error ("gevrnd: dimensions must be non-negative integers"); endif sz = [varargin{:}]; endif if (!isscalar (k) && !isequal (size (k), sz)) error ("gevrnd: k, sigma, mu must be scalar or of size SZ"); endif if (isa (k, "single") || isa (sigma, "single") || isa (mu, "single")) cls = "single"; else cls = "double"; endif rnd = gevinv (rand(sz), k, sigma, mu); if (strcmp (cls, "single")) rnd = single (rnd); endif endfunction %!assert(size (gevrnd (1,2,1)), [1, 1]); %!assert(size (gevrnd (ones(2,1), 2, 1)), [2, 1]); %!assert(size (gevrnd (ones(2,2), 2, 1)), [2, 2]); %!assert(size (gevrnd (1, 2*ones(2,1), 1)), [2, 1]); %!assert(size (gevrnd (1, 2*ones(2,2), 1)), [2, 2]); %!assert(size (gevrnd (1, 2, 1, 3)), [3, 3]); %!assert(size (gevrnd (1, 2, 1, [4 1])), [4, 1]); %!assert(size (gevrnd (1, 2, 1, 4, 1)), [4, 1]); %% Test input validation %!error gevrnd () %!error gevrnd (1, 2) %!error gevrnd (ones(3),ones(2),1) %!error gevrnd (ones(2),ones(3),1) %!error gevrnd (i, 2, 1) %!error gevrnd (2, i, 1) %!error gevrnd (2, 0, 1) %!error gevrnd (1,2, 1, -1) %!error gevrnd (1,2, 1, ones(2)) %!error gevrnd (1,2, 1, [2 -1 2]) %!error gevrnd (1,2, 1, 1, ones(2)) %!error gevrnd (1,2, 1, 1, -1) %!error gevrnd (ones(2,2), 2, 1, 3) %!error gevrnd (ones(2,2), 2, 1, [3, 2]) %!error gevrnd (ones(2,2), 2, 1, 2, 3) statistics-1.4.3/inst/gevstat.m0000644000000000000000000000570314153320774014722 0ustar0000000000000000## Copyright (C) 2012 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} gevstat (@var{k}, @var{sigma}, @var{mu}) ## Compute the mean and variance of the generalized extreme value (GEV) distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{k} is the shape parameter of the GEV distribution. (Also denoted gamma or xi.) ## @item ## @var{sigma} is the scale parameter of the GEV distribution. The elements ## of @var{sigma} must be positive. ## @item ## @var{mu} is the location parameter of the GEV distribution. ## @end itemize ## The inputs must be of common size, or some of them must be scalar. ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the GEV distribution ## ## @item ## @var{v} is the variance of the GEV distribution ## @end itemize ## @seealso{gevcdf, gevfit, gevinv, gevlike, gevpdf, gevrnd} ## @end deftypefn ## Author: Nir Krakauer ## Description: Moments of the generalized extreme value distribution function [m, v] = gevstat (k, sigma, mu) # Check arguments if (nargin < 3) print_usage (); endif if (isempty (k) || isempty (sigma) || isempty (mu) || ~ismatrix (k) || ~ismatrix (sigma) || ~ismatrix (mu)) error ("gevstat: inputs must be numeric matrices"); endif [retval, k, sigma, mu] = common_size (k, sigma, mu); if (retval > 0) error ("gevstat: inputs must be of common size or scalars"); endif eg = 0.57721566490153286; %Euler-Mascheroni constant m = v = k; #find the mean m(k >= 1) = Inf; m(k == 0) = mu(k == 0) + eg*sigma(k == 0); m(k < 1 & k ~= 0) = mu(k < 1 & k ~= 0) + sigma(k < 1 & k ~= 0) .* (gamma(1-k(k < 1 & k ~= 0)) - 1) ./ k(k < 1 & k ~= 0); #find the variance v(k >= 0.5) = Inf; v(k == 0) = (pi^2 / 6) * sigma(k == 0) .^ 2; v(k < 0.5 & k ~= 0) = (gamma(1-2*k(k < 0.5 & k ~= 0)) - gamma(1-k(k < 0.5 & k ~= 0)).^2) .* (sigma(k < 0.5 & k ~= 0) ./ k(k < 0.5 & k ~= 0)) .^ 2; endfunction %!test %! k = [-1 -0.5 0 0.2 0.4 0.5 1]; %! sigma = 2; %! mu = 1; %! [m, v] = gevstat (k, sigma, mu); %! expected_m = [1 1.4551 2.1544 2.6423 3.4460 4.0898 Inf]; %! expected_v = [4 3.4336 6.5797 13.3761 59.3288 Inf Inf]; %! assert (m, expected_m, -0.001); %! assert (v, expected_v, -0.001); statistics-1.4.3/inst/gmdistribution.m0000644000000000000000000003134014153320774016304 0ustar0000000000000000## Copyright (C) 2015 Lachlan Andrew ## Copyright (C) 2018-2020 John Donoghue ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . classdef gmdistribution ## -*- texinfo -*- ## @deftypefn {Function File} {@var{GMdist} =} gmdistribution (@var{mu}, @var{Sigma}) ## @deftypefnx {Function File} {@var{GMdist} =} gmdistribution (@var{mu}, @var{Sigma}, @var{p}) ## @deftypefnx {Function File} {@var{GMdist} =} gmdistribution (@var{mu}, @var{Sigma}, @var{p}, @var{extra}) ## Create an object of the gmdistribution class which represents a Gaussian ## mixture model with k components of n-dimensional Gaussians. ## ## Input @var{mu} is a k-by-n matrix specifying the n-dimensional mean of each ## of the k components of the distribution. ## ## Input @var{Sigma} is an array that specifies the variances of the ## distributions, in one of four forms depending on its dimension. ## @itemize ## @item n-by-n-by-k: Slice @var{Sigma}(:,:,i) is the variance of the ## i'th component ## @item 1-by-n-by-k: Slice diag(@var{Sigma}(1,:,i)) is the variance of the ## i'th component ## @item n-by-n: @var{Sigma} is the variance of every component ## @item 1-by-n-by-k: Slice diag(@var{Sigma}) is the variance of every ## component ## @end itemize ## ## If @var{p} is specified, it is a vector of length k specifying the proportion ## of each component. If it is omitted or empty, each component has an equal ## proportion. ## ## Input @var{extra} is used by fitgmdist to indicate the parameters of the ## fitting process. ## @seealso{fitgmdist} ## @end deftypefn properties mu ## means Sigma ## covariances ComponentProportion ## mixing proportions DistributionName ## "gaussian mixture distribution" NumComponents ## Number of mixture components NumVariables ## Dimension d of each Gaussian component CovarianceType ## 'diagonal' if DiagonalCovariance, 'full' othw SharedCovariance ## true if all components have equal covariance ## Set by a call to gmdistribution.fit or fitgmdist AIC ## Akaike Information Criterion BIC ## Bayes Information Criterion Converged ## true if algorithm converged by MaxIter NegativeLogLikelihood ## Negative of log-likelihood NlogL ## Negative of log-likelihood NumIterations ## Number of iterations RegularizationValue ## const added to diag of cov to make +ve def endproperties properties (Access = private) DiagonalCovariance ## bool summary of "CovarianceType" endproperties methods ######################################## ## Constructor function obj = gmdistribution (mu,sigma,p = [],extra = []) obj.DistributionName = "gaussian mixture distribution"; obj.mu = mu; obj.Sigma = sigma; obj.NumComponents = rows (mu); obj.NumVariables = columns (mu); if (isempty (p)) obj.ComponentProportion = ones (1,obj.NumComponents) / obj.NumComponents; else if any (p < 0) error ("gmmdistribution: component weights must be non-negative"); endif s = sum(p); if (s == 0) error ("gmmdistribution: component weights must not be all zero"); elseif (s != 1) p = p / s; endif obj.ComponentProportion = p(:)'; endif if (length (size (sigma)) == 3) obj.SharedCovariance = false; else obj.SharedCovariance = true; endif if (rows (sigma) == 1 && columns (mu) > 1) obj.DiagonalCovariance = true; obj.CovarianceType = 'diagonal'; else obj.DiagonalCovariance = false; ## full obj.CovarianceType = 'full'; endif if (!isempty (extra)) obj.AIC = extra.AIC; obj.BIC = extra.BIC; obj.Converged = extra.Converged; obj.NegativeLogLikelihood = extra.NegativeLogLikelihood; obj.NlogL = extra.NegativeLogLikelihood; obj.NumIterations = extra.NumIterations; obj.RegularizationValue = extra.RegularizationValue; endif endfunction ######################################## ## Cumulative distribution function for Gaussian mixture distribution function c = cdf (obj, X) X = checkX (obj, X, "cdf"); p_x_l = zeros (rows (X), obj.NumComponents); if (obj.SharedCovariance) if (obj.DiagonalCovariance) sig = diag (obj.Sigma); else sig = obj.Sigma; endif endif for i = 1:obj.NumComponents if (!obj.SharedCovariance) if (obj.DiagonalCovariance) sig = diag (obj.Sigma(:,:,i)); else sig = obj.Sigma(:,:,i); endif endif p_x_l(:,i) = mvncdf (X,obj.mu(i,:),sig)*obj.ComponentProportion(i); endfor c = sum (p_x_l, 2); endfunction ######################################## ## Construct clusters from Gaussian mixture distribution ## function [idx,nlogl,P,logpdf,M] = cluster (obj,X) X = checkX (obj, X, "cluster"); [p_x_l, M] = componentProb (obj, X); [~, idx] = max (p_x_l, [], 2); if (nargout >= 2) PDF = sum (p_x_l, 2); logpdf = log (PDF); nlogl = -sum (logpdf); if (nargout >= 3) P = bsxfun (@rdivide, p_x_l, PDF); endif endif endfunction ######################################## ## Display Gaussian mixture distribution object function c = disp (obj) fprintf("Gaussian mixture distribution with %d components in %d dimension(s)\n", obj.NumComponents, columns (obj.mu)); for i = 1:obj.NumComponents fprintf("Clust %d: weight %d\n\tMean: ", i, obj.ComponentProportion(i)); fprintf("%g ", obj.mu(i,:)); fprintf("\n"); if (!obj.SharedCovariance) fprintf("\tVariance:"); if (!obj.DiagonalCovariance) if columns (obj.mu) > 1 fprintf("\n"); endif disp(squeeze(obj.Sigma(:,:,i))) else fprintf(" diag("); fprintf("%g ", obj.Sigma(:,:,i)); fprintf(")\n"); endif endif endfor if (obj.SharedCovariance) fprintf("Shared variance\n"); if (!obj.DiagonalCovariance) obj.Sigma else fprintf(" diag("); fprintf("%g ", obj.Sigma); fprintf(")\n"); endif endif if (!isempty (obj.AIC)) fprintf("AIC=%g BIC=%g NLogL=%g Iter=%d Cged=%d Reg=%g\n", ... obj.AIC, obj.BIC, obj.NegativeLogLikelihood, ... obj.NumIterations, obj.Converged, obj.RegularizationValue); endif endfunction ######################################## ## Display Gaussian mixture distribution object function c = display (obj) disp(obj); endfunction ######################################## ## Mahalanobis distance to component means function D = mahal (obj,X) X = checkX (obj, X, "mahal"); [~, D] = componentProb (obj,X); endfunction ######################################## ## Probability density function for Gaussian mixture distribution function c = pdf (obj,X) X = checkX (obj, X, "pdf"); p_x_l = componentProb (obj, X); c = sum (p_x_l, 2); endfunction ######################################## ## Posterior probabilities of components function c = posterior (obj,X) X = checkX (obj, X, "posterior"); p_x_l = componentProb (obj, X); c = bsxfun(@rdivide, p_x_l, sum (p_x_l, 2)); endfunction ######################################## ## Random numbers from Gaussian mixture distribution function c = random (obj,n) if nargin == 1 n = 1; endif c = zeros (n, obj.NumVariables); classes = randsample (obj.NumComponents, n, true, obj.ComponentProportion); if (obj.SharedCovariance) if (obj.DiagonalCovariance) sig = diag (obj.Sigma); else sig = obj.Sigma; endif endif for i = 1:obj.NumComponents idx = (classes == i); k = sum(idx); if k > 0 if (!obj.SharedCovariance) if (obj.DiagonalCovariance) sig = diag (obj.Sigma(:,:,i)); else sig = obj.Sigma(:,:,i); endif endif # [sig] forces [sig] not to have class "diagonal", # since mvnrnd uses automatic broadcast, # which fails on structured matrices c(idx,:) = mvnrnd ([obj.mu(i,:)], [sig], k); endif endfor endfunction endmethods ######################################## methods (Static) ## Gaussian mixture parameter estimates function c = fit (X,k,varargin) c = fitgmdist (X,k,varargin{:}); endfunction endmethods ######################################## methods (Access = private) ## Probability density of (row of) X *and* component l ## Second argument is an array of the Mahalonis distances function [p_x_l, M] = componentProb (obj, X) M = zeros (rows (X), obj.NumComponents); dets = zeros (1, obj.NumComponents); % sqrt(determinant) if (obj.SharedCovariance) if (obj.DiagonalCovariance) r = diag (sqrt(obj.Sigma)); else r = chol (obj.Sigma); endif endif for i = 1:obj.NumComponents dev = bsxfun (@minus, X, obj.mu(i,:)); if (!obj.SharedCovariance) if (obj.DiagonalCovariance) r = diag (sqrt (obj.Sigma(:,:,i))); else r = chol (obj.Sigma(:,:,i)); endif endif M(:,i) = sumsq (dev / r, 2); dets(i) = prod (diag (r)); endfor p_x_l = exp (-M/2); coeff = obj.ComponentProportion ./ ((2*pi)^(obj.NumVariables/2).*dets); p_x_l = bsxfun (@times, p_x_l, coeff); endfunction ######################################## ## Check format of argument X function X = checkX (obj, X, name) if (columns (X) != obj.NumVariables) if (columns (X) == 1 && rows (X) == obj.NumVariables) X = X'; else error ("gmdistribution.%s: X has %d columns instead of %d\n", ... name, columns (X), obj.NumVariables); end endif endfunction endmethods endclassdef %!test %! mu = eye(2); %! Sigma = eye(2); %! GM = gmdistribution (mu, Sigma); %! density = GM.pdf ([0 0; 1 1]); %! assert (density(1) - density(2), 0, 1e-6); %! %! [idx, nlogl, P, logpdf,M] = cluster (GM, eye(2)); %! assert (idx, [1; 2]); %! [idx2,nlogl2,P2,logpdf2] = GM.cluster (eye(2)); %! assert (nlogl - nlogl2, 0, 1e-6); %! [idx3,nlogl3,P3] = cluster (GM, eye(2)); %! assert (P - P3, zeros (2), 1e-6); %! [idx4,nlogl4] = cluster (GM, eye(2)); %! assert (size (nlogl4), [1 1]); %! idx5 = cluster (GM, eye(2)); %! assert (idx - idx5, zeros (2,1)); %! %! D = GM.mahal ([1;0]); %! assert (D - M(1,:), zeros (1,2), 1e-6); %! %! P = GM.posterior ([0 1]); %! assert (P - P2(2,:), zeros (1,2), 1e-6); %! %! R = GM.random(20); %! assert (size(R), [20, 2]); %! %! R = GM.random(); %! assert (size(R), [1, 2]); statistics-1.4.3/inst/gpcdf.m0000644000000000000000000001510614153320774014326 0ustar0000000000000000## Copyright (C) 2018 John Donoghue ## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1997-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} gpcdf (@var{x}, @var{shape}, @var{scale}, @var{location}) ## Compute the cumulative distribution function (CDF) at @var{x} of the ## generalized Pareto distribution with parameters @var{location}, @var{scale}, ## and @var{shape}. ## @end deftypefn ## Author: Dag Lyberg ## Description: PDF of the generalized Pareto distribution function cdf = gpcdf (x, shape, scale, location) if (nargin != 4) print_usage (); endif if (! isscalar (location) || ! isscalar (scale) || ! isscalar (shape)) [retval, x, location, scale, shape] = ... common_size (x, location, scale, shape); if (retval > 0) error ("gpcdf: X, LOCATION, SCALE and SHAPE must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (location) || iscomplex (scale) ... || iscomplex (shape)) error ("gpcdf: X, LOCATION, SCALE and SHAPE must not be complex"); endif if (isa (x, "single") || isa (location, "single") || isa (scale, "single") ... || isa (shape, "single")) cdf = zeros (size (x), "single"); else cdf = zeros (size (x)); endif k = isnan (x) | ! (-Inf < location) | ! (location < Inf) | ! (scale > 0) ... | ! (-Inf < shape) | ! (shape < Inf); cdf(k) = NaN; k = (x == Inf) & (-Inf < location) & (location < Inf) & (scale > 0) ... & (-Inf < shape) & (shape < Inf); cdf(k) = 1; k = (-Inf < x) & (x < Inf) & (-Inf < location) & (location < Inf) ... & (scale > 0) & (scale < Inf) & (-Inf < shape) & (shape < Inf); if (isscalar (location) && isscalar (scale) && isscalar (shape)) z = (x - location) / scale; j = k & (shape == 0) & (z >= 0); if (any (j)) cdf(j) = 1 - exp (-z(j)); endif j = k & (shape > 0) & (z >= 0); if (any (j)) cdf(j) = 1 - (shape * z(j) + 1).^(-1 / shape); endif if (shape < 0) j = k & (shape < 0) & (0 <= z) & (z <= -1 ./ shape); if (any (j)) cdf(j) = 1 - (shape * z(j) + 1).^(-1 / shape); endif endif else z = (x - location) ./ scale; j = k & (shape == 0) & (z >= 0); if (any (j)) cdf(j) = 1 - exp (-z(j)); endif j = k & (shape > 0) & (z >= 0); if (any (j)) cdf(j) = 1 - (shape(j) .* z(j) + 1).^(-1 ./ shape(j)); endif if (any (shape < 0)) j = k & (shape < 0) & (0 <= z) & (z <= -1 ./ shape); if (any (j)) cdf(j) = 1 - (shape(j) .* z(j) + 1).^(-1 ./ shape(j)); endif endif endif endfunction %!shared x,y1,y2,y3 %! x = [-Inf, -1, 0, 1/2, 1, Inf]; %! y1 = [0, 0, 0, 0.3934693402873666, 0.6321205588285577, 1]; %! y2 = [0, 0, 0, 1/3, 1/2, 1]; %! y3 = [0, 0, 0, 1/2, 1, 1]; %! seps = eps('single')*5; %!assert (gpcdf (x, zeros (1,6), ones (1,6), zeros (1,6)), y1, eps) %!assert (gpcdf (x, 0, 1, zeros (1,6)), y1, eps) %!assert (gpcdf (x, 0, ones (1,6), 0), y1, eps) %!assert (gpcdf (x, zeros (1,6), 1, 0), y1, eps) %!assert (gpcdf (x, 0, 1, 0), y1, eps) %!assert (gpcdf (x, 0, 1, [0, 0, 0, NaN, 0, 0]), [y1(1:3), NaN, y1(5:6)], eps) %!assert (gpcdf (x, 0, [1, 1, 1, NaN, 1, 1], 0), [y1(1:3), NaN, y1(5:6)], eps) %!assert (gpcdf (x, [0, 0, 0, NaN, 0, 0], 1, 0), [y1(1:3), NaN, y1(5:6)], eps) %!assert (gpcdf ([x(1:3), NaN, x(5:6)], 0, 1, 0), [y1(1:3), NaN, y1(5:6)], eps) %!assert (gpcdf (x, ones (1,6), ones (1,6), zeros (1,6)), y2, eps) %!assert (gpcdf (x, 1, 1, zeros (1,6)), y2, eps) %!assert (gpcdf (x, 1, ones (1,6), 0), y2, eps) %!assert (gpcdf (x, ones (1,6), 1, 0), y2, eps) %!assert (gpcdf (x, 1, 1, 0), y2, eps) %!assert (gpcdf (x, 1, 1, [0, 0, 0, NaN, 0, 0]), [y2(1:3), NaN, y2(5:6)], eps) %!assert (gpcdf (x, 1, [1, 1, 1, NaN, 1, 1], 0), [y2(1:3), NaN, y2(5:6)], eps) %!assert (gpcdf (x, [1, 1, 1, NaN, 1, 1], 1, 0), [y2(1:3), NaN, y2(5:6)], eps) %!assert (gpcdf ([x(1:3), NaN, x(5:6)], 1, 1, 0), [y2(1:3), NaN, y2(5:6)], eps) %!assert (gpcdf (x, -ones (1,6), ones (1,6), zeros (1,6)), y3, eps) %!assert (gpcdf (x, -1, 1, zeros (1,6)), y3, eps) %!assert (gpcdf (x, -1, ones (1,6), 0), y3, eps) %!assert (gpcdf (x, -ones (1,6), 1, 0), y3, eps) %!assert (gpcdf (x, -1, 1, 0), y3, eps) %!assert (gpcdf (x, -1, 1, [0, 0, 0, NaN, 0, 0]), [y1(1:3), NaN, y3(5:6)], eps) %!assert (gpcdf (x, -1, [1, 1, 1, NaN, 1, 1], 0), [y1(1:3), NaN, y3(5:6)], eps) %!assert (gpcdf (x, [-1, -1, -1, NaN, -1, -1], 1, 0), [y1(1:3), NaN, y3(5:6)], eps) %!assert (gpcdf ([x(1:3), NaN, x(5:6)], -1, 1, 0), [y1(1:3), NaN, y3(5:6)], eps) ## Test class of input preserved %!assert (gpcdf (single ([x, NaN]), 0, 1, 0), single ([y1, NaN]), eps('single')) %!assert (gpcdf ([x, NaN], 0, 1, single (0)), single ([y1, NaN]), eps('single')) %!assert (gpcdf ([x, NaN], 0, single (1), 0), single ([y1, NaN]), eps('single')) %!assert (gpcdf ([x, NaN], single (0), 1, 0), single ([y1, NaN]), eps('single')) %!assert (gpcdf (single ([x, NaN]), 1, 1, 0), single ([y2, NaN]), eps('single')) %!assert (gpcdf ([x, NaN], 1, 1, single (0)), single ([y2, NaN]), eps('single')) %!assert (gpcdf ([x, NaN], 1, single (1), 0), single ([y2, NaN]), eps('single')) %!assert (gpcdf ([x, NaN], single (1), 1, 0), single ([y2, NaN]), eps('single')) %!assert (gpcdf (single ([x, NaN]), -1, 1, 0), single ([y3, NaN]), eps('single')) %!assert (gpcdf ([x, NaN], -1, 1, single (0)), single ([y3, NaN]), eps('single')) %!assert (gpcdf ([x, NaN], -1, single (1), 0), single ([y3, NaN]), eps('single')) %!assert (gpcdf ([x, NaN], single (-1), 1, 0), single ([y3, NaN]), eps('single')) ## Test input validation %!error gpcdf () %!error gpcdf (1) %!error gpcdf (1,2) %!error gpcdf (1,2,3) %!error gpcdf (1,2,3,4,5) %!error gpcdf (ones (3), ones (2), ones (2), ones (2)) %!error gpcdf (ones (2), ones (2), ones (2), ones (3)) %!error gpcdf (ones (2), ones (2), ones (3), ones (2)) %!error gpcdf (ones (2), ones (3), ones (2), ones (2)) %!error gpcdf (i, 2, 2, 2) %!error gpcdf (2, i, 2, 2) %!error gpcdf (2, 2, i, 2) %!error gpcdf (2, 2, 2, i) statistics-1.4.3/inst/gpinv.m0000644000000000000000000001413014153320774014362 0ustar0000000000000000## Copyright (C) 2018 John Donoghue ## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1997-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} gpinv (@var{x}, @var{shape}, @var{scale}, @var{location}) ## For each element of @var{x}, compute the quantile (the inverse of the CDF) ## at @var{x} of the generalized Pareto distribution with parameters ## @var{location}, @var{scale}, and @var{shape}. ## @end deftypefn ## Author: Dag Lyberg ## Description: Quantile function of the generalized Pareto distribution function inv = gpinv (x, shape, scale, location) if (nargin != 4) print_usage (); endif if (! isscalar (location) || ! isscalar (scale) || ! isscalar (shape)) [retval, x, location, scale, shape] = ... common_size (x, location, scale, shape); if (retval > 0) error ("gpinv: X, LOCATION, SCALE and SHAPE must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (location) ... || iscomplex (scale) || iscomplex (shape)) error ("gpinv: X, LOCATION, SCALE and SHAPE must not be complex"); endif if (isa (x, "single") || isa (location, "single") ... || isa (scale, "single") || isa (shape, "single")) inv = zeros (size (x), "single"); else inv = zeros (size (x)); endif k = isnan (x) | ! (0 <= x) | ! (x <= 1) ... | ! (-Inf < location) | ! (location < Inf) ... | ! (scale > 0) | ! (scale < Inf) ... | ! (-Inf < shape) | ! (shape < Inf); inv(k) = NaN; k = (0 <= x) & (x <= 1) & (-Inf < location) & (location < Inf) ... & (scale > 0) & (scale < Inf) & (-Inf < shape) & (shape < Inf); if (isscalar (location) && isscalar (scale) && isscalar (shape)) if (shape == 0) inv(k) = -log(1 - x(k)); inv(k) = scale * inv(k) + location; elseif (shape > 0) inv(k) = (1 - x(k)).^(-shape) - 1; inv(k) = (scale / shape) * inv(k) + location; elseif (shape < 0) inv(k) = (1 - x(k)).^(-shape) - 1; inv(k) = (scale / shape) * inv(k) + location; end else j = k & (shape == 0); if (any (j)) inv(j) = -log (1 - x(j)); inv(j) = scale(j) .* inv(j) + location(j); endif j = k & (shape > 0); if (any (j)) inv(j) = (1 - x(j)).^(-shape(j)) - 1; inv(j) = (scale(j) ./ shape(j)) .* inv(j) + location(j); endif j = k & (shape < 0); if (any (j)) inv(j) = (1 - x(j)).^(-shape(j)) - 1; inv(j) = (scale(j) ./ shape(j)) .* inv(j) + location(j); endif endif endfunction %!shared x,y1,y2,y3 %! x = [-1, 0, 1/2, 1, 2]; %! y1 = [NaN, 0, 0.6931471805599453, Inf, NaN]; %! y2 = [NaN, 0, 1, Inf, NaN]; %! y3 = [NaN, 0, 1/2, 1, NaN]; %!assert (gpinv (x, zeros (1,5), ones (1,5), zeros (1,5)), y1) %!assert (gpinv (x, 0, 1, zeros (1,5)), y1) %!assert (gpinv (x, 0, ones (1,5), 0), y1) %!assert (gpinv (x, zeros (1,5), 1, 0), y1) %!assert (gpinv (x, 0, 1, 0), y1) %!assert (gpinv (x, 0, 1, [0, 0, NaN, 0, 0]), [y1(1:2), NaN, y1(4:5)]) %!assert (gpinv (x, 0, [1, 1, NaN, 1, 1], 0), [y1(1:2), NaN, y1(4:5)]) %!assert (gpinv (x, [0, 0, NaN, 0, 0], 1, 0), [y1(1:2), NaN, y1(4:5)]) %!assert (gpinv ([x(1:2), NaN, x(4:5)], 0, 1, 0), [y1(1:2), NaN, y1(4:5)]) %!assert (gpinv (x, ones (1,5), ones (1,5), zeros (1,5)), y2) %!assert (gpinv (x, 1, 1, zeros (1,5)), y2) %!assert (gpinv (x, 1, ones (1,5), 0), y2) %!assert (gpinv (x, ones (1,5), 1, 0), y2) %!assert (gpinv (x, 1, 1, 0), y2) %!assert (gpinv (x, 1, 1, [0, 0, NaN, 0, 0]), [y2(1:2), NaN, y2(4:5)]) %!assert (gpinv (x, 1, [1, 1, NaN, 1, 1], 0), [y2(1:2), NaN, y2(4:5)]) %!assert (gpinv (x, [1, 1, NaN, 1, 1], 1, 0), [y2(1:2), NaN, y2(4:5)]) %!assert (gpinv ([x(1:2), NaN, x(4:5)], 1, 1, 0), [y2(1:2), NaN, y2(4:5)]) %!assert (gpinv (x, -ones (1,5), ones (1,5), zeros (1,5)), y3) %!assert (gpinv (x, -1, 1, zeros (1,5)), y3) %!assert (gpinv (x, -1, ones (1,5), 0), y3) %!assert (gpinv (x, -ones (1,5), 1, 0), y3) %!assert (gpinv (x, -1, 1, 0), y3) %!assert (gpinv (x, -1, 1, [0, 0, NaN, 0, 0]), [y3(1:2), NaN, y3(4:5)]) %!assert (gpinv (x, -1, [1, 1, NaN, 1, 1], 0), [y3(1:2), NaN, y3(4:5)]) %!assert (gpinv (x, -[1, 1, NaN, 1, 1], 1, 0), [y3(1:2), NaN, y3(4:5)]) %!assert (gpinv ([x(1:2), NaN, x(4:5)], -1, 1, 0), [y3(1:2), NaN, y3(4:5)]) ## Test class of input preserved %!assert (gpinv (single ([x, NaN]), 0, 1, 0), single ([y1, NaN])) %!assert (gpinv ([x, NaN], 0, 1, single (0)), single ([y1, NaN])) %!assert (gpinv ([x, NaN], 0, single (1), 0), single ([y1, NaN])) %!assert (gpinv ([x, NaN], single (0), 1, 0), single ([y1, NaN])) %!assert (gpinv (single ([x, NaN]), 1, 1, 0), single ([y2, NaN])) %!assert (gpinv ([x, NaN], 1, 1, single (0)), single ([y2, NaN])) %!assert (gpinv ([x, NaN], 1, single (1), 0), single ([y2, NaN])) %!assert (gpinv ([x, NaN], single (1), 1, 0), single ([y2, NaN])) %!assert (gpinv (single ([x, NaN]), -1, 1, 0), single ([y3, NaN])) %!assert (gpinv ([x, NaN], -1, 1, single (0)), single ([y3, NaN])) %!assert (gpinv ([x, NaN], -1, single (1), 0), single ([y3, NaN])) %!assert (gpinv ([x, NaN], single (-1), 1, 0), single ([y3, NaN])) ## Test input validation %!error gpinv () %!error gpinv (1) %!error gpinv (1,2) %!error gpinv (1,2,3) %!error gpinv (1,2,3,4,5) %!error gpinv (ones (3), ones (2), ones (2), ones (2)) %!error gpinv (ones (2), ones (3), ones (2), ones (2)) %!error gpinv (ones (2), ones (2), ones (3), ones (2)) %!error gpinv (ones (2), ones (2), ones (2), ones (3)) %!error gpinv (i, 2, 2, 2) %!error gpinv (2, i, 2, 2) %!error gpinv (2, 2, i, 2) %!error gpinv (2, 2, 2, i) statistics-1.4.3/inst/gppdf.m0000644000000000000000000001427514153320774014351 0ustar0000000000000000## Copyright (C) 2018 John Donoghue ## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1997-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} gppdf (@var{x}, @var{shape}, @var{scale}, @var{location}) ## Compute the probability density function (PDF) at @var{x} of the ## generalized Pareto distribution with parameters @var{location}, @var{scale}, ## and @var{shape}. ## @end deftypefn ## Author: Dag Lyberg ## Description: PDF of the generalized Pareto distribution function pdf = gppdf (x, shape, scale, location) if (nargin != 4) print_usage (); endif if (! isscalar (location) || ! isscalar (scale) || ! isscalar (shape)) [retval, x, location, scale, shape] = ... common_size (x, location, scale, shape); if (retval > 0) error ("gppdf: X, LOCATION, SCALE and SHAPE must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (location) || iscomplex (scale) ... || iscomplex (shape)) error ("gppdf: X, LOCATION, SCALE and SHAPE must not be complex"); endif if (isa (x, "single") || isa (location, "single") || isa (scale, "single") ... || isa (shape, "single")) pdf = zeros (size (x), "single"); else pdf = zeros (size (x)); endif k = isnan (x) | ! (-Inf < location) | ! (location < Inf) | ... ! (scale > 0) | ! (scale < Inf) | ! (-Inf < shape) | ! (shape < Inf); pdf(k) = NaN; k = (-Inf < x) & (x < Inf) & (-Inf < location) & (location < Inf) & ... (scale > 0) & (scale < Inf) & (-Inf < shape) & (shape < Inf); if (isscalar (location) && isscalar (scale) && isscalar (shape)) z = (x - location) / scale; j = k & (shape == 0) & (z >= 0); if (any (j)) pdf(j) = exp (-z(j)); endif j = k & (shape > 0) & (z >= 0); if (any (j)) pdf(j) = (shape * z(j) + 1).^(-(shape + 1) / shape) ./ scale; endif if (shape < 0) j = k & (shape < 0) & (0 <= z) & (z <= -1. / shape); if (any (j)) pdf(j) = (shape * z(j) + 1).^(-(shape + 1) / shape) ./ scale; endif endif else z = (x - location) ./ scale; j = k & (shape == 0) & (z >= 0); if (any (j)) pdf(j) = exp( -z(j)); endif j = k & (shape > 0) & (z >= 0); if (any (j)) pdf(j) = (shape(j) .* z(j) + 1).^(-(shape(j) + 1) ./ shape(j)) ./ scale(j); endif if (any (shape < 0)) j = k & (shape < 0) & (0 <= z) & (z <= -1 ./ shape); if (any (j)) pdf(j) = (shape(j) .* z(j) + 1).^(-(shape(j) + 1) ./ shape(j)) ./ scale(j); endif endif endif endfunction %!shared x,y1,y2,y3 %! x = [-Inf, -1, 0, 1/2, 1, Inf]; %! y1 = [0, 0, 1, 0.6065306597126334, 0.36787944117144233, 0]; %! y2 = [0, 0, 1, 4/9, 1/4, 0]; %! y3 = [0, 0, 1, 1, 1, 0]; %!assert (gppdf (x, zeros (1,6), ones (1,6), zeros (1,6)), y1, eps) %!assert (gppdf (x, 0, 1, zeros (1,6)), y1, eps) %!assert (gppdf (x, 0, ones (1,6), 0), y1, eps) %!assert (gppdf (x, zeros (1,6), 1, 0), y1, eps) %!assert (gppdf (x, 0, 1, 0), y1, eps) %!assert (gppdf (x, 0, 1, [0, 0, 0, NaN, 0, 0]), [y1(1:3), NaN, y1(5:6)]) %!assert (gppdf (x, 0, [1, 1, 1, NaN, 1, 1], 0), [y1(1:3), NaN, y1(5:6)]) %!assert (gppdf (x, [0, 0, 0, NaN, 0, 0], 1, 0), [y1(1:3), NaN, y1(5:6)]) %!assert (gppdf ([x(1:3), NaN, x(5:6)], 0, 1, 0), [y1(1:3), NaN, y1(5:6)]) %!assert (gppdf (x, ones (1,6), ones (1,6), zeros (1,6)), y2, eps) %!assert (gppdf (x, 1, 1, zeros (1,6)), y2, eps) %!assert (gppdf (x, 1, ones (1,6), 0), y2, eps) %!assert (gppdf (x, ones (1,6), 1, 0), y2, eps) %!assert (gppdf (x, 1, 1, 0), y2, eps) %!assert (gppdf (x, 1, 1, [0, 0, 0, NaN, 0, 0]), [y2(1:3), NaN, y2(5:6)]) %!assert (gppdf (x, 1, [1, 1, 1, NaN, 1, 1], 0), [y2(1:3), NaN, y2(5:6)]) %!assert (gppdf (x, [1, 1, 1, NaN, 1, 1], 1, 0), [y2(1:3), NaN, y2(5:6)]) %!assert (gppdf ([x(1:3), NaN, x(5:6)], 1, 1, 0), [y2(1:3), NaN, y2(5:6)]) %!assert (gppdf (x, -ones (1,6), ones (1,6), zeros (1,6)), y3, eps) %!assert (gppdf (x, -1, 1, zeros (1,6)), y3, eps) %!assert (gppdf (x, -1, ones (1,6), 0), y3, eps) %!assert (gppdf (x, -ones (1,6), 1, 0), y3, eps) %!assert (gppdf (x, -1, 1, 0), y3, eps) %!assert (gppdf (x, -1, 1, [0, 0, 0, NaN, 0, 0]), [y3(1:3), NaN, y3(5:6)]) %!assert (gppdf (x, -1, [1, 1, 1, NaN, 1, 1], 0), [y3(1:3), NaN, y3(5:6)]) %!assert (gppdf (x, [-1, -1, -1, NaN, -1, -1], 1, 0), [y3(1:3), NaN, y3(5:6)]) %!assert (gppdf ([x(1:3), NaN, x(5:6)], -1, 1, 0), [y3(1:3), NaN, y3(5:6)]) ## Test class of input preserved %!assert (gppdf (single ([x, NaN]), 0, 1, 0), single ([y1, NaN])) %!assert (gppdf ([x, NaN], 0, 1, single (0)), single ([y1, NaN])) %!assert (gppdf ([x, NaN], 0, single (1), 0), single ([y1, NaN])) %!assert (gppdf ([x, NaN], single (0), 1, 0), single ([y1, NaN])) %!assert (gppdf (single ([x, NaN]), 1, 1, 0), single ([y2, NaN])) %!assert (gppdf ([x, NaN], 1, 1, single (0)), single ([y2, NaN])) %!assert (gppdf ([x, NaN], 1, single (1), 0), single ([y2, NaN])) %!assert (gppdf ([x, NaN], single (1), 1, 0), single ([y2, NaN])) %!assert (gppdf (single ([x, NaN]), -1, 1, 0), single ([y3, NaN])) %!assert (gppdf ([x, NaN], -1, 1, single (0)), single ([y3, NaN])) %!assert (gppdf ([x, NaN], -1, single (1), 0), single ([y3, NaN])) %!assert (gppdf ([x, NaN], single (-1), 1, 0), single ([y3, NaN])) ## Test input validation %!error gppdf () %!error gppdf (1) %!error gppdf (1,2) %!error gppdf (1,2,3) %!error gppdf (1,2,3,4,5) %!error gppdf (1, ones (2), ones (2), ones (3)) %!error gppdf (1, ones (2), ones (3), ones (2)) %!error gppdf (1, ones (3), ones (2), ones (2)) %!error gppdf (i, 2, 2, 2) %!error gppdf (2, i, 2, 2) %!error gppdf (2, 2, i, 2) %!error gppdf (2, 2, 2, i) statistics-1.4.3/inst/gprnd.m0000644000000000000000000001471014153320774014355 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} gprnd (@var{shape}, @var{scale}, @var{location}) ## @deftypefnx {} {} gprnd (@var{shape}, @var{scale}, @var{location}, @var{r}) ## @deftypefnx {} {} gprnd (@var{shape}, @var{scale}, @var{location}, @var{r}, @var{c}, @dots{}) ## @deftypefnx {} {} gprnd (@var{shape}, @var{scale}, @var{location}, [@var{sz}]) ## Return a matrix of random samples from the generalized Pareto distribution ## with parameters @var{location}, @var{scale} and @var{shape}. ## ## When called with a single size argument, return a square matrix with ## the dimension specified. When called with more than one scalar argument the ## first two arguments are taken as the number of rows and columns and any ## further arguments specify additional matrix dimensions. The size may also ## be specified with a vector of dimensions @var{sz}. ## ## If no size arguments are given then the result matrix is the common size of ## @var{location}, @var{scale} and @var{shape}. ## @end deftypefn ## Author: Dag Lyberg ## Description: Random deviates from the generalized Pareto distribution function rnd = gprnd (shape, scale, location, varargin) if (nargin < 3) print_usage (); endif if (! isscalar (location) || ! isscalar (scale) || ! isscalar (shape)) [retval, location, scale, shape] = common_size (location, scale, shape); if (retval > 0) error ("gpgrnd: LOCATION, SCALE and SHAPE must be of common size or scalars"); endif endif if (iscomplex (location) || iscomplex (scale) || iscomplex (shape)) error ("gprnd: LOCATION, SCALE and SHAPE must not be complex"); endif if (nargin == 3) sz = size (location); elseif (nargin == 4) if (isscalar (varargin{1}) && varargin{1} >= 0) sz = [varargin{1}, varargin{1}]; elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) sz = varargin{1}; else error ("gprnd: dimension vector must be row vector of non-negative integers"); endif elseif (nargin > 4) if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) error ("gprnd: dimensions must be non-negative integers"); endif sz = [varargin{:}]; endif if (! isscalar (location) && ! isequal (size (location), sz)) error ("gprnd: LOCATION, SCALE and SHAPE must be scalar or of size SZ"); endif if (isa (location, "single") || isa (scale, "single") || isa (shape, "single")) cls = "single"; else cls = "double"; endif if (isscalar (location) && isscalar (scale) && isscalar (shape)) if ((-Inf < location) && (location < Inf) && (0 < scale) && (scale < Inf) ... && (-Inf < shape) && (shape < Inf)) rnd = rand(sz,cls); if (shape == 0) rnd = -log(1 - rnd); rnd = scale * rnd + location; elseif ((shape < 0) || (shape > 0)) rnd = (1 - rnd).^(-shape) - 1; rnd = (scale / shape) * rnd + location; end else rnd = NaN (sz, cls); endif else rnd = NaN (sz, cls); k = (-Inf < location) & (location < Inf) & (scale > 0) ... & (-Inf < shape) & (shape < Inf); rnd(k(:)) = rand (1, sum(k(:)), cls); if (any (shape == 0)) rnd(k) = -log(1 - rnd(k)); rnd(k) = scale(k) .* rnd(k) + location(k); elseif (any (shape < 0 | shape > 0)) rnd(k) = (1 - rnd(k)).^(-shape(k)) - 1; rnd(k) = (scale(k) ./ shape(k)) .* rnd(k) + location(k); end endif endfunction %!assert (size (gprnd (0,1,0)), [1, 1]) %!assert (size (gprnd (0, 1, zeros (2,1))), [2, 1]) %!assert (size (gprnd (0, 1, zeros (2,2))), [2, 2]) %!assert (size (gprnd (0, ones (2,1), 0)), [2, 1]) %!assert (size (gprnd (0, ones (2,2), 0)), [2, 2]) %!assert (size (gprnd (zeros (2,1), 1, 0)), [2, 1]) %!assert (size (gprnd (zeros (2,2), 1, 0)), [2, 2]) %!assert (size (gprnd (0, 1, 0, 3)), [3, 3]) %!assert (size (gprnd (0, 1, 0, [4 1])), [4, 1]) %!assert (size (gprnd (0, 1, 0, 4, 1)), [4, 1]) %!assert (size (gprnd (1,1,0)), [1, 1]) %!assert (size (gprnd (1, 1, zeros (2,1))), [2, 1]) %!assert (size (gprnd (1, 1, zeros (2,2))), [2, 2]) %!assert (size (gprnd (1, ones (2,1), 0)), [2, 1]) %!assert (size (gprnd (1, ones (2,2), 0)), [2, 2]) %!assert (size (gprnd (ones (2,1), 1, 0)), [2, 1]) %!assert (size (gprnd (ones (2,2), 1, 0)), [2, 2]) %!assert (size (gprnd (1, 1, 0, 3)), [3, 3]) %!assert (size (gprnd (1, 1, 0, [4 1])), [4, 1]) %!assert (size (gprnd (1, 1, 0, 4, 1)), [4, 1]) %!assert (size (gprnd (-1, 1, 0)), [1, 1]) %!assert (size (gprnd (-1, 1, zeros (2,1))), [2, 1]) %!assert (size (gprnd (1, -1, zeros (2,2))), [2, 2]) %!assert (size (gprnd (-1, ones (2,1), 0)), [2, 1]) %!assert (size (gprnd (-1, ones (2,2), 0)), [2, 2]) %!assert (size (gprnd (-ones (2,1), 1, 0)), [2, 1]) %!assert (size (gprnd (-ones (2,2), 1, 0)), [2, 2]) %!assert (size (gprnd (-1, 1, 0, 3)), [3, 3]) %!assert (size (gprnd (-1, 1, 0, [4 1])), [4, 1]) %!assert (size (gprnd (-1, 1, 0, 4, 1)), [4, 1]) ## Test class of input preserved %!assert (class (gprnd (0,1,0)), "double") %!assert (class (gprnd (0, 1, single (0))), "single") %!assert (class (gprnd (0, 1, single ([0 0]))), "single") %!assert (class (gprnd (0,single (1),0)), "single") %!assert (class (gprnd (0,single ([1 1]),0)), "single") %!assert (class (gprnd (single (0), 1, 0)), "single") %!assert (class (gprnd (single ([0 0]), 1, 0)), "single") ## Test input validation %!error gprnd () %!error gprnd (1) %!error gprnd (1,2) %!error gprnd (zeros (2), ones (2), zeros (3)) %!error gprnd (zeros (2), ones (3), zeros (2)) %!error gprnd (zeros (3), ones (2), zeros (2)) %!error gprnd (i, 1, 0) %!error gprnd (0, i, 0) %!error gprnd (0, 1, i) %!error gprnd (0,1,0, -1) %!error gprnd (0,1,0, ones (2)) %!error gprnd (0,1,0, [2 -1 2]) %!error gprnd (0,1, zeros (2), 3) %!error gprnd (0,1, zeros (2), [3, 2]) %!error gprnd (0,1, zeros (2), 3, 2) statistics-1.4.3/inst/grp2idx.m0000644000000000000000000001135214153320774014621 0ustar0000000000000000## Copyright (C) 2015 CarnĂ« Draug ## ## This program is free software; you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation; either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; if not, see ## . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{g}, @var{gn}, @var{gl}] =} grp2idx (@var{s}) ## Get index for group variables. ## ## For variable @var{s}, returns the indices @var{g}, into the variable ## groups @var{gn} and @var{gl}. The first has a string representation of ## the groups while the later has its actual values. ## ## NaNs and empty strings in @var{s} appear as NaN in @var{g} and are ## not present on either @var{gn} and @var{gl}. ## ## @seealso{cellstr, num2str, unique} ## @end deftypefn function [g, gn, gl] = grp2idx (s) if (nargin != 1) print_usage (); endif s_was_char = false; if (ischar (s)) s_was_char = true; s = cellstr (s); elseif (! isvector (s)) error ("grp2idx: S must be a vector, cell array of strings, or char matrix"); endif ## FIXME once Octave core implements "sorted" and "stable" argument to ## unique(), we can use the following snippet so that we are fully ## Matlab compatible. # set_order = "sorted"; # if (iscellstr (s)) # set_order = "stable"; # endif # [gl, ~, g] = unique (s(:), set_order); [gl, ~, g] = unique (s(:)); ## handle NaNs and empty strings if (iscellstr (s)) ## FIXME empty strings appear at the front because unique is sorting ## them, so we only need to subtract one. However, when fix the ## order for strings (when core's unique has the stable option), ## then we'll have to come up with something clever. empties = cellfun (@isempty, s); if (any (empties)) g(empties) = NaN; g--; gl(1) = []; endif else ## This works fine because NaN come at the end after sorting, we don't ## have to worry about change on the indices. g(isnan (s)) = NaN; gl(isnan (gl)) = []; endif if (isargout (2)) if (iscellstr (gl)) gn = gl; elseif (iscell (gl)) gn = cellfun (@num2str, gl, "UniformOutput", false); else gn = arrayfun (@num2str, gl, "UniformOutput", false); endif endif if (isargout (3) && s_was_char) gl = char (gl); endif endfunction ## test boolean input and note that row or column vector makes no difference %!test %! in = [true false false true]; %! out = {[2; 1; 1; 2] {"0"; "1"} [false; true]}; %! assert (nthargout (1:3, @grp2idx, in), out) %! assert (nthargout (1:3, @grp2idx, in), nthargout (1:3, @grp2idx, in')) ## test that groups are ordered in boolean %!test %! assert (nthargout (1:3, @grp2idx, [false true]), %! {[1; 2] {"0"; "1"} [false; true]}); %! assert (nthargout (1:3, @grp2idx, [true false]), %! {[2; 1] {"0"; "1"} [false; true]}); ## test char matrix and cell array of strings %!assert (nthargout (1:3, @grp2idx, ["oct"; "sci"; "oct"; "oct"; "sci"]), %! {[1; 2; 1; 1; 2] {"oct"; "sci"} ["oct"; "sci"]}); ## and cell array of strings %!assert (nthargout (1:3, @grp2idx, {"oct"; "sci"; "oct"; "oct"; "sci"}), %! {[1; 2; 1; 1; 2] {"oct"; "sci"} {"oct"; "sci"}}); ## test numeric arrays %!assert (nthargout (1:3, @grp2idx, [ 1 -3 -2 -3 -3 2 1 -1 3 -3]), %! {[4; 1; 2; 1; 1; 5; 4; 3; 6; 1] {"-3"; "-2"; "-1"; "1"; "2"; "3"} ... %! [-3; -2; -1; 1; 2; 3]}); ## test for NaN and empty strings %!assert (nthargout (1:3, @grp2idx, [2 2 3 NaN 2 3]), %! {[1; 1; 2; NaN; 1; 2] {"2"; "3"} [2; 3]}) %!assert (nthargout (1:3, @grp2idx, {"et" "sa" "sa" "" "et"}), %! {[1; 2; 2; NaN; 1] {"et"; "sa"} {"et"; "sa"}}) ## FIXME this fails because unique() in core does not yet have set_order ## option implemented. See code for code to uncomment once it is ## implemented in core. ## Test that order when handling strings is by order of appearance %!xtest <51928> assert (nthargout (1:3, @grp2idx, ["sci"; "oct"; "sci"; "oct"; "oct"]), %! {[1; 2; 1; 2; 2] {"sci"; "oct"} ["sci"; "oct"]}); %!xtest <51928> assert (nthargout (1:3, @grp2idx, {"sci"; "oct"; "sci"; "oct"; "oct"}), %! {[1; 2; 1; 2; 2] {"sci"; "oct"} {"sci"; "oct"}}); %!xtest <51928> assert (nthargout (1:3, @grp2idx, {"sa" "et" "et" "" "sa"}), %! {[1; 2; 2; NaN; 1] {"sa"; "et"} {"sa"; "et"}}) statistics-1.4.3/inst/gscatter.m0000644000000000000000000001715614153320774015066 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} gscatter (@var{x}, @var{y}, @var{g}) ## @deftypefnx {Function File} @ ## {} gscatter (@var{x}, @var{y}, @var{g}, @var{clr}, @var{sym}, @var{siz}) ## @deftypefnx {Function File} @ ## {} gscatter (@dots{}, @var{doleg}, @var{xnam}, @var{ynam}) ## @deftypefnx {Function File} {@var{h} =} gscatter (@dots{}) ## ## Draw a scatter plot with grouped data. ## ## @code{gscatter} is a utility function to draw a scatter plot of @var{x} and ## @var{y}, according to the groups defined by @var{g}. Input @var{x} and ## @var{y} are numeric vectors of the same size, while @var{g} is either a ## vector of the same size as @var{x} or a character matrix with the same number ## of rows as the size of @var{x}. As a vector @var{g} can be numeric, logical, ## a character array, a string array (not implemented), a cell string or cell ## array. ## ## A number of optional inputs change the appearance of the plot: ## @itemize @bullet ## @item @var{"clr"} ## defines the color for each group; if not enough colors are defined by ## @var{"clr"}, @code{gscatter} cycles through the specified colors. Colors can ## be defined as named colors, as rgb triplets or as indices for the current ## @code{colormap}. The default value is a different color for each group, ## according to the current @code{colormap}. ## ## @item @var{"sym"} ## is a char array of symbols for each group; if not enough symbols are defined ## by @var{"sym"}, @code{gscatter} cycles through the specified symbols. ## ## @item @var{"siz"} ## is a numeric array of sizes for each group; if not enough sizes are defined ## by @var{"siz"}, @code{gscatter} cycles through the specified sizes. ## ## @item @var{"doleg"} ## is a boolean value to show the legend; it can be either @qcode{on} (default) ## or @qcode{off}. ## ## @item @var{"xnam"} ## is a character array, the name for the x axis. ## ## @item @var{"ynam"} ## is a character array, the name for the y axis. ## @end itemize ## ## Output @var{h} is an array of graphics handles to the @code{line} object of ## each group. ## ## @end deftypefn ## ## @seealso{scatter} function h = gscatter (varargin) ## optional axes handle if (isaxes (varargin{1})) ## parameter is an axes handle hax = varargin{1}; varargin = varargin(2:end); nargin--; endif ## check the input parameters if (nargin < 3) print_usage (); endif ## ## necessary parameters ## ## x coordinates if (isvector (varargin{1}) && isnumeric (varargin{1})) x = varargin{1}; n = numel (x); else error ("gscatter: x must be a numeric vector"); endif ## y coordinates if (isvector (varargin{2}) && isnumeric (varargin{2})) if (numel (varargin{2}) == n) y = varargin{2}; else error ("gscatter: x and y must have the same size"); endif else error ("gscatter: y must be a numeric vector"); endif ## groups if (isrow (varargin{3})) varargin{3} = transpose (varargin{3}); endif if (ismatrix (varargin{3}) && ischar (varargin{3})) varargin{3} = cellstr (varargin{3}); # char matrix to cellstr elseif (iscell (varargin{3}) && ! iscellstr (varargin{3})) varargin{3} = cell2mat (varargin{3}); # numeric cell to vector endif if (isvector (varargin{3})) # only numeric vectors or cellstr if (rows (varargin{3}) == n) gv = varargin{3}; g_names = unique (gv, "rows"); g_len = numel (g_names); if (iscellstr (g_names)) for i = 1 : g_len g(find (strcmp(gv, g_names{i}))) = i; endfor else for i = 1 : g_len g(find (gv == g_names(i))) = i; endfor endif else error ("gscatter: g must have the same size as x and y"); endif else error (["gscatter: g must be a numeric or logical or char vector, "... "or a cell or cellstr array, or a char matrix"]); endif ## ## optional parameters ## ## Note: this parameters are passed as they are to 'line', ## the validity check is delegated to 'line' g_col = lines (g_len); g_size = 6 * ones (g_len, 1); g_sym = repmat ('o', 1, g_len); ## optional parameters for legend and axes labels do_legend = 1; # legend shown by default ## MATLAB compatibility: by default MATLAB uses the variable name as ## label for either axis mygetname = @(x) inputname(1); # to retrieve the name of a variable x_nam = mygetname (varargin{1}); # this should retrieve the name of the var, y_nam = mygetname (varargin{2}); # but it does not work ## parameters are all in fixed positions for i = 4 : nargin switch (i) case 4 ## colours c_list = varargin{4}; if (isrow (c_list)) c_list = transpose (c_list); endif c_list_len = rows (c_list); g_col = repmat (c_list, ceil (g_len / c_list_len)); case {5, 6} ## size and symbols s_list = varargin{i}; s_list_len = length (s_list); g_tmp = repmat (s_list, ceil (g_len / s_list_len)); if (i == 6) g_size = g_tmp; else g_sym = g_tmp; endif case 7 ## legend switch (lower (varargin{7})) case "on" do_legend = 1; case "off" do_legend = 0; otherwise error ("gscatter: invalid dolegend parameter '%s'", varargin{7}); endswitch case {8, 9} ## x and y label if (! ischar (varargin{i}) && ! isvector (varargin{i})) error ("gscatter: xnam and ynam must be strings"); endif if (i == 8) x_nam = varargin{8}; else y_nam = varargin{9}; endif endswitch endfor ## scatter plot with grouping if (! exist ("hax", "var")) hax = gca (); endif ## return value h = []; hold on; for i = 1 : g_len idcs = find (g == i); h(i) = line (hax, x(idcs), y(idcs), "linestyle", "none", ... "markersize", g_size(i), "color", g_col(i,:), "marker", g_sym(i)); endfor if (do_legend) if (isnumeric (g_names)) g_names = num2str (g_names); endif warning ("off", "Octave:legend:unimplemented-location", "local"); legend (hax, g_names, "location", "best"); endif xlabel (hax, x_nam); ylabel (hax, y_nam); hold off; endfunction ## input tests %!error gscatter(); %!error gscatter([1]); %!error gscatter([1], [2]); %!error gscatter('abc', [1 2 3], [1]); %!error gscatter([1 2 3], [1 2], [1]); %!error gscatter([1 2 3], 'abc', [1]); %!error gscatter([1 2], [1 2], [1]); %!error gscatter([1 2], [1 2], [1 2], 'rb', 'so', 12, 'xxx'); ## demonstration %!demo %! load fisheriris; %! X = meas(:,3:4); %! cidcs = kmeans (X, 3, "Replicates", 5); %! gscatter (X(:,1), X(:,2), cidcs, [.75 .75 0; 0 .75 .75; .75 0 .75], "os^"); %! title ("Fisher's iris data"); statistics-1.4.3/inst/harmmean.m0000644000000000000000000000215114153320774015027 0ustar0000000000000000## Copyright (C) 2001 Paul Kienzle ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} harmmean (@var{x}) ## @deftypefnx{Function File} harmmean (@var{x}, @var{dim}) ## Compute the harmonic mean. ## ## This function does the same as @code{mean (x, "h")}. ## ## @seealso{mean} ## @end deftypefn function a = harmmean(x, dim) if (nargin == 1) a = mean(x, "h"); elseif (nargin == 2) a = mean(x, "h", dim); else print_usage; endif endfunction statistics-1.4.3/inst/hist3.m0000644000000000000000000003105114153320774014272 0ustar0000000000000000## Copyright (C) 2015 CarnĂ« Draug ## ## This program is free software; you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation; either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; if not, see ## . ## -*- texinfo -*- ## @deftypefn {Function File} {} hist3 (@var{X}) ## @deftypefnx {Function File} {} hist3 (@var{X}, @var{nbins}) ## @deftypefnx {Function File} {} hist3 (@var{X}, @qcode{"Nbins"}, @var{nbins}) ## @deftypefnx {Function File} {} hist3 (@var{X}, @var{centers}) ## @deftypefnx {Function File} {} hist3 (@var{X}, @qcode{"Ctrs"}, @var{centers}) ## @deftypefnx {Function File} {} hist3 (@var{X}, @qcode{"Edges"}, @var{edges}) ## @deftypefnx {Function File} {[@var{N}, @var{C}] =} hist3 (@dots{}) ## @deftypefnx {Function File} {} hist3 (@dots{}, @var{prop}, @var{val}, @dots{}) ## @deftypefnx {Function File} {} hist3 (@var{hax}, @dots{}) ## Produce bivariate (2D) histogram counts or plots. ## ## The elements to produce the histogram are taken from the Nx2 matrix ## @var{X}. Any row with NaN values are ignored. The actual bins can ## be configured in 3 different: number, centers, or edges of the bins: ## ## @table @asis ## @item Number of bins (default) ## Produces equally spaced bins between the minimum and maximum values ## of @var{X}. Defined as a 2 element vector, @var{nbins}, one for each ## dimension. Defaults to @code{[10 10]}. ## ## @item Center of bins ## Defined as a cell array of 2 monotonically increasing vectors, ## @var{centers}. The width of each bin is determined from the adjacent ## values in the vector with the initial and final bin, extending to Infinity. ## ## @item Edge of bins ## Defined as a cell array of 2 monotonically increasing vectors, ## @var{edges}. @code{@var{N}(i,j)} contains the number of elements ## in @var{X} for which: ## ## @itemize @w{} ## @item ## @var{edges}@{1@}(i) <= @var{X}(:,1) < @var{edges}@{1@}(i+1) ## @item ## @var{edges}@{2@}(j) <= @var{X}(:,2) < @var{edges}@{2@}(j+1) ## @end itemize ## ## The consequence of this definition is that values outside the initial ## and final edge values are ignored, and that the final bin only contains ## the number of elements exactly equal to the final edge. ## ## @end table ## ## The return values, @var{N} and @var{C}, are the bin counts and centers ## respectively. These are specially useful to produce intensity maps: ## ## @example ## [counts, centers] = hist3 (data); ## imagesc (centers@{1@}, centers@{2@}, counts) ## @end example ## ## If there is no output argument, or if the axes graphics handle ## @var{hax} is defined, the function will plot a 3 dimensional bar ## graph. Any extra property/value pairs are passed directly to the ## underlying surface object. ## ## @seealso{hist, histc, lookup, mesh} ## @end deftypefn function [N, C] = hist3 (X, varargin) if (nargin < 1) print_usage (); endif next_argin = 1; should_draw = true; if (isaxes (X)) hax = X; X = varargin{next_argin++}; elseif (nargout == 0) hax = gca (); else should_draw = false; endif if (! ismatrix (X) || columns (X) != 2) error ("hist3: X must be a 2 columns matrix"); endif method = "nbins"; val = [10 10]; if (numel (varargin) >= next_argin) this_arg = varargin{next_argin++}; if (isnumeric (this_arg)) method = "nbins"; val = this_arg; elseif (iscell (this_arg)) method = "ctrs"; val = this_arg; elseif (numel (varargin) >= next_argin && any (strcmpi ({"nbins", "ctrs", "edges"}, this_arg))) method = tolower (this_arg); val = varargin{next_argin++}; else next_argin--; endif endif have_centers = false; switch (tolower (method)) case "nbins" [r_edges, c_edges] = edges_from_nbins (X, val); case "ctrs" have_centers = true; centers = val; [r_edges, c_edges] = edges_from_centers (val); case "centers" ## This was supported until 1.2.4 when the Matlab compatible option ## 'Ctrs' was added. persistent warned = false; if (! warned) warning ("hist3: option `centers' is deprecated. Use `ctrs'"); endif have_centers = true; centers = val; [r_edges, c_edges] = edges_from_centers (val); case "edges" if (! iscell (val) || numel (val) != 2 || ! all (cellfun (@isvector, val))) error ("hist3: EDGES must be a cell array with 2 vectors"); endif [r_edges] = vec (val{1}, 2); [c_edges] = vec (val{2}, 2); out_rows = any (X < [r_edges(1) c_edges(1)] | X > [r_edges(end) c_edges(end)], 2); X(out_rows,:) = []; otherwise ## we should never get here... error ("hist3: invalid binning method `%s'", method); endswitch ## We only remove the NaN now, after having computed the bin edges, ## because the extremes from each column that define the edges may ## be paired with a NaN. While such values do not appear on the ## histogram, they must still be used to compute the histogram ## edges. X(any (isnan (X), 2), :) = []; r_idx = lookup (r_edges, X(:,1), "l"); c_idx = lookup (c_edges, X(:,2), "l"); counts_size = [numel(r_edges) numel(c_edges)]; counts = accumarray ([r_idx, c_idx], 1, counts_size); if (should_draw) counts = counts.'; z = zeros ((size (counts) +1) *2); z(2:end-1,2:end-1) = kron (counts, ones (2, 2)); ## Setting the values for the end of the histogram bin like this ## seems straight wrong but that's hwo Matlab plots look. y = [kron(c_edges, ones (1, 2)) (c_edges(end)*2-c_edges(end-1))([1 1])]; x = [kron(r_edges, ones (1, 2)) (r_edges(end)*2-r_edges(end-1))([1 1])]; mesh (hax, x, y, z, "facecolor", [.75 .85 .95], varargin{next_argin:end}); else N = counts; if (isargout (2)) if (! have_centers) C = {(r_edges + [diff(r_edges)([1:end end])]/ 2) ... (c_edges + [diff(c_edges)([1:end end])]/ 2)}; else C = centers(:)'; C{1} = vec (C{1}, 2); C{2} = vec (C{2}, 2); endif endif endif endfunction function [r_edges, c_edges] = edges_from_nbins (X, nbins) if (! isnumeric (nbins) || numel (nbins) != 2) error ("hist3: NBINS must be a 2 element vector"); endif inits = min (X, [], 1); ends = max (X, [], 1); ends -= (ends - inits) ./ vec (nbins, 2); ## If any histogram side has an empty range, then still make NBINS ## but then place that value at the centre of the centre bin so that ## they appear in the centre in the plot. single_bins = inits == ends; if (any (single_bins)) inits(single_bins) -= (floor (nbins(single_bins) ./2)) + 0.5; ends(single_bins) = inits(single_bins) + nbins(single_bins) -1; endif r_edges = linspace (inits(1), ends(1), nbins(1)); c_edges = linspace (inits(2), ends(2), nbins(2)); endfunction function [r_edges, c_edges] = edges_from_centers (ctrs) if (! iscell (ctrs) || numel (ctrs) != 2 || ! all (cellfun (@isvector, ctrs))) error ("hist3: CTRS must be a cell array with 2 vectors"); endif r_edges = vec (ctrs{1}, 2); c_edges = vec (ctrs{2}, 2); r_edges(2:end) -= diff (r_edges) / 2; c_edges(2:end) -= diff (c_edges) / 2; endfunction %!demo %! X = [ %! 1 1 %! 1 1 %! 1 10 %! 1 10 %! 5 5 %! 5 5 %! 5 5 %! 5 5 %! 5 5 %! 7 3 %! 7 3 %! 7 3 %! 10 10 %! 10 10]; %! hist3 (X) %!test %! N_exp = [ 0 0 0 5 20 %! 0 0 10 15 0 %! 0 15 10 0 0 %! 20 5 0 0 0]; %! %! n = 100; %! x = [1:n]'; %! y = [n:-1:1]'; %! D = [x y]; %! N = hist3 (D, [4 5]); %! assert (N, N_exp); %!test %! N_exp = [0 0 0 0 1 %! 0 0 0 0 1 %! 0 0 0 0 1 %! 1 1 1 1 93]; %! %! n = 100; %! x = [1:n]'; %! y = [n:-1:1]'; %! D = [x y]; %! C{1} = [1 1.7 3 4]; %! C{2} = [1:5]; %! N = hist3 (D, C); %! assert (N, N_exp); ## bug 44987 %!test %! D = [1 1; 3 1; 3 3; 3 1]; %! [c, nn] = hist3 (D, {0:4, 0:4}); %! exp_c = zeros (5); %! exp_c([7 9 19]) = [1 2 1]; %! assert (c, exp_c); %! assert (nn, {0:4, 0:4}); %!test %! for i = 10 %! assert (size (hist3 (rand (9, 2), "Edges", {[0:.2:1]; [0:.2:1]})), [6 6]) %! endfor %!test %! edge_1 = linspace (0, 10, 10); %! edge_2 = linspace (0, 50, 10); %! [c, nn] = hist3 ([1:10; 1:5:50]', "Edges", {edge_1, edge_2}); %! exp_c = zeros (10, 10); %! exp_c([1 12 13 24 35 46 57 68 79 90]) = 1; %! assert (c, exp_c); %! %! assert (nn{1}, edge_1 + edge_1(2)/2, eps*10^4) %! assert (nn{2}, edge_2 + edge_2(2)/2, eps*10^4) %!shared X %! X = [ %! 5 2 %! 5 3 %! 1 4 %! 5 3 %! 4 4 %! 1 2 %! 2 3 %! 3 3 %! 5 4 %! 5 3]; %!test %! N = zeros (10); %! N([1 10 53 56 60 91 98 100]) = [1 1 1 1 3 1 1 1]; %! C = {(1.2:0.4:4.8), (2.1:0.2:3.9)}; %! assert (nthargout ([1 2], @hist3, X), {N C}, eps*10^3) %!test %! N = zeros (5, 7); %! N([1 5 17 18 20 31 34 35]) = [1 1 1 1 3 1 1 1]; %! C = {(1.4:0.8:4.6), ((2+(1/7)):(2/7):(4-(1/7)))}; %! assert (nthargout ([1 2], @hist3, X, [5 7]), {N C}, eps*10^3) %! assert (nthargout ([1 2], @hist3, X, "Nbins", [5 7]), {N C}, eps*10^3) %!test %! N = [0 1 0; 0 1 0; 0 0 1; 0 0 0]; %! C = {(2:5), (2.5:1:4.5)}; %! assert (nthargout ([1 2], @hist3, X, "Edges", {(1.5:4.5), (2:4)}), {N C}) %!test %! N = [0 0 1 0 1 0; 0 0 0 1 0 0; 0 0 1 4 2 0]; %! C = {(1.2:3.2), (0:5)}; %! assert (nthargout ([1 2], @hist3, X, "Ctrs", C), {N C}) %! assert (nthargout ([1 2], @hist3, X, C), {N C}) %!test %! [~, C] = hist3 (rand (10, 2), "Edges", {[0 .05 .15 .35 .55 .95], %! [-1 .05 .07 .2 .3 .5 .89 1.2]}); %! C_exp = {[ 0.025 0.1 0.25 0.45 0.75 1.15], ... %! [-0.475 0.06 0.135 0.25 0.4 0.695 1.045 1.355]}; %! assert (C, C_exp, eps*10^2) ## Test how handling of out of borders is different whether we are ## defining Centers or Edges. %!test %! Xv = repmat ([1:10]', [1 2]); %! %! ## Test Centers %! assert (hist3 (Xv, "Ctrs", {1:10, 1:10}), eye (10)) %! %! N_exp = eye (6); %! N_exp([1 end]) = 3; %! assert (hist3 (Xv, "Ctrs", {3:8, 3:8}), N_exp) %! %! N_exp = zeros (8, 6); %! N_exp([1 2 11 20 29 38 47 48]) = [2 1 1 1 1 1 1 2]; %! assert (hist3 (Xv, "Ctrs", {2:9, 3:8}), N_exp) %! %! ## Test Edges %! assert (hist3 (Xv, "Edges", {1:10, 1:10}), eye (10)) %! assert (hist3 (Xv, "Edges", {3:8, 3:8}), eye (6)) %! assert (hist3 (Xv, "Edges", {2:9, 3:8}), [zeros(1, 6); eye(6); zeros(1, 6)]) %! %! N_exp = zeros (14); %! N_exp(3:12, 3:12) = eye (10); %! assert (hist3 (Xv, "Edges", {-1:12, -1:12}), N_exp) %! %! ## Test for Nbins %! assert (hist3 (Xv), eye (10)) %! assert (hist3 (Xv, [10 10]), eye (10)) %! assert (hist3 (Xv, "nbins", [10 10]), eye (10)) %! assert (hist3 (Xv, [5 5]), eye (5) * 2) %! %! N_exp = zeros (7, 5); %! N_exp([1 9 10 18 26 27 35]) = [2 1 1 2 1 1 2]; %! assert (hist3 (Xv, [7 5]), N_exp) %!test # bug #51059 %! D = [1 1; NaN 2; 3 1; 3 3; 1 NaN; 3 1]; %! [c, nn] = hist3 (D, {0:4, 0:4}); %! exp_c = zeros (5); %! exp_c([7 9 19]) = [1 2 1]; %! assert (c, exp_c) %! assert (nn, {0:4, 0:4}) ## Single row of data or cases where all elements have the same value ## on one side of the histogram. %!test %! [c, nn] = hist3 ([1 8]); %! exp_c = zeros (10, 10); %! exp_c(6, 6) = 1; %! exp_nn = {-4:5, 3:12}; %! assert (c, exp_c) %! assert (nn, exp_nn, eps) %! %! [c, nn] = hist3 ([1 8], [10 11]); %! exp_c = zeros (10, 11); %! exp_c(6, 6) = 1; %! exp_nn = {-4:5, 3:13}; %! assert (c, exp_c) %! assert (nn, exp_nn, eps) ## NaNs paired with values defining the histogram edges. %!test %! [c, nn] = hist3 ([1 NaN; 2 3; 6 9; 8 NaN]); %! exp_c = zeros (10, 10); %! exp_c(2, 1) = 1; %! exp_c(8, 10) = 1; %! exp_nn = {linspace(1.35, 7.65, 10) linspace(3.3, 8.7, 10)}; %! assert (c, exp_c) %! assert (nn, exp_nn, eps*100) ## Columns full of NaNs (recent Matlab versions seem to throw an error ## but this did work like this on R2010b at least). %!test %! [c, nn] = hist3 ([1 NaN; 2 NaN; 6 NaN; 8 NaN]); %! exp_c = zeros (10, 10); %! exp_nn = {linspace(1.35, 7.65, 10) NaN(1, 10)}; %! assert (c, exp_c) %! assert (nn, exp_nn, eps*100) ## Behaviour of an empty X after removal of rows with NaN. %!test %! [c, nn] = hist3 ([1 NaN; NaN 3; NaN 9; 8 NaN]); %! exp_c = zeros (10, 10); %! exp_nn = {linspace(1.35, 7.65, 10) linspace(3.3, 8.7, 10)}; %! assert (c, exp_c) %! assert (nn, exp_nn, eps*100) statistics-1.4.3/inst/histfit.m0000644000000000000000000000422614153320774014716 0ustar0000000000000000## Copyright (C) 2003 Alberto Terruzzi ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} histfit (@var{data}, @var{nbins}) ## ## Plot histogram with superimposed fitted normal density. ## ## @code{histfit (@var{data}, @var{nbins})} plots a histogram of the values in ## the vector @var{data} using @var{nbins} bars in the histogram. With one input ## argument, @var{nbins} is set to the square root of the number of elements in ## data. ## ## Example ## ## @example ## histfit (randn (100, 1)) ## @end example ## ## @seealso{bar,hist, pareto} ## @end deftypefn ## Author: Alberto Terruzzi ## Version: 1.0 ## Created: 3 March 2004 function histfit (data,nbins) if nargin < 1 || nargin > 2 print_usage; endif if isvector (data) != 1 error ("data must be a vector."); endif row = sum(~isnan(data)); if nargin < 2 nbins = ceil(sqrt(row)); endif [n,xbin]=hist(data,nbins); if any(abs(diff(xbin,2)) > 10*max(abs(xbin))*eps) error("histfit bins must be uniform width"); endif mr = nanmean(data); ## Estimates the parameter, MU, of the normal distribution. sr = nanstd(data); ## Estimates the parameter, SIGMA, of the normal distribution. x=(-3*sr+mr:0.1*sr:3*sr+mr)';## Evenly spaced samples of the expected data range. [xb,yb] = bar(xbin,n); y = normpdf(x,mr,sr); binwidth = xbin(2)-xbin(1); y = row*y*binwidth; ## Normalization necessary to overplot the histogram. plot(xb,yb,";;b",x,y,";;r-"); ## Plots density line over histogram. endfunction statistics-1.4.3/inst/hmmestimate.m0000644000000000000000000003254414153320774015565 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{transprobest}, @var{outprobest}] =} hmmestimate (@var{sequence}, @var{states}) ## @deftypefnx {Function File} {} hmmestimate (@dots{}, 'statenames', @var{statenames}) ## @deftypefnx {Function File} {} hmmestimate (@dots{}, 'symbols', @var{symbols}) ## @deftypefnx {Function File} {} hmmestimate (@dots{}, 'pseudotransitions', @var{pseudotransitions}) ## @deftypefnx {Function File} {} hmmestimate (@dots{}, 'pseudoemissions', @var{pseudoemissions}) ## Estimate the matrix of transition probabilities and the matrix of output ## probabilities of a given sequence of outputs and states generated by a ## hidden Markov model. The model assumes that the generation starts in ## state @code{1} at step @code{0} but does not include step @code{0} in the ## generated states and sequence. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{sequence} is a vector of a sequence of given outputs. The outputs ## must be integers ranging from @code{1} to the number of outputs of the ## hidden Markov model. ## ## @item ## @var{states} is a vector of the same length as @var{sequence} of given ## states. The states must be integers ranging from @code{1} to the number ## of states of the hidden Markov model. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{transprobest} is the matrix of the estimated transition ## probabilities of the states. @code{transprobest(i, j)} is the estimated ## probability of a transition to state @code{j} given state @code{i}. ## ## @item ## @var{outprobest} is the matrix of the estimated output probabilities. ## @code{outprobest(i, j)} is the estimated probability of generating ## output @code{j} given state @code{i}. ## @end itemize ## ## If @code{'symbols'} is specified, then @var{sequence} is expected to be a ## sequence of the elements of @var{symbols} instead of integers. ## @var{symbols} can be a cell array. ## ## If @code{'statenames'} is specified, then @var{states} is expected to be ## a sequence of the elements of @var{statenames} instead of integers. ## @var{statenames} can be a cell array. ## ## If @code{'pseudotransitions'} is specified then the integer matrix ## @var{pseudotransitions} is used as an initial number of counted ## transitions. @code{pseudotransitions(i, j)} is the initial number of ## counted transitions from state @code{i} to state @code{j}. ## @var{transprobest} will have the same size as @var{pseudotransitions}. ## Use this if you have transitions that are very unlikely to occur. ## ## If @code{'pseudoemissions'} is specified then the integer matrix ## @var{pseudoemissions} is used as an initial number of counted outputs. ## @code{pseudoemissions(i, j)} is the initial number of counted outputs ## @code{j} given state @code{i}. If @code{'pseudoemissions'} is also ## specified then the number of rows of @var{pseudoemissions} must be the ## same as the number of rows of @var{pseudotransitions}. @var{outprobest} ## will have the same size as @var{pseudoemissions}. Use this if you have ## outputs or states that are very unlikely to occur. ## ## @subheading Examples ## ## @example ## @group ## transprob = [0.8, 0.2; 0.4, 0.6]; ## outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1]; ## [sequence, states] = hmmgenerate (25, transprob, outprob); ## [transprobest, outprobest] = hmmestimate (sequence, states) ## @end group ## ## @group ## symbols = @{'A', 'B', 'C'@}; ## statenames = @{'One', 'Two'@}; ## [sequence, states] = hmmgenerate (25, transprob, outprob, ## 'symbols', symbols, 'statenames', statenames); ## [transprobest, outprobest] = hmmestimate (sequence, states, ## 'symbols', symbols, ## 'statenames', statenames) ## @end group ## ## @group ## pseudotransitions = [8, 2; 4, 6]; ## pseudoemissions = [2, 4, 4; 7, 2, 1]; ## [sequence, states] = hmmgenerate (25, transprob, outprob); ## [transprobest, outprobest] = hmmestimate (sequence, states, 'pseudotransitions', pseudotransitions, 'pseudoemissions', pseudoemissions) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Lawrence R. Rabiner. A Tutorial on Hidden Markov Models and Selected ## Applications in Speech Recognition. @cite{Proceedings of the IEEE}, ## 77(2), pages 257-286, February 1989. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Estimation of a hidden Markov model for a given sequence function [transprobest, outprobest] = hmmestimate (sequence, states, varargin) # Check arguments if (nargin < 2 || mod (length (varargin), 2) != 0) print_usage (); endif len = length (sequence); if (length (states) != len) error ("hmmestimate: sequence and states must have equal length"); endif # Flag for symbols usesym = false; # Flag for statenames usesn = false; # Variables for return values transprobest = []; outprobest = []; # Process varargin for i = 1:2:length (varargin) # There must be an identifier: 'symbols', 'statenames', # 'pseudotransitions' or 'pseudoemissions' if (! ischar (varargin{i})) print_usage (); endif # Upper case is also fine lowerarg = lower (varargin{i}); if (strcmp (lowerarg, 'symbols')) usesym = true; # Use the following argument as symbols symbols = varargin{i + 1}; # The same for statenames elseif (strcmp (lowerarg, 'statenames')) usesn = true; # Use the following argument as statenames statenames = varargin{i + 1}; elseif (strcmp (lowerarg, 'pseudotransitions')) # Use the following argument as an initial count for transitions transprobest = varargin{i + 1}; if (! ismatrix (transprobest)) error ("hmmestimate: pseudotransitions must be a non-empty numeric matrix"); endif if (rows (transprobest) != columns (transprobest)) error ("hmmestimate: pseudotransitions must be a square matrix"); endif elseif (strcmp (lowerarg, 'pseudoemissions')) # Use the following argument as an initial count for outputs outprobest = varargin{i + 1}; if (! ismatrix (outprobest)) error ("hmmestimate: pseudoemissions must be a non-empty numeric matrix"); endif else error ("hmmestimate: expected 'symbols', 'statenames', 'pseudotransitions' or 'pseudoemissions' but found '%s'", varargin{i}); endif endfor # Transform sequence from symbols to integers if necessary if (usesym) # sequenceint is used to build the transformed sequence sequenceint = zeros (1, len); for i = 1:length (symbols) # Search for symbols(i) in the sequence, isequal will have 1 at # corresponding indices; i is the right integer for that symbol isequal = ismember (sequence, symbols(i)); # We do not want to change sequenceint if the symbol appears a second # time in symbols if (any ((sequenceint == 0) & (isequal == 1))) isequal *= i; sequenceint += isequal; endif endfor if (! all (sequenceint)) index = max ((sequenceint == 0) .* (1:len)); error (["hmmestimate: sequence(" int2str (index) ") not in symbols"]); endif sequence = sequenceint; else if (! isvector (sequence)) error ("hmmestimate: sequence must be a non-empty vector"); endif if (! all (ismember (sequence, 1:max (sequence)))) index = max ((ismember (sequence, 1:max (sequence)) == 0) .* (1:len)); error (["hmmestimate: sequence(" int2str (index) ") not feasible"]); endif endif # Transform states from statenames to integers if necessary if (usesn) # statesint is used to build the transformed states statesint = zeros (1, len); for i = 1:length (statenames) # Search for statenames(i) in states, isequal will have 1 at # corresponding indices; i is the right integer for that statename isequal = ismember (states, statenames(i)); # We do not want to change statesint if the statename appears a second # time in statenames if (any ((statesint == 0) & (isequal == 1))) isequal *= i; statesint += isequal; endif endfor if (! all (statesint)) index = max ((statesint == 0) .* (1:len)); error (["hmmestimate: states(" int2str (index) ") not in statenames"]); endif states = statesint; else if (! isvector (states)) error ("hmmestimate: states must be a non-empty vector"); endif if (! all (ismember (states, 1:max (states)))) index = max ((ismember (states, 1:max (states)) == 0) .* (1:len)); error (["hmmestimate: states(" int2str (index) ") not feasible"]); endif endif # Estimate the number of different states as the max of states nstate = max (states); # Estimate the number of different outputs as the max of sequence noutput = max (sequence); # transprobest is empty if pseudotransitions is not specified if (isempty (transprobest)) # outprobest is not empty if pseudoemissions is specified if (! isempty (outprobest)) if (nstate > rows (outprobest)) error ("hmmestimate: not enough rows in pseudoemissions"); endif # The number of states is specified by pseudoemissions nstate = rows (outprobest); endif transprobest = zeros (nstate, nstate); else if (nstate > rows (transprobest)) error ("hmmestimate: not enough rows in pseudotransitions"); endif # The number of states is given by pseudotransitions nstate = rows (transprobest); endif # outprobest is empty if pseudoemissions is not specified if (isempty (outprobest)) outprobest = zeros (nstate, noutput); else if (noutput > columns (outprobest)) error ("hmmestimate: not enough columns in pseudoemissions"); endif # Number of outputs is specified by pseudoemissions noutput = columns (outprobest); if (rows (outprobest) != nstate) error ("hmmestimate: pseudoemissions must have the same number of rows as pseudotransitions"); endif endif # Assume that the model started in state 1 cstate = 1; for i = 1:len # Count the number of transitions for each state pair transprobest(cstate, states(i)) ++; cstate = states (i); # Count the number of outputs for each state output pair outprobest(cstate, sequence(i)) ++; endfor # transprobest and outprobest contain counted numbers # Each row in transprobest and outprobest should contain estimated # probabilities # => scale so that the sum is 1 # A zero row remains zero # - for transprobest s = sum (transprobest, 2); s(s == 0) = 1; transprobest = transprobest ./ (s * ones (1, nstate)); # - for outprobest s = sum (outprobest, 2); s(s == 0) = 1; outprobest = outprobest ./ (s * ones (1, noutput)); endfunction %!test %! sequence = [1, 2, 1, 1, 1, 2, 2, 1, 2, 3, 3, 3, 3, 2, 3, 1, 1, 1, 1, 3, 3, 2, 3, 1, 3]; %! states = [1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1]; %! [transprobest, outprobest] = hmmestimate (sequence, states); %! expectedtransprob = [0.88889, 0.11111; 0.28571, 0.71429]; %! expectedoutprob = [0.16667, 0.33333, 0.50000; 1.00000, 0.00000, 0.00000]; %! assert (transprobest, expectedtransprob, 0.001); %! assert (outprobest, expectedoutprob, 0.001); %!test %! sequence = {'A', 'B', 'A', 'A', 'A', 'B', 'B', 'A', 'B', 'C', 'C', 'C', 'C', 'B', 'C', 'A', 'A', 'A', 'A', 'C', 'C', 'B', 'C', 'A', 'C'}; %! states = {'One', 'One', 'Two', 'Two', 'Two', 'One', 'One', 'One', 'One', 'One', 'One', 'One', 'One', 'One', 'One', 'Two', 'Two', 'Two', 'Two', 'One', 'One', 'One', 'One', 'One', 'One'}; %! symbols = {'A', 'B', 'C'}; %! statenames = {'One', 'Two'}; %! [transprobest, outprobest] = hmmestimate (sequence, states, 'symbols', symbols, 'statenames', statenames); %! expectedtransprob = [0.88889, 0.11111; 0.28571, 0.71429]; %! expectedoutprob = [0.16667, 0.33333, 0.50000; 1.00000, 0.00000, 0.00000]; %! assert (transprobest, expectedtransprob, 0.001); %! assert (outprobest, expectedoutprob, 0.001); %!test %! sequence = [1, 2, 1, 1, 1, 2, 2, 1, 2, 3, 3, 3, 3, 2, 3, 1, 1, 1, 1, 3, 3, 2, 3, 1, 3]; %! states = [1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1]; %! pseudotransitions = [8, 2; 4, 6]; %! pseudoemissions = [2, 4, 4; 7, 2, 1]; %! [transprobest, outprobest] = hmmestimate (sequence, states, 'pseudotransitions', pseudotransitions, 'pseudoemissions', pseudoemissions); %! expectedtransprob = [0.85714, 0.14286; 0.35294, 0.64706]; %! expectedoutprob = [0.178571, 0.357143, 0.464286; 0.823529, 0.117647, 0.058824]; %! assert (transprobest, expectedtransprob, 0.001); %! assert (outprobest, expectedoutprob, 0.001); statistics-1.4.3/inst/hmmgenerate.m0000644000000000000000000002102414153320774015533 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{sequence}, @var{states}] =} hmmgenerate (@var{len}, @var{transprob}, @var{outprob}) ## @deftypefnx {Function File} {} hmmgenerate (@dots{}, 'symbols', @var{symbols}) ## @deftypefnx {Function File} {} hmmgenerate (@dots{}, 'statenames', @var{statenames}) ## Generate an output sequence and hidden states of a hidden Markov model. ## The model starts in state @code{1} at step @code{0} but will not include ## step @code{0} in the generated states and sequence. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{len} is the number of steps to generate. @var{sequence} and ## @var{states} will have @var{len} entries each. ## ## @item ## @var{transprob} is the matrix of transition probabilities of the states. ## @code{transprob(i, j)} is the probability of a transition to state ## @code{j} given state @code{i}. ## ## @item ## @var{outprob} is the matrix of output probabilities. ## @code{outprob(i, j)} is the probability of generating output @code{j} ## given state @code{i}. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{sequence} is a vector of length @var{len} of the generated ## outputs. The outputs are integers ranging from @code{1} to ## @code{columns (outprob)}. ## ## @item ## @var{states} is a vector of length @var{len} of the generated hidden ## states. The states are integers ranging from @code{1} to ## @code{columns (transprob)}. ## @end itemize ## ## If @code{'symbols'} is specified, then the elements of @var{symbols} are ## used for the output sequence instead of integers ranging from @code{1} to ## @code{columns (outprob)}. @var{symbols} can be a cell array. ## ## If @code{'statenames'} is specified, then the elements of ## @var{statenames} are used for the states instead of integers ranging from ## @code{1} to @code{columns (transprob)}. @var{statenames} can be a cell ## array. ## ## @subheading Examples ## ## @example ## @group ## transprob = [0.8, 0.2; 0.4, 0.6]; ## outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1]; ## [sequence, states] = hmmgenerate (25, transprob, outprob) ## @end group ## ## @group ## symbols = @{'A', 'B', 'C'@}; ## statenames = @{'One', 'Two'@}; ## [sequence, states] = hmmgenerate (25, transprob, outprob, ## 'symbols', symbols, 'statenames', statenames) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Lawrence R. Rabiner. A Tutorial on Hidden Markov Models and Selected ## Applications in Speech Recognition. @cite{Proceedings of the IEEE}, ## 77(2), pages 257-286, February 1989. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Output sequence and hidden states of a hidden Markov model function [sequence, states] = hmmgenerate (len, transprob, outprob, varargin) # Check arguments if (nargin < 3 || mod (length (varargin), 2) != 0) print_usage (); endif if (! isscalar (len) || len < 0 || round (len) != len) error ("hmmgenerate: len must be a non-negative scalar integer") endif if (! ismatrix (transprob)) error ("hmmgenerate: transprob must be a non-empty numeric matrix"); endif if (! ismatrix (outprob)) error ("hmmgenerate: outprob must be a non-empty numeric matrix"); endif # nstate is the number of states of the hidden Markov model nstate = rows (transprob); # noutput is the number of different outputs that the hidden Markov model # can generate noutput = columns (outprob); # Check whether transprob and outprob are feasible for a hidden Markov # model if (columns (transprob) != nstate) error ("hmmgenerate: transprob must be a square matrix"); endif if (rows (outprob) != nstate) error ("hmmgenerate: outprob must have the same number of rows as transprob"); endif # Flag for symbols usesym = false; # Flag for statenames usesn = false; # Process varargin for i = 1:2:length (varargin) # There must be an identifier: 'symbols' or 'statenames' if (! ischar (varargin{i})) print_usage (); endif # Upper case is also fine lowerarg = lower (varargin{i}); if (strcmp (lowerarg, 'symbols')) if (length (varargin{i + 1}) != noutput) error ("hmmgenerate: number of symbols does not match number of possible outputs"); endif usesym = true; # Use the following argument as symbols symbols = varargin{i + 1}; # The same for statenames elseif (strcmp (lowerarg, 'statenames')) if (length (varargin{i + 1}) != nstate) error ("hmmgenerate: number of statenames does not match number of states"); endif usesn = true; # Use the following argument as statenames statenames = varargin{i + 1}; else error ("hmmgenerate: expected 'symbols' or 'statenames' but found '%s'", varargin{i}); endif endfor # Each row in transprob and outprob should contain probabilities # => scale so that the sum is 1 # A zero row remains zero # - for transprob s = sum (transprob, 2); s(s == 0) = 1; transprob = transprob ./ repmat (s, 1, nstate); # - for outprob s = sum (outprob, 2); s(s == 0) = 1; outprob = outprob ./ repmat (s, 1, noutput); # Generate sequences of uniformly distributed random numbers between 0 and # 1 # - for the state transitions transdraw = rand (1, len); # - for the outputs outdraw = rand (1, len); # Generate the return vectors # They remain unchanged if the according probability row of transprob # and outprob contain, respectively, only zeros sequence = ones (1, len); states = ones (1, len); if (len > 0) # Calculate cumulated probabilities backwards for easy comparison with # the generated random numbers # Cumulated probability in first column must always be 1 # We might have a zero row # - for transprob transprob(:, end:-1:1) = cumsum (transprob(:, end:-1:1), 2); transprob(:, 1) = 1; # - for outprob outprob(:, end:-1:1) = cumsum (outprob(:, end:-1:1), 2); outprob(:, 1) = 1; # cstate is the current state # Start in state 1 but do not include it in the states vector cstate = 1; for i = 1:len # Compare the randon number i of transdraw to the cumulated # probability of the state transition and set the transition # accordingly states(i) = sum (transdraw(i) <= transprob(cstate, :)); cstate = states(i); endfor # Compare the random numbers of outdraw to the cumulated probabilities # of the outputs and set the sequence vector accordingly sequence = sum (repmat (outdraw, noutput, 1) <= outprob(states, :)', 1); # Transform default matrices into symbols/statenames if requested if (usesym) sequence = reshape (symbols(sequence), 1, len); endif if (usesn) states = reshape (statenames(states), 1, len); endif endif endfunction %!test %! len = 25; %! transprob = [0.8, 0.2; 0.4, 0.6]; %! outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1]; %! [sequence, states] = hmmgenerate (len, transprob, outprob); %! assert (length (sequence), len); %! assert (length (states), len); %! assert (min (sequence) >= 1); %! assert (max (sequence) <= columns (outprob)); %! assert (min (states) >= 1); %! assert (max (states) <= rows (transprob)); %!test %! len = 25; %! transprob = [0.8, 0.2; 0.4, 0.6]; %! outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1]; %! symbols = {'A', 'B', 'C'}; %! statenames = {'One', 'Two'}; %! [sequence, states] = hmmgenerate (len, transprob, outprob, 'symbols', symbols, 'statenames', statenames); %! assert (length (sequence), len); %! assert (length (states), len); %! assert (strcmp (sequence, 'A') + strcmp (sequence, 'B') + strcmp (sequence, 'C') == ones (1, len)); %! assert (strcmp (states, 'One') + strcmp (states, 'Two') == ones (1, len)); statistics-1.4.3/inst/hmmviterbi.m0000644000000000000000000002205114153320774015406 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{vpath} =} hmmviterbi (@var{sequence}, @var{transprob}, @var{outprob}) ## @deftypefnx {Function File} {} hmmviterbi (@dots{}, 'symbols', @var{symbols}) ## @deftypefnx {Function File} {} hmmviterbi (@dots{}, 'statenames', @var{statenames}) ## Use the Viterbi algorithm to find the Viterbi path of a hidden Markov ## model given a sequence of outputs. The model assumes that the generation ## starts in state @code{1} at step @code{0} but does not include step ## @code{0} in the generated states and sequence. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{sequence} is the vector of length @var{len} of given outputs. The ## outputs must be integers ranging from @code{1} to ## @code{columns (outprob)}. ## ## @item ## @var{transprob} is the matrix of transition probabilities of the states. ## @code{transprob(i, j)} is the probability of a transition to state ## @code{j} given state @code{i}. ## ## @item ## @var{outprob} is the matrix of output probabilities. ## @code{outprob(i, j)} is the probability of generating output @code{j} ## given state @code{i}. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{vpath} is the vector of the same length as @var{sequence} of the ## estimated hidden states. The states are integers ranging from @code{1} to ## @code{columns (transprob)}. ## @end itemize ## ## If @code{'symbols'} is specified, then @var{sequence} is expected to be a ## sequence of the elements of @var{symbols} instead of integers ranging ## from @code{1} to @code{columns (outprob)}. @var{symbols} can be a cell array. ## ## If @code{'statenames'} is specified, then the elements of ## @var{statenames} are used for the states in @var{vpath} instead of ## integers ranging from @code{1} to @code{columns (transprob)}. ## @var{statenames} can be a cell array. ## ## @subheading Examples ## ## @example ## @group ## transprob = [0.8, 0.2; 0.4, 0.6]; ## outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1]; ## [sequence, states] = hmmgenerate (25, transprob, outprob) ## vpath = hmmviterbi (sequence, transprob, outprob) ## @end group ## ## @group ## symbols = @{'A', 'B', 'C'@}; ## statenames = @{'One', 'Two'@}; ## [sequence, states] = hmmgenerate (25, transprob, outprob, ## 'symbols', symbols, 'statenames', statenames) ## vpath = hmmviterbi (sequence, transprob, outprob, ## 'symbols', symbols, 'statenames', statenames) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Lawrence R. Rabiner. A Tutorial on Hidden Markov Models and Selected ## Applications in Speech Recognition. @cite{Proceedings of the IEEE}, ## 77(2), pages 257-286, February 1989. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Viterbi path of a hidden Markov model function vpath = hmmviterbi (sequence, transprob, outprob, varargin) # Check arguments if (nargin < 3 || mod (length (varargin), 2) != 0) print_usage (); endif if (! ismatrix (transprob)) error ("hmmviterbi: transprob must be a non-empty numeric matrix"); endif if (! ismatrix (outprob)) error ("hmmviterbi: outprob must be a non-empty numeric matrix"); endif len = length (sequence); # nstate is the number of states of the hidden Markov model nstate = rows (transprob); # noutput is the number of different outputs that the hidden Markov model # can generate noutput = columns (outprob); # Check whether transprob and outprob are feasible for a hidden Markov model if (columns (transprob) != nstate) error ("hmmviterbi: transprob must be a square matrix"); endif if (rows (outprob) != nstate) error ("hmmviterbi: outprob must have the same number of rows as transprob"); endif # Flag for symbols usesym = false; # Flag for statenames usesn = false; # Process varargin for i = 1:2:length (varargin) # There must be an identifier: 'symbols' or 'statenames' if (! ischar (varargin{i})) print_usage (); endif # Upper case is also fine lowerarg = lower (varargin{i}); if (strcmp (lowerarg, 'symbols')) if (length (varargin{i + 1}) != noutput) error ("hmmviterbi: number of symbols does not match number of possible outputs"); endif usesym = true; # Use the following argument as symbols symbols = varargin{i + 1}; # The same for statenames elseif (strcmp (lowerarg, 'statenames')) if (length (varargin{i + 1}) != nstate) error ("hmmviterbi: number of statenames does not match number of states"); endif usesn = true; # Use the following argument as statenames statenames = varargin{i + 1}; else error ("hmmviterbi: expected 'symbols' or 'statenames' but found '%s'", varargin{i}); endif endfor # Transform sequence from symbols to integers if necessary if (usesym) # sequenceint is used to build the transformed sequence sequenceint = zeros (1, len); for i = 1:noutput # Search for symbols(i) in the sequence, isequal will have 1 at # corresponding indices; i is the right integer for that symbol isequal = ismember (sequence, symbols(i)); # We do not want to change sequenceint if the symbol appears a second # time in symbols if (any ((sequenceint == 0) & (isequal == 1))) isequal *= i; sequenceint += isequal; endif endfor if (! all (sequenceint)) index = max ((sequenceint == 0) .* (1:len)); error (["hmmviterbi: sequence(" int2str (index) ") not in symbols"]); endif sequence = sequenceint; else if (! isvector (sequence) && ! isempty (sequence)) error ("hmmviterbi: sequence must be a vector"); endif if (! all (ismember (sequence, 1:noutput))) index = max ((ismember (sequence, 1:noutput) == 0) .* (1:len)); error (["hmmviterbi: sequence(" int2str (index) ") out of range"]); endif endif # Each row in transprob and outprob should contain log probabilities # => scale so that the sum is 1 and convert to log space # - for transprob s = sum (transprob, 2); s(s == 0) = 1; transprob = log (transprob ./ (s * ones (1, columns (transprob)))); # - for outprob s = sum (outprob, 2); s(s == 0) = 1; outprob = log (outprob ./ (s * ones (1, columns (outprob)))); # Store the path starting from i in spath(i, :) spath = ones (nstate, len + 1); # Set the first state for each path spath(:, 1) = (1:nstate)'; # Store the probability of path i in spathprob(i) spathprob = transprob(1, :); # Find the most likely paths for the given output sequence for i = 1:len # Calculate the new probabilities of the continuation with each state nextpathprob = ((spathprob' + outprob(:, sequence(i))) * ones (1, nstate)) + transprob; # Find the paths with the highest probabilities [spathprob, mindex] = max (nextpathprob); # Update spath and spathprob with the new paths spath = spath(mindex, :); spath(:, i + 1) = (1:nstate)'; endfor # Set vpath to the most likely path # We do not want the last state because we do not have an output for it [m, mindex] = max (spathprob); vpath = spath(mindex, 1:len); # Transform vpath into statenames if requested if (usesn) vpath = reshape (statenames(vpath), 1, len); endif endfunction %!test %! sequence = [1, 2, 1, 1, 1, 2, 2, 1, 2, 3, 3, 3, 3, 2, 3, 1, 1, 1, 1, 3, 3, 2, 3, 1, 3]; %! transprob = [0.8, 0.2; 0.4, 0.6]; %! outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1]; %! vpath = hmmviterbi (sequence, transprob, outprob); %! expected = [1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1]; %! assert (vpath, expected); %!test %! sequence = {'A', 'B', 'A', 'A', 'A', 'B', 'B', 'A', 'B', 'C', 'C', 'C', 'C', 'B', 'C', 'A', 'A', 'A', 'A', 'C', 'C', 'B', 'C', 'A', 'C'}; %! transprob = [0.8, 0.2; 0.4, 0.6]; %! outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1]; %! symbols = {'A', 'B', 'C'}; %! statenames = {'One', 'Two'}; %! vpath = hmmviterbi (sequence, transprob, outprob, 'symbols', symbols, 'statenames', statenames); %! expected = {'One', 'One', 'Two', 'Two', 'Two', 'One', 'One', 'One', 'One', 'One', 'One', 'One', 'One', 'One', 'One', 'Two', 'Two', 'Two', 'Two', 'One', 'One', 'One', 'One', 'One', 'One'}; %! assert (vpath, expected); statistics-1.4.3/inst/hygestat.m0000644000000000000000000000746114153320774015100 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mn}, @var{v}] =} hygestat (@var{t}, @var{m}, @var{n}) ## Compute mean and variance of the hypergeometric distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{t} is the total size of the population of the hypergeometric ## distribution. The elements of @var{t} must be positive natural numbers ## ## @item ## @var{m} is the number of marked items of the hypergeometric distribution. ## The elements of @var{m} must be natural numbers ## ## @item ## @var{n} is the size of the drawn sample of the hypergeometric ## distribution. The elements of @var{n} must be positive natural numbers ## @end itemize ## @var{t}, @var{m}, and @var{n} must be of common size or scalar ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{mn} is the mean of the hypergeometric distribution ## ## @item ## @var{v} is the variance of the hypergeometric distribution ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## t = 4:9; ## m = 0:5; ## n = 1:6; ## [mn, v] = hygestat (t, m, n) ## @end group ## ## @group ## [mn, v] = hygestat (t, m, 2) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the hypergeometric distribution function [mn, v] = hygestat (t, m, n) # Check arguments if (nargin != 3) print_usage (); endif if (! isempty (t) && ! ismatrix (t)) error ("hygestat: t must be a numeric matrix"); endif if (! isempty (m) && ! ismatrix (m)) error ("hygestat: m must be a numeric matrix"); endif if (! isempty (n) && ! ismatrix (n)) error ("hygestat: n must be a numeric matrix"); endif if (! isscalar (t) || ! isscalar (m) || ! isscalar (n)) [retval, t, m, n] = common_size (t, m, n); if (retval > 0) error ("hygestat: t, m and n must be of common size or scalar"); endif endif # Calculate moments mn = (n .* m) ./ t; v = (n .* (m ./ t) .* (1 - m ./ t) .* (t - n)) ./ (t - 1); # Continue argument check k = find (! (t >= 0) | ! (m >= 0) | ! (n > 0) | ! (t == round (t)) | ! (m == round (m)) | ! (n == round (n)) | ! (m <= t) | ! (n <= t)); if (any (k)) mn(k) = NaN; v(k) = NaN; endif endfunction %!test %! t = 4:9; %! m = 0:5; %! n = 1:6; %! [mn, v] = hygestat (t, m, n); %! expected_mn = [0.0000, 0.4000, 1.0000, 1.7143, 2.5000, 3.3333]; %! expected_v = [0.0000, 0.2400, 0.4000, 0.4898, 0.5357, 0.5556]; %! assert (mn, expected_mn, 0.001); %! assert (v, expected_v, 0.001); %!test %! t = 4:9; %! m = 0:5; %! [mn, v] = hygestat (t, m, 2); %! expected_mn = [0.0000, 0.4000, 0.6667, 0.8571, 1.0000, 1.1111]; %! expected_v = [0.0000, 0.2400, 0.3556, 0.4082, 0.4286, 0.4321]; %! assert (mn, expected_mn, 0.001); %! assert (v, expected_v, 0.001); statistics-1.4.3/inst/inconsistent.m0000644000000000000000000001026514153320774015764 0ustar0000000000000000## Copyright (C) 2020-2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{Y} =} inconsistent (@var{Z}) ## @deftypefnx {Function File} {@var{Y} =} inconsistent (@var{Z}, @var{d}) ## ## Compute the inconsistency coefficient for each link of a hierarchical cluster ## tree. ## ## Given a hierarchical cluster tree @var{Z} generated by the @code{linkage} ## function, @code{inconsistent} computes the inconsistency coefficient for each ## link of the tree, using all the links down to the @var{d}-th level below that ## link. ## ## The default depth @var{d} is 2, which means that only two levels are ## considered: the level of the computed link and the level below that. ## ## Each row of @var{Y} corresponds to the row of same index of @var{Z}. ## The columns of @var{Y} are respectively: the mean of the heights of the links ## used for the calculation, the standard deviation of the heights of those ## links, the number of links used, the inconsistency coefficient. ## ## @strong{Reference} ## Jain, A., and R. Dubes. Algorithms for Clustering Data. ## Upper Saddle River, NJ: Prentice-Hall, 1988. ## @end deftypefn ## ## @seealso{cluster, clusterdata, dendrogram, linkage, pdist, squareform} ## Author: Stefano Guidoni function Y = inconsistent (Z, d = 2) ## check the input if (nargin < 1) || (nargin > 2) print_usage (); endif ## MATLAB compatibility: ## when d = 0, which does not make sense, the result of inconsistent is the ## same as d = 1, which is... inconsistent if ((d < 0) || (! isscalar (d)) || (mod (d, 1))) error ("inconsistent: d must be a positive integer scalar"); endif if ((columns (Z) != 3) || (! isnumeric (Z)) || ... (! (max (Z(end, 1:2)) == rows (Z) * 2))) error (["inconsistent: Z must be a matrix generated by the linkage " ... "function"]); endif ## number of observations n = rows (Z) + 1; ## compute the inconsistency coefficient for every link for i = 1:rows (Z) v = inconsistent_recursion (i, d); # nested recursive function - see below Y(i, 1) = mean (v); Y(i, 2) = std (v); Y(i, 3) = length (v); ## the inconsistency coefficient is (current_link_height - mean) / std; ## if the standard deviation is zero, it is zero by definition if (Y(i, 2) != 0) Y(i, 4) = (v(end) - Y(i, 1)) / Y(i, 2); else Y(i, 4) = 0; endif endfor ## recursive function ## while depth > 1 search the links (columns 1 and 2 of Z) below the current ## link and then append the height of the current link to the vector v. ## The height of the starting link should be the last one of the vector. function v = inconsistent_recursion (index, depth) v = []; if (depth > 1) for j = 1:2 if (Z(index, j) > n) new_index = Z(index, j) - n; v = [v (inconsistent_recursion (new_index, depth - 1))]; endif endfor endif v(end+1) = Z(index, 3); endfunction endfunction ## Test input validation %!error inconsistent () %!error inconsistent ([1 2 1], 2, 3) %!error inconsistent (ones (2, 2)) %!error inconsistent ([1 2 1], -1) %!error inconsistent ([1 2 1], 1.3) %!error inconsistent ([1 2 1], [1 1]) %!error inconsistent (ones (2, 3)) ## Test output %!test %! load fisheriris; %! Z = linkage(meas, 'average', 'chebychev'); %! assert (cond (inconsistent (Z)), 39.9, 1e-3); statistics-1.4.3/inst/iwishpdf.m0000644000000000000000000000545114153320774015062 0ustar0000000000000000## Copyright (C) 2013 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License along with Octave; see the file COPYING. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} @var{y} = iwishpdf (@var{W}, @var{Tau}, @var{df}, @var{log_y}=false) ## Compute the probability density function of the Wishart distribution ## ## Inputs: A @var{p} x @var{p} matrix @var{W} where to find the PDF and the @var{p} x @var{p} positive definite scale matrix @var{Tau} and scalar degrees of freedom parameter @var{df} characterizing the inverse Wishart distribution. (For the density to be finite, need @var{df} > (@var{p} - 1).) ## If the flag @var{log_y} is set, return the log probability density -- this helps avoid underflow when the numerical value of the density is very small ## ## Output: @var{y} is the probability density of Wishart(@var{Sigma}, @var{df}) at @var{W}. ## ## @seealso{iwishrnd, wishpdf} ## @end deftypefn ## Author: Nir Krakauer ## Description: Compute the probability density function of the inverse Wishart distribution function [y] = iwishpdf(W, Tau, df, log_y=false) if (nargin < 3) print_usage (); endif p = size(Tau, 1); if (df <= (p - 1)) error('df too small, no finite densities exist') endif #calculate the logarithm of G_d(df/2), the multivariate gamma function g = (p * (p-1) / 4) * log(pi); for i = 1:p g = g + log(gamma((df + (1 - i))/2)); #using lngamma_gsl(.) from the gsl package instead of log(gamma(.)) might help avoid underflow/overflow endfor C = chol(W); #use formulas for determinant of positive definite matrix for better efficiency and numerical accuracy logdet_W = 2*sum(log(diag(C))); logdet_Tau = 2*sum(log(diag(chol(Tau)))); y = -(df*p)/2 * log(2) + (df/2)*logdet_Tau - g - ((df + p + 1)/2)*logdet_W - trace(Tau*chol2inv(C))/2; if ~log_y y = exp(y); endif endfunction ##test results cross-checked against diwish function in R MCMCpack library %!assert(iwishpdf(4, 3, 3.1), 0.04226595, 1E-7); %!assert(iwishpdf([2 -0.3;-0.3 4], [1 0.3;0.3 1], 4), 1.60166e-05, 1E-10); %!assert(iwishpdf([6 2 5; 2 10 -5; 5 -5 25], [9 5 5; 5 10 -8; 5 -8 22], 5.1), 4.946831e-12, 1E-17); %% Test input validation %!error iwishpdf () %!error iwishpdf (1, 2) %!error iwishpdf (1, 2, 0) %!error wishpdf (1, 2) statistics-1.4.3/inst/iwishrnd.m0000644000000000000000000000543714153320774015100 0ustar0000000000000000## Copyright (C) 2013 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License along with Octave; see the file COPYING. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} [@var{W}[, @var{DI}]] = iwishrnd (@var{Psi}, @var{df}[, @var{DI}][, @var{n}=1]) ## Return a random matrix sampled from the inverse Wishart distribution with given parameters ## ## Inputs: the @var{p} x @var{p} positive definite matrix @var{Tau} and scalar degrees of freedom parameter @var{df} (and optionally the transposed Cholesky factor @var{DI} of @var{Sigma} = @code{inv(Tau)}). ## @var{df} can be non-integer as long as @var{df} > @var{d} ## ## Output: a random @var{p} x @var{p} matrix @var{W} from the inverse Wishart(@var{Tau}, @var{df}) distribution. (@code{inv(W)} is from the Wishart(@code{inv(Tau)}, @var{df}) distribution.) If @var{n} > 1, then @var{W} is @var{p} x @var{p} x @var{n} and holds @var{n} such random matrices. (Optionally, the transposed Cholesky factor @var{DI} of @var{Sigma} is also returned.) ## ## Averaged across many samples, the mean of @var{W} should approach @var{Tau} / (@var{df} - @var{p} - 1). ## ## Reference: Yu-Cheng Ku and Peter Bloomfield (2010), Generating Random Wishart Matrices with Fractional Degrees of Freedom in OX, http://www.gwu.edu/~forcpgm/YuChengKu-030510final-WishartYu-ChengKu.pdf ## ## @seealso{wishrnd, iwishpdf} ## @end deftypefn ## Author: Nir Krakauer ## Description: Random matrices from the inverse Wishart distribution function [W, DI] = iwishrnd(Tau, df, DI, n = 1) if (nargin < 2) print_usage (); endif if nargin < 3 || isempty(DI) try D = chol(inv(Tau)); catch error('Cholesky decomposition failed; Tau probably not positive definite') end_try_catch DI = D'; else D = DI'; endif w = wishrnd([], df, D, n); if n > 1 p = size(D, 1); W = nan(p, p, n); endif for i = 1:n W(:, :, i) = inv(w(:, :, i)); endfor endfunction %!assert(size (iwishrnd (1,2,1)), [1, 1]); %!assert(size (iwishrnd ([],2,1)), [1, 1]); %!assert(size (iwishrnd ([3 1; 1 3], 2.00001, [], 1)), [2, 2]); %!assert(size (iwishrnd (eye(2), 2, [], 3)), [2, 2, 3]); %% Test input validation %!error iwishrnd () %!error iwishrnd (1) %!error iwishrnd ([-3 1; 1 3],1) %!error iwishrnd ([1; 1],1) statistics-1.4.3/inst/jackknife.m0000644000000000000000000001177114153320774015174 0ustar0000000000000000## Copyright (C) 2011 Alexander Klein ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn{Function File} {@var{jackstat} =} jackknife (@var{E}, @var{x}, @dots{}) ## Compute jackknife estimates of a parameter taking one or more given samples as parameters. ## In particular, @var{E} is the estimator to be jackknifed as a function name, handle, ## or inline function, and @var{x} is the sample for which the estimate is to be taken. ## The @var{i}-th entry of @var{jackstat} will contain the value of the estimator ## on the sample @var{x} with its @var{i}-th row omitted. ## ## @example ## @group ## jackstat(@var{i}) = @var{E}(@var{x}(1 : @var{i} - 1, @var{i} + 1 : length(@var{x}))) ## @end group ## @end example ## ## Depending on the number of samples to be used, the estimator must have the appropriate form: ## If only one sample is used, then the estimator need not be concerned with cell arrays, ## for example jackknifing the standard deviation of a sample can be performed with ## @code{@var{jackstat} = jackknife (@@std, rand (100, 1))}. ## If, however, more than one sample is to be used, the samples must all be of equal size, ## and the estimator must address them as elements of a cell-array, ## in which they are aggregated in their order of appearance: ## ## @example ## @group ## @var{jackstat} = jackknife(@@(x) std(x@{1@})/var(x@{2@}), rand (100, 1), randn (100, 1) ## @end group ## @end example ## ## If all goes well, a theoretical value @var{P} for the parameter is already known, ## @var{n} is the sample size, ## @code{@var{t} = @var{n} * @var{E}(@var{x}) - (@var{n} - 1) * mean(@var{jackstat})}, and ## @code{@var{v} = sumsq(@var{n} * @var{E}(@var{x}) - (@var{n} - 1) * @var{jackstat} - @var{t}) / (@var{n} * (@var{n} - 1))}, then ## @code{(@var{t}-@var{P})/sqrt(@var{v})} should follow a t-distribution with @var{n}-1 degrees of freedom. ## ## Jackknifing is a well known method to reduce bias; further details can be found in: ## @itemize @bullet ## @item Rupert G. Miller: The jackknife-a review; Biometrika (1974) 61(1): 1-15; doi:10.1093/biomet/61.1.1 ## @item Rupert G. Miller: Jackknifing Variances; Ann. Math. Statist. Volume 39, Number 2 (1968), 567-582; doi:10.1214/aoms/1177698418 ## @item M. H. Quenouille: Notes on Bias in Estimation; Biometrika Vol. 43, No. 3/4 (Dec., 1956), pp. 353-360; doi:10.1093/biomet/43.3-4.353 ## @end itemize ## @end deftypefn ## Author: Alexander Klein ## Created: 2011-11-25 function jackstat = jackknife ( anEstimator, varargin ) ## Convert function name to handle if necessary, or throw ## an error. if ( !strcmp ( typeinfo ( anEstimator ), "function handle" ) ) if ( isascii ( anEstimator ) ) anEstimator = str2func ( anEstimator ); else error ( "Estimators must be passed as function names or handles!" ); end end ## Simple jackknifing can be done with a single vector argument, and ## first and foremost with a function that does not care about ## cell-arrays. if ( length ( varargin ) == 1 && isnumeric ( varargin { 1 } ) ) aSample = varargin { 1 }; g = length ( aSample ); jackstat = zeros ( 1, g ); for k = 1 : g jackstat ( k ) = anEstimator ( aSample ( [ 1 : k - 1, k + 1 : g ] ) ); end ## More complicated input requires more work, however. else g = cellfun ( @(x) length ( x ), varargin ); if ( any ( g - g ( 1 ) ) ) error ( "All passed data must be of equal length!" ); end g = g ( 1 ); jackstat = zeros ( 1, g ); for k = 1 : g jackstat ( k ) = anEstimator ( cellfun ( @(x) x( [ 1 : k - 1, k + 1 : g ] ), varargin, "UniformOutput", false ) ); end end endfunction %!test %! ##Example from Quenouille, Table 1 %! d=[0.18 4.00 1.04 0.85 2.14 1.01 3.01 2.33 1.57 2.19]; %! jackstat = jackknife ( @(x) 1/mean(x), d ); %! assert ( 10 / mean(d) - 9 * mean(jackstat), 0.5240, 1e-5 ); %!demo %! for k = 1:1000 %! x=rand(10,1); %! s(k)=std(x); %! jackstat=jackknife(@std,x); %! j(k)=10*std(x) - 9*mean(jackstat); %! end %! figure();hist([s',j'], 0:sqrt(1/12)/10:2*sqrt(1/12)) %!demo %! for k = 1:1000 %! x=randn(1,50); %! y=rand(1,50); %! jackstat=jackknife(@(x) std(x{1})/std(x{2}),y,x); %! j(k)=50*std(y)/std(x) - 49*mean(jackstat); %! v(k)=sumsq((50*std(y)/std(x) - 49*jackstat) - j(k)) / (50 * 49); %! end %! t=(j-sqrt(1/12))./sqrt(v); %! figure();plot(sort(tcdf(t,49)),"-;Almost linear mapping indicates good fit with t-distribution.;") statistics-1.4.3/inst/jsucdf.m0000644000000000000000000000402514153320774014517 0ustar0000000000000000## Copyright (C) 2006 Frederick (Rick) A Niles ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} jsucdf (@var{x}, @var{alpha1}, @var{alpha2}) ## For each element of @var{x}, compute the cumulative distribution ## function (CDF) at @var{x} of the Johnson SU distribution with shape parameters ## @var{alpha1} and @var{alpha2}. ## ## Default values are @var{alpha1} = 1, @var{alpha2} = 1. ## @end deftypefn ## Author: Frederick (Rick) A Niles ## Description: CDF of the Johnson SU distribution ## This function is derived from normcdf.m ## This is the TeX equation of this function: ## ## \[ F(x) = \Phi\left(\alpha_1 + \alpha_2 ## \log\left(x + \sqrt{x^2 + 1} \right)\right) \] ## ## where \[ -\infty < x < \infty ; \alpha_2 > 0 \] and $\Phi$ is the ## standard normal cumulative distribution function. $\alpha_1$ and ## $\alpha_2$ are shape parameters. function cdf = jsucdf (x, alpha1, alpha2) if (! ((nargin == 1) || (nargin == 3))) print_usage; endif if (nargin == 1) m = 0; v = 1; endif if (!isscalar (alpha1) || !isscalar(alpha2)) [retval, x, alpha1, alpha2] = common_size (x, alpha1, alpha2); if (retval > 0) error ("normcdf: x, alpha1 and alpha2 must be of common size or scalar"); endif endif one = ones (size (x)); cdf = stdnormal_cdf (alpha1 .* one + alpha2 .* log (x + sqrt(x.*x + one))); endfunction statistics-1.4.3/inst/jsupdf.m0000644000000000000000000000414714153320774014541 0ustar0000000000000000## Copyright (C) 2006 Frederick (Rick) A Niles ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} jsupdf (@var{x}, @var{alpha1}, @var{alpha2}) ## For each element of @var{x}, compute the probability density function ## (PDF) at @var{x} of the Johnson SU distribution with shape parameters @var{alpha1} ## and @var{alpha2}. ## ## Default values are @var{alpha1} = 1, @var{alpha2} = 1. ## @end deftypefn ## Author: Frederick (Rick) A Niles ## Description: PDF of Johnson SU distribution ## This function is derived from normpdf.m ## This is the TeX equation of this function: ## ## \[ f(x) = \frac{\alpha_2}{\sqrt{x^2+1}} \phi\left(\alpha_1+\alpha_2 ## \log{\left(x+\sqrt{x^2+1}\right)}\right) \] ## ## where \[ -\infty < x < \infty ; \alpha_2 > 0 \] and $\phi$ is the ## standard normal probability distribution function. $\alpha_1$ and ## $\alpha_2$ are shape parameters. function pdf = jsupdf (x, alpha1, alpha2) if (nargin != 1 && nargin != 3) print_usage; endif if (nargin == 1) alpha1 = 1; alpha2 = 1; endif if (!isscalar (alpha1) || !isscalar(alpha2)) [retval, x, alpha1, alpha2] = common_size (x, alpha1, alpha2); if (retval > 0) error ("normpdf: x, alpha1 and alpha2 must be of common size or scalars"); endif endif one = ones(size(x)); sr = sqrt(x.*x + one); pdf = (alpha2 ./ sr) .* stdnormal_pdf (alpha1 .* one + alpha2 .* log (x + sr)); endfunction statistics-1.4.3/inst/kmeans.m0000644000000000000000000004560614153320774014531 0ustar0000000000000000## Copyright (C) 2011 Soren Hauberg ## Copyright (C) 2012 Daniel Ward ## Copyright (C) 2015-2016 Lachlan Andrew ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {} {[@var{idx}, @var{centers}, @var{sumd}, @var{dist}] =} kmeans (@var{data}, @var{k}, @var{param1}, @var{value1}, @dots{}) ## Perform a @var{k}-means clustering of the @var{N}x@var{D} table @var{data}. ## If parameter @qcode{start} is specified, then @var{k} may be empty ## in which case @var{k} is set to the number of rows of @var{start}. ## ## The outputs are: ## @table @code ## @item @var{idx} ## An @var{N}x1 vector whose @var{i}th element is the class to which row @var{i} ## of @var{data} is assigned. ## ## @item @var{centers} ## A @var{K}x@var{D} array whose @var{i}th row is the centroid of cluster ## @var{i}. ## ## @item @var{sumd} ## A @var{k}x1 vector whose @var{i}th entry is the sum of the distances ## from samples in cluster @var{i} to centroid @var{i}. ## ## @item @var{dist} ## An @var{N}x@var{k} matrix whose @var{i}@var{j}th element is ## the distance from sample @var{i} to centroid @var{j}. ## @end table ## ## The following parameters may be placed in any order. Each parameter ## must be followed by its value. ## @table @code ## @item @var{Start} ## The initialization method for the centroids. ## @table @code ## @item @code{plus} ## (Default) The k-means++ algorithm. ## @item @code{sample} # A subset of @var{k} rows from @var{data}, ## sampled uniformly without replacement. ## @item @code{cluster} ## Perform a pilot clustering on 10% of the rows of @var{data}. ## @item @code{uniform} ## Each component of each centroid is drawn uniformly ## from the interval between the maximum and minimum values of that ## component within @var{data}. ## This performs poorly and is implemented only for Matlab compatibility. ## @item A ## A @var{k}x@var{D}x@var{r} matrix, where @var{r} is the number of ## replicates. ## @end table ## ## @item @var{Replicates} ## An positive integer specifying the number of independent clusterings to ## perform. ## The output values are the values for the best clustering, i.e., ## the one with the smallest value of @var{sumd}. ## If @var{Start} is numeric, then @var{Replicates} defaults to # (and must equal) the size of the third dimension of @var{Start}. ## Otherwise it defaults to 1. ## ## @item @var{MaxIter} ## The maximum number of iterations to perform for each replicate. ## If the maximum change of any centroid is less than 0.001, then ## the replicate terminates even if @var{MaxIter} iterations have no occurred. ## The default is 100. ## ## @item @var{Distance} ## The distance measure used for partitioning and calculating centroids. ## @table @code ## @item @qcode{sqeuclidean} ## The squared Euclidean distance, i.e., ## the sum of the squares of the differences between corresponding components. ## In this case, the centroid is the arithmetic mean of all samples in ## its cluster. ## This is the only distance for which this algorithm is truly "k-means". ## ## @item @qcode{cityblock} ## The sum metric, or L1 distance, i.e., ## the sum of the absolute differences between corresponding components. ## In this case, the centroid is the median of all samples in its cluster. ## This gives the k-medians algorithm. ## ## @item @qcode{cosine} ## (Documentation incomplete.) ## ## @item @qcode{correlation} ## (Documentation incomplete.) ## ## @item @qcode{hamming} ## The number of components in which the sample and the centroid differ. ## In this case, the centroid is the median of all samples in its cluster. ## Unlike Matlab, Octave allows non-logical @var{data}. ## ## @end table ## ## @item @var{EmptyAction} ## What to do when a centroid is not the closest to any data sample. ## @table @code ## @item @qcode{error} ## Throw an error. ## @item @qcode{singleton} ## (Default) Select the row of @var{data} that has the highest error and ## use that as the new centroid. ## @item @qcode{drop} ## Remove the centroid, and continue computation with one fewer centroid. ## The dimensions of the outputs @var{centroids} and @var{d} ## are unchanged, with values for omitted centroids replaced by NA. ## ## @end table ## ## @item @var{Display} ## Display a text summary. ## @table @code ## @item @qcode{off} ## (Default) Display no summary. ## @item @qcode{final} ## Display a summary for each clustering operation. ## @item @qcode{iter} ## Display a summary for each iteration of a clustering operation. ## ## @end table ## @end table ## ## Example: ## ## [~,c] = kmeans (rand(10, 3), 2, "emptyaction", "singleton"); ## ## @seealso{linkage} ## @end deftypefn function [classes, centers, sumd, D] = kmeans (data, k, varargin) [reg, prop] = parseparams (varargin); ## defaults for options emptyaction = "singleton"; start = "plus"; replicates = 1; max_iter = 100; distance = "sqeuclidean"; display = "off"; replicates_set_explicitly = false; ## Remove rows containing NaN / NA, but record which rows are used data_idx = ! any (isnan (data), 2); original_rows = rows (data); data = data(data_idx,:); #used for getting the number of samples n_rows = rows (data); #used for convergence of the centroids err = 1; ## Input checking, validate the matrix if (! isnumeric (data) || ! ismatrix (data) || ! isreal (data)) error ("kmeans: first input argument must be a DxN real data matrix"); elseif (! isnumeric (k)) error ("kmeans: second argument must be numeric"); endif ## Parse options while (length (prop) > 0) if (length (prop) < 2) error ("kmeans: Option '%s' has no argument", prop{1}); endif switch (lower (prop{1})) case "emptyaction" emptyaction = prop{2}; case "start" start = prop{2}; case "maxiter" max_iter = prop{2}; case "distance" distance = prop{2}; case "replicates" replicates = prop{2}; replicates_set_explicitly = true; case "display" display = prop{2}; case {"onlinephase", "options"} warning ("kmeans: Ignoring unimplemented option '%s'", prop{1}); otherwise error ("kmeans: Unknown option %s", prop{1}); endswitch prop = {prop{3:end}}; endwhile ## Process options ## check for the 'emptyaction' property switch (emptyaction) case {"singleton", "error", "drop"} ; otherwise d = [", " disp(emptyaction)] (1:end-1); # strip trailing \n if (length (d) > 20) d = ""; endif error ("kmeans: unsupported empty cluster action parameter%s", d); endswitch ## check for the 'replicates' property if (! isnumeric (replicates) || ! isscalar (replicates) || ! isreal (replicates) || replicates < 1) d = [", " disp(replicates)] (1:end-1); # strip trailing \n if (length (d) > 20) d = ""; endif error ("kmeans: invalid number of replicates%s", d); endif ## check for the 'MaxIter' property if (! isnumeric (max_iter) || ! isscalar (max_iter) || ! isreal (max_iter) || max_iter < 1) d = [", " disp(max_iter)] (1:end-1); # strip trailing \n if (length (d) > 20) d = ""; endif error ("kmeans: invalid MaxIter%s", d); endif ## check for the 'start' property switch (lower (start)) case {"sample", "plus", "cluster"} start = lower (start); case {"uniform"} start = "uniform"; min_data = min (data); range = max (data) - min_data; otherwise if (! isnumeric (start)) d = [", " disp(start)] (1:end-1); # strip trailing \n if (length (d) > 20) d = ""; endif error ("kmeans: invalid start parameter%s", d); endif if (isempty (k)) k = rows (start); elseif (rows (start) != k) error (["kmeans: Number of initializers (%d) " ... "should match number of centroids (%d)"], rows (start), k); endif if (replicates_set_explicitly) if (replicates != size (start, 3)) error (["kmeans: The third dimension of the initializer (%d) " ... "should match the number of replicates (%d)"], ... size (start, 3), replicates); endif else replicates = size (start, 3); endif endswitch ## check for the 'distance' property ## dist returns the distance btwn each row of matrix x and a row vector c switch (lower (distance)) case "sqeuclidean" dist = @(x, c) sumsq (bsxfun (@minus, x, c), 2); centroid = @(x) mean (x, 1); case "cityblock" dist = @(x, c) sum (abs (bsxfun (@minus, x, c)), 2); centroid = @(x) median (x, 1); case "cosine" ## Pre-normalize all data. ## (when Octave implements normr, will use data = normr (data) ) for i = 1:rows (data) data(i,:) = data(i,:) / sqrt (sumsq (data(i,:))); endfor dist = @(x, c) 1 - (x * c') ./ sqrt (sumsq (c)); centroid = @(x) mean (x, 1); ## already normalized case "correlation" ## Pre-normalize all data. data = data - mean (data, 2); ## (when Octave implements normr, will use data = normr (data) ) for i = 1:rows (data) data(i,:) = data(i,:) / sqrt (sumsq (data(i,:))); endfor dist = @(x, c) 1 - (x * (c - mean (c))') ... ./ sqrt (sumsq (c - mean (c))); centroid = @(x) mean (x, 1); ## already normalized case "hamming" dist = @(x, c) sum (bsxfun (@ne, x, c), 2); centroid = @(x) median (x, 1); otherwise error ("kmeans: unsupported distance parameter %s", distance); endswitch ## check for the 'display' property if (! strcmp (display, "off")) display = lower (display); switch (display) case {"off", "final"} ; case "iter" printf ("%6s\t%6s\t%8s\t%12s\n", "iter", "phase", "num", "sum"); otherwise error ("kmeans: invalid display parameter %s", display); endswitch endif ## Done processing options ######################################## ## Now that k has been set (possibly by 'replicates' option), check/use it. if (! isscalar (k)) error ("kmeans: second input argument must be a scalar"); endif ## used to hold the distances from each sample to each class D = zeros (n_rows, k); best = Inf; best_centers = []; for rep = 1:replicates ## keep track of the number of data points that change class old_classes = zeros (rows (data), 1); n_changes = -1; ## check for the 'start' property switch (lower (start)) case "sample" idx = randperm (n_rows, k); centers = data(idx, :); case "plus" # k-means++, by Arthur and Vassilios(?) centers(1,:) = data(randi (n_rows),:); d = inf (n_rows, 1); # Distance to nearest centroid so far for i = 2:k d = min (d, dist (data, centers(i - 1, :))); centers(i,:) = data(find (cumsum (d) > rand * sum (d), 1), :); endfor case "cluster" idx = randperm (n_rows, max (k, ceil (n_rows / 10))); [~, centers] = kmeans (data(idx,:), k, "start", "sample", ... "distance", distance); case "uniform" # vectorised 'min_data + range .* rand' centers = bsxfun (@plus, min_data, bsxfun (@times, range, rand (k, columns (data)))); otherwise centers = start(:,:,rep); endswitch ## Run the algorithm iter = 1; ## Classify once before the loop; to set sumd, and if max_iter == 0 ## Compute distances and classify [D, classes, sumd] = update_dist (data, centers, D, k, dist); while (err > 0.001 && iter++ <= max_iter && n_changes != 0) ## Calculate new centroids replaced_centroids = []; ## Used by "emptyaction = singleton" for i = 1:k ## Get binary vector indicating membership in cluster i membership = (classes == i); ## Check for empty clusters if (! any (membership)) switch emptyaction ## if 'singleton', then find the point that is the ## farthest from any centroid (and not replacing an empty cluster ## from earlier in this pass) and add it to the empty cluster case 'singleton' available = setdiff (1:n_rows, replaced_centroids); [~, idx] = max (min (D(available,:)')); idx = available(idx); replaced_centroids = [replaced_centroids, idx]; classes(idx) = i; membership(idx) = 1; ## if 'drop' then set C and D to NA case 'drop' centers(i,:) = NA; D(i,:) = NA; ## if 'error' then throw the error otherwise error ("kmeans: empty cluster created"); endswitch endif ## end check for empty clusters ## update the centroids if (any (membership)) ## if we didn't "drop" the cluster centers(i, :) = centroid (data(membership, :)); endif endfor ## Compute distances, classes and sums [D, classes, new_sumd] = update_dist (data, centers, D, k, dist); ## calculate the difference in the sum of distances err = sum (sumd - new_sumd); ## update the current sum of distances sumd = new_sumd; ## compute the number of class changes n_changes = sum (old_classes != classes); old_classes = classes; ## display iteration status if (strcmp (display, "iter")) printf ("%6d\t%6d\t%8d\t%12.3f\n", (iter - 1), 1, ... n_changes, sum (sumd)); endif endwhile ## throw a warning if the algorithm did not converge if (iter > max_iter && err > 0.001 && n_changes != 0) warning ("kmeans: failed to converge in %d iterations", max_iter); endif if (sum (sumd) < sum (best) || isinf (best)) best = sumd; best_centers = centers; endif ## display final results if (strcmp (display, "final")) printf ("Replicate %d, %d iterations, total sum of distances = %.3f.\n", ... rep, iter, sum (sumd)); endif endfor centers = best_centers; ## Compute final distances, classes and sums [D, classes, sumd] = update_dist (data, centers, D, k, dist); ## display final results if (strcmp (display, "final") || strcmp (display, "iter")) printf ("Best total sum of distances = %.3f\n", sum (sumd)); endif ## Return with equal size as inputs if (original_rows != rows (data)) final = NA (original_rows,1); final(data_idx) = classes; ## other positions already NaN / NA classes = final; endif endfunction ## Update distances, classes and sums function [D, classes, sumd] = update_dist (data, centers, D, k, dist) for i = 1:k D (:, i) = dist (data, centers(i, :)); endfor [~, classes] = min (D, [], 2); ## calculate the sum of within-class distances sumd = zeros (k, 1); for i = 1:k sumd(i) = sum (D(classes == i,i)); endfor endfunction ## Test input parsing %!error kmeans (rand (3,2), 4); %!test %! samples = 4; %! dims = 3; %! k = 2; %! [cls, c, d, z] = kmeans (rand (samples,dims), k, "start", rand (k,dims, 5), %! "emptyAction", "singleton"); %! assert (size (cls), [samples, 1]); %! assert (size (c), [k, dims]); %! assert (size (d), [k, 1]); %! assert (size (z), [samples, k]); %!test %! samples = 4; %! dims = 3; %! k = 2; %! [cls, c, d, z] = kmeans (rand (samples,dims), [], "start", rand (k,dims, 5), %! "emptyAction", "singleton"); %! assert (size (cls), [samples, 1]); %! assert (size (c), [k, dims]); %! assert (size (d), [k, 1]); %! assert (size (z), [samples, k]); %!test %! kmeans (rand (4,3), 2, "start", rand (2,3, 5), "replicates", 5, %! "emptyAction", "singleton"); %!error kmeans (rand (4,3), 2, "start", rand (2,3, 5), "replicates", 1); %!error kmeans (rand (4,3), 2, "start", rand (2,2)); %!test %! kmeans (rand (3,4), 2, "start", "sample", "emptyAction", "singleton"); %!test %! kmeans (rand (3,4), 2, "start", "plus", "emptyAction", "singleton"); %!test %! kmeans (rand (3,4), 2, "start", "cluster", "emptyAction", "singleton"); %!test %! kmeans (rand (3,4), 2, "start", "uniform", "emptyAction", "singleton"); %!error kmeans (rand (3,4), 2, "start", "normal"); %!error kmeans (rand (4,3), 2, "replicates", i); %!error kmeans (rand (4,3), 2, "replicates", -1); %!error kmeans (rand (4,3), 2, "replicates", []); %!error kmeans (rand (4,3), 2, "replicates", [1 2]); %!error kmeans (rand (4,3), 2, "replicates", "one"); %!error kmeans (rand (4,3), 2, "MAXITER", i); %!error kmeans (rand (4,3), 2, "MaxIter", -1); %!error kmeans (rand (4,3), 2, "maxiter", []); %!error kmeans (rand (4,3), 2, "maxiter", [1 2]); %!error kmeans (rand (4,3), 2, "maxiter", "one"); %!test %! kmeans (rand (4,3), 2, "distance", "sqeuclidean", "emptyAction", "singleton"); %!test %! kmeans (rand (4,3), 2, "distance", "cityblock", "emptyAction", "singleton"); %!test %! kmeans (rand (4,3), 2, "distance", "cosine", "emptyAction", "singleton"); %!test %! kmeans (rand (4,3), 2, "distance", "correlation", "emptyAction", "singleton"); %!test %! kmeans (rand (4,3), 2, "distance", "hamming", "emptyAction", "singleton"); %!error kmeans (rand (4,3), 2, "distance", "manhattan"); %!error kmeans ([1 0; 1.1 0], 2, "start", eye(2), "emptyaction", "error"); %!test %! kmeans ([1 0; 1.1 0], 2, "start", eye(2), "emptyaction", "singleton"); %!test %! [cls, c] = kmeans ([1 0; 2 0], 2, "start", [8,0;0,8], "emptyaction", "drop"); %! assert (cls, [1; 1]); %! assert (c, [1.5, 0; NA, NA]); %!error kmeans ([1 0; 1.1 0], 2, "start", eye(2), "emptyaction", "panic"); %!demo %! ## Generate a two-cluster problem %! C1 = randn (100, 2) + 1; %! C2 = randn (100, 2) - 1; %! data = [C1; C2]; %! %! ## Perform clustering %! [idx, centers] = kmeans (data, 2); %! %! ## Plot the result %! figure; %! plot (data (idx==1, 1), data (idx==1, 2), 'ro'); %! hold on; %! plot (data (idx==2, 1), data (idx==2, 2), 'bs'); %! plot (centers (:, 1), centers (:, 2), 'kv', 'markersize', 10); %! hold off; statistics-1.4.3/inst/kruskalwallis.m0000644000000000000000000002442114153320774016133 0ustar0000000000000000## Copyright (C) 2021 Andreas Bertsatos ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} =} kruskalwallis (@var{x}) ## @deftypefnx {Function File} {@var{p} =} kruskalwallis (@var{x}, @var{group}) ## @deftypefnx {Function File} {@var{p} =} kruskalwallis (@var{x}, @var{group}, @var{displayopt}) ## @deftypefnx {Function File} {[@var{p}, @var{tbl}] =} kruskalwallis (@var{x}, @dots{}) ## @deftypefnx {Function File} {[@var{p}, @var{tbl}, @var{stats}] =} kruskalwallis (@var{x}, @dots{}) ## ## Perform a Kruskal-Wallis test, the non-parametric alternative of a one-way ## analysis of variance (ANOVA), for comparing the means of two or more groups ## of data under the null hypothesis that the groups are drawn from the same ## population, i.e. the group means are equal. ## ## kruskalwallis can take up to three input arguments: ## ## @itemize ## @item ## @var{x} contains the data and it can either be a vector or matrix. ## If @var{x} is a matrix, then each column is treated as a separate group. ## If @var{x} is a vector, then the @var{group} argument is mandatory. ## @item ## @var{group} contains the names for each group. If @var{x} is a matrix, then ## @var{group} can either be a cell array of strings of a character array, with ## one row per column of @var{x}. If you want to omit this argument, enter an ## empty array ([]). If @var{x} is a vector, then @var{group} must be a vector ## of the same lenth, or a string array or cell array of strings with one row ## for each element of @var{x}. @var{x} values corresponding to the same value ## of @var{group} are placed in the same group. ## @item ## @var{displayopt} is an optional parameter for displaying the groups contained ## in the data in a boxplot. If omitted, it is 'on' by default. If group names ## are defined in @var{group}, these are used to identify the groups in the ## boxplot. Use 'off' to omit displaying this figure. ## @end itemize ## ## kruskalwallis can return up to three output arguments: ## ## @itemize ## @item ## @var{p} is the p-value of the null hypothesis that all group means are equal. ## @item ## @var{tbl} is a cell array containing the results in a standard ANOVA table. ## @item ## @var{stats} is a structure containing statistics useful for performing ## a multiple comparison of means with the MULTCOMPARE function. ## @end itemize ## ## If kruskalwallis is called without any output arguments, then it prints the ## results in a one-way ANOVA table to the standard output. It is also printed ## when @var{displayopt} is 'on'. ## ## Examples: ## ## @example ## x = meshgrid (1:6); ## x = x + normrnd (0, 1, 6, 6); ## [p, atab] = kruskalwallis(x); ## @end example ## ## ## @example ## x = ones (50, 4) .* [-2, 0, 1, 5]; ## x = x + normrnd (0, 2, 50, 4); ## group = @{"A", "B", "C", "D"@}; ## kruskalwallis (x, group); ## @end example ## ## @end deftypefn function [p, tbl, stats] = kruskalwallis (x, group, displayopt) ## check for valid number of input arguments narginchk (1, 3); ## add defaults if (nargin < 2) group = []; endif if (nargin < 3) displayopt = 'on'; endif plotdata = ~(strcmp (displayopt, 'off')); ## Convert group to cell array from character array, make it a column if (! isempty (group) && ischar (group)) group = cellstr(group); endif if (size (group, 1) == 1) group = group'; endif ## If X is a matrix, convert it to column vector and create a ## corresponging column vector for groups if (length (x) < prod (size (x))) [n, m] = size (x); x = x(:); gi = reshape (repmat ((1:m), n, 1), n*m, 1); if (length (group) == 0) ## no group names are provided group = gi; elseif (size (group, 1) == m) ## group names exist and match columns group = group(gi,:); else error("X columns and GROUP length do not match."); endif endif ## Identify NaN values (if any) and remove them from X along with ## their corresponding values from group vector nonan = ~isnan (x); x = x(nonan); group = group(nonan, :); ## Convert group to indices and separate names [group_id, group_names] = grp2idx (group); group_id = group_id(:); named = 1; ## Rank data for non-parametric analysis [xr, tieadj] = tieranks (x); ## Get group size and mean for each group groups = size (group_names, 1); xs = zeros (1, groups); xm = xs; for j = 1:groups group_size = find (group_id == j); xs(j) = length (group_size); xm(j) = mean (xr(group_size)); endfor ## Calculate statistics lx = length (xr); ## Number of samples in groups gm = mean (xr); ## Grand mean of groups dfm = length (xm) - 1; ## degrees of freedom for model dfe = lx - dfm - 1; ## degrees of freedom for error SSM = xs .* (xm - gm) * (xm - gm)'; ## Sum of Squares for Model SST = (xr(:) - gm)' * (xr(:) - gm); ## Sum of Squares Total SSE = SST - SSM; ## Sum of Squares Error if (dfm > 0) MSM = SSM / dfm; ## Mean Square for Model else MSM = NaN; endif if (dfe > 0) MSE = SSE / dfe; ## Mean Squared Error else MSE = NaN; endif ## Calculate Chi-sq statistic ChiSq = (12 * SSM) / (lx * (lx + 1)); if (tieadj > 0) ChiSq = ChiSq / (1 - 2 * tieadj / (lx ^ 3 - lx)); end p = 1 - chi2cdf (ChiSq, dfm); ## Create results table (if requested) if (nargout > 1) tbl = {"Source", "SS", "df", "MS", "Chi-sq", "Prob>Chi-sq"; ... "Groups", SSM, dfm, MSM, ChiSq, p; ... "Error", SSE, dfe, MSE, "", ""; ... "Total", SST, dfm + dfe, "", "", ""}; endif ## Create stats structure (if requested) for MULTCOMPARE if (nargout > 2) if (length (group_names) > 0) stats.gnames = group_names; else stats.gnames = strjust (num2str ((1:length (xm))'), 'left'); end stats.n = xs; stats.source = 'kruskalwallis'; stats.meanranks = xm; stats.sumt = 2 * tieadj; endif ## Print results table on screen if no output argument was requested if (nargout == 0 || plotdata) printf(" Kruskal-Wallis ANOVA Table\n"); printf("Source SS df MS Chi-sq Prob>Chi-sq\n"); printf("---------------------------------------------------------\n"); printf("Columns %10.2f %5.0f %10.2f %8.2f %11.5e\n", ... SSM, dfm, MSM, ChiSq, p); printf("Error %10.2f %5.0f %10.2f\n", SSE, dfe, MSE); printf("Total %10.2f %5.0f\n", SST, dfm + dfe); endif ## Plot data using BOXPLOT (unless opted out) if (plotdata) boxplot (x, group_id, 'Notch', "on", 'Labels', group_names); endif endfunction ## local function for computing tied ranks on column vectors function [r, tieadj] = tieranks (x) ## Sort data [value, x_idx] = sort (x); epsx = zeros (size (x)); epsx = epsx(x_idx); x_l = numel (x); ## Count ranks from start (min value) ranks = [1:x_l]'; ## Initialize tie adjustments tieadj = 0; ## Adjust for ties. ties = value(1:x_l-1) + epsx(1:x_l-1) >= value(2:x_l) - epsx(2:x_l); t_idx = find (ties); t_idx(end+1) = 0; maxTies = numel (t_idx); ## Calculate tie adjustments tiecount = 1; while (tiecount < maxTies) tiestart = t_idx(tiecount); ntied = 2; while (t_idx(tiecount+1) == t_idx(tiecount) + 1) tiecount = tiecount + 1; ntied = ntied + 1; endwhile ## Check for tieflag tieadj = tieadj + ntied * (ntied - 1) * (ntied + 1) / 2; ## Average tied ranks ranks(tiestart:tiestart + ntied - 1) = ... sum (ranks(tiestart:tiestart + ntied - 1)) / ntied; tiecount = tiecount + 1; endwhile ## Remap data to original dimensions r(x_idx) = ranks; endfunction %!demo %! x = meshgrid (1:6); %! x = x + normrnd (0, 1, 6, 6); %! kruskalwallis (x, [], 'off'); %!demo %! x = meshgrid (1:6); %! x = x + normrnd (0, 1, 6, 6); %! [p, atab] = kruskalwallis(x); %!demo %! x = ones (30, 4) .* [-2, 0, 1, 5]; %! x = x + normrnd (0, 2, 30, 4); %! group = {"A", "B", "C", "D"}; %! kruskalwallis (x, group); ## testing results against SPSS and R on the GEAR.DAT data file available from ## https://www.itl.nist.gov/div898/handbook/eda/section3/eda354.htm %!test %! data = [1.006, 0.996, 0.998, 1.000, 0.992, 0.993, 1.002, 0.999, 0.994, 1.000, ... %! 0.998, 1.006, 1.000, 1.002, 0.997, 0.998, 0.996, 1.000, 1.006, 0.988, ... %! 0.991, 0.987, 0.997, 0.999, 0.995, 0.994, 1.000, 0.999, 0.996, 0.996, ... %! 1.005, 1.002, 0.994, 1.000, 0.995, 0.994, 0.998, 0.996, 1.002, 0.996, ... %! 0.998, 0.998, 0.982, 0.990, 1.002, 0.984, 0.996, 0.993, 0.980, 0.996, ... %! 1.009, 1.013, 1.009, 0.997, 0.988, 1.002, 0.995, 0.998, 0.981, 0.996, ... %! 0.990, 1.004, 0.996, 1.001, 0.998, 1.000, 1.018, 1.010, 0.996, 1.002, ... %! 0.998, 1.000, 1.006, 1.000, 1.002, 0.996, 0.998, 0.996, 1.002, 1.006, ... %! 1.002, 0.998, 0.996, 0.995, 0.996, 1.004, 1.004, 0.998, 0.999, 0.991, ... %! 0.991, 0.995, 0.984, 0.994, 0.997, 0.997, 0.991, 0.998, 1.004, 0.997]; %! group = [1:10] .* ones (10,10); %! group = group(:); %! [p, tbl] = kruskalwallis (data, group, "off"); %! assert (p, 0.048229, 1e-6); %! assert (tbl{2,5}, 17.03124, 1e-5); %! assert (tbl{2,3}, 9, 0); %! assert (tbl{4,2}, 82655.5, 1e-16); %! data = reshape (data, 10, 10); %! [p, tbl, stats] = kruskalwallis (data, [], "off"); %! assert (p, 0.048229, 1e-6); %! assert (tbl{2,5}, 17.03124, 1e-5); %! assert (tbl{2,3}, 9, 0); %! assert (tbl{4,2}, 82655.5, 1e-16); %! means = [51.85, 60.45, 37.6, 51.1, 29.5, 54.25, 64.55, 66.7, 53.65, 35.35]; %! N = 10 * ones (1, 10); %! assert (stats.meanranks, means, 1e-6); %! assert (length (stats.gnames), 10, 0); %! assert (stats.n, N, 0); statistics-1.4.3/inst/linkage.m0000644000000000000000000002532214153320774014656 0ustar0000000000000000## Copyright (C) 2008 Francesco Potortì ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} linkage (@var{d}) ## @deftypefnx {Function File} {@var{y} =} linkage (@var{d}, @var{method}) ## @deftypefnx {Function File} {@var{y} =} linkage (@var{x}) ## @deftypefnx {Function File} {@var{y} =} linkage (@var{x}, @var{method}) ## @deftypefnx {Function File} @ ## {@var{y} =} linkage (@var{x}, @var{method}, @var{metric}) ## @deftypefnx {Function File} @ ## {@var{y} =} linkage (@var{x}, @var{method}, @var{arglist}) ## ## Produce a hierarchical clustering dendrogram ## ## @var{d} is the dissimilarity matrix relative to n observations, ## formatted as a @math{(n-1)*n/2}x1 vector as produced by @code{pdist}. ## Alternatively, @var{x} contains data formatted for input to ## @code{pdist}, @var{metric} is a metric for @code{pdist} and ## @var{arglist} is a cell array containing arguments that are passed to ## @code{pdist}. ## ## @code{linkage} starts by putting each observation into a singleton ## cluster and numbering those from 1 to n. Then it merges two ## clusters, chosen according to @var{method}, to create a new cluster ## numbered n+1, and so on until all observations are grouped into ## a single cluster numbered 2(n-1). Row k of the ## (m-1)x3 output matrix relates to cluster n+k: the first ## two columns are the numbers of the two component clusters and column ## 3 contains their distance. ## ## @var{method} defines the way the distance between two clusters is ## computed and how they are recomputed when two clusters are merged: ## ## @table @samp ## @item "single" (default) ## Distance between two clusters is the minimum distance between two ## elements belonging each to one cluster. Produces a cluster tree ## known as minimum spanning tree. ## ## @item "complete" ## Furthest distance between two elements belonging each to one cluster. ## ## @item "average" ## Unweighted pair group method with averaging (UPGMA). ## The mean distance between all pair of elements each belonging to one ## cluster. ## ## @item "weighted" ## Weighted pair group method with averaging (WPGMA). ## When two clusters A and B are joined together, the new distance to a ## cluster C is the mean between distances A-C and B-C. ## ## @item "centroid" ## Unweighted Pair-Group Method using Centroids (UPGMC). ## Assumes Euclidean metric. The distance between cluster centroids, ## each centroid being the center of mass of a cluster. ## ## @item "median" ## Weighted pair-group method using centroids (WPGMC). ## Assumes Euclidean metric. Distance between cluster centroids. When ## two clusters are joined together, the new centroid is the midpoint ## between the joined centroids. ## ## @item "ward" ## Ward's sum of squared deviations about the group mean (ESS). ## Also known as minimum variance or inner squared distance. ## Assumes Euclidean metric. How much the moment of inertia of the ## merged cluster exceeds the sum of those of the individual clusters. ## @end table ## ## @strong{Reference} ## Ward, J. H. Hierarchical Grouping to Optimize an Objective Function ## J. Am. Statist. Assoc. 1963, 58, 236-244, ## @url{http://iv.slis.indiana.edu/sw/data/ward.pdf}. ## @end deftypefn ## ## @seealso{pdist,squareform} ## Author: Francesco Potortì function dgram = linkage (d, method = "single", distarg, savememory) ## check the input if (nargin == 4) && (strcmpi (savememory, "savememory")) warning ("Octave:linkage_savemem", ... "linkage: option 'savememory' not implemented"); elseif (nargin < 1) || (nargin > 3) print_usage (); endif if (isempty (d)) error ("linkage: d cannot be empty"); endif methods = struct ... ("name", { "single"; "complete"; "average"; "weighted"; "centroid"; "median"; "ward" }, "distfunc", {(@(x) min(x)) # single (@(x) max(x)) # complete (@(x,i,j,w) sum(diag(w([i,j]))*x)/sum(w([i,j]))) # average (@(x) mean(x)) # weighted (@massdist) # centroid (@(x,i) massdist(x,i)) # median (@inertialdist) # ward }); mask = strcmp (lower (method), {methods.name}); if (! any (mask)) error ("linkage: %s: unknown method", method); endif dist = {methods.distfunc}{mask}; if (nargin >= 3 && ! isvector (d)) if (ischar (distarg)) d = pdist (d, distarg); elseif (iscell (distarg)) d = pdist (d, distarg{:}); else print_usage (); endif elseif (nargin < 3) if (! isvector (d)) d = pdist (d); endif else print_usage (); endif d = squareform (d, "tomatrix"); # dissimilarity NxN matrix n = rows (d); # the number of observations diagidx = sub2ind ([n,n], 1:n, 1:n); # indices of diagonal elements d(diagidx) = Inf; # consider a cluster as far from itself ## For equal-distance nodes, the order in which clusters are ## merged is arbitrary. Rotating the initial matrix produces an ## ordering similar to Matlab's. cname = n:-1:1; # cluster names in d d = rot90 (d, 2); # exchange low and high cluster numbers weight = ones (1, n); # cluster weights dgram = zeros (n-1, 3); # clusters from n+1 to 2*n-1 for cluster = n+1 : 2*n-1 ## Find the two nearest clusters [m midx] = min (d(:)); [r, c] = ind2sub (size (d), midx); ## Here is the new cluster dgram(cluster-n, :) = [cname(r) cname(c) d(r, c)]; ## Put it in place of the first one and remove the second cname(r) = cluster; cname(c) = []; ## Compute the new distances. ## (Octave-7+ needs switch stmt to avoid 'called with too many inputs' err.) switch find (mask) case {1, 2, 4} # 1 arg newd = dist (d([r c], :)); case {3, 5, 7} # 4 args newd = dist (d([r c], :), r, c, weight); case 6 # 2 args newd = dist (d([r c], :), r); otherwise endswitch newd(r) = Inf; # Take care of the diagonal element ## Put distances in place of the first ones, remove the second ones d(r,:) = newd; d(:,r) = newd'; d(c,:) = []; d(:,c) = []; ## The new weight is the sum of the components' weights weight(r) += weight(c); weight(c) = []; endfor ## Sort the cluster numbers, as Matlab does dgram(:,1:2) = sort (dgram(:,1:2), 2); ## Check that distances are monotonically increasing if (any (diff (dgram(:,3)) < 0)) warning ("Octave:clustering", "linkage: cluster distances do not monotonically increase\n\ you should probably use a method different from \"%s\"", method); endif endfunction ## Take two row vectors, which are the Euclidean distances of clusters I ## and J from the others. Column I of second row contains the distance ## between clusters I and J. The centre of gravity of the new cluster ## is on the segment joining the old ones. W are the weights of all ## clusters. Use the law of cosines to find the distances of the new ## cluster from all the others. function y = massdist (x, i, j, w) x .^= 2; # Squared Euclidean distances if (nargin == 2) # Median distance qi = 0.5; # Equal weights ("weighted") else # Centroid distance qi = 1 / (1 + w(j) / w(i)); # Proportional weights ("unweighted") endif y = sqrt (qi * x(1, :) + (1 - qi) * (x(2, :) - qi * x(2, i))); endfunction ## Take two row vectors, which are the inertial distances of clusters I ## and J from the others. Column I of second row contains the inertial ## distance between clusters I and J. The centre of gravity of the new ## cluster K is on the segment joining I and J. W are the weights of ## all clusters. Convert inertial to Euclidean distances, then use the ## law of cosines to find the Euclidean distances of K from all the ## other clusters, convert them back to inertial distances and return ## them. function y = inertialdist (x, i, j, w) wi = w(i); # The cluster wj = w(j); # weights. s = [wi + w; # Sum of weights for wj + w]; # all cluster pairs. p = [wi * w; # Product of weights for wj * w]; # all cluster pairs. x = x.^2 .* s ./ p; # Convert inertial dist. to squared Eucl. sij = wi + wj; # Sum of weights of I and J qi = wi / sij; # Normalise the weight of I ## Squared Euclidean distances between all clusters and new cluster K x = qi * x(1, :) + (1 - qi) * (x(2, :) - qi * x(2, i)); y = sqrt (x * sij .* w ./ (sij + w)); # convert Eucl. dist. to inertial endfunction %!shared x, t %! x = reshape (mod (magic (6),5), [], 3); %! t = 1e-6; %!assert (cond (linkage (pdist (x))), 34.119045, t); %!assert (cond (linkage (pdist (x), "complete")), 21.793345, t); %!assert (cond (linkage (pdist (x), "average")), 27.045012, t); %!assert (cond (linkage (pdist (x), "weighted")), 27.412889, t); %! lastwarn(); # Clear last warning before the test %!warning linkage (pdist (x), "centroid"); %!test %! warning off Octave:clustering %! assert (cond (linkage (pdist (x), "centroid")), 27.457477, t); %! warning on Octave:clustering %!warning linkage (pdist (x), "median"); %!test %! warning off Octave:clustering %! assert (cond (linkage (pdist (x), "median")), 27.683325, t); %! warning on Octave:clustering %!assert (cond (linkage (pdist (x), "ward")), 17.195198, t); %!assert (cond (linkage (x, "ward", "euclidean")), 17.195198, t); %!assert (cond (linkage (x, "ward", {"euclidean"})), 17.195198, t); %!assert (cond (linkage (x, "ward", {"minkowski", 2})), 17.195198, t); statistics-1.4.3/inst/lognstat.m0000644000000000000000000000662614153320774015105 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} lognstat (@var{mu}, @var{sigma}) ## Compute mean and variance of the lognormal distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{mu} is the first parameter of the lognormal distribution ## ## @item ## @var{sigma} is the second parameter of the lognormal distribution. ## @var{sigma} must be positive or zero ## @end itemize ## @var{mu} and @var{sigma} must be of common size or one of them must be ## scalar ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the lognormal distribution ## ## @item ## @var{v} is the variance of the lognormal distribution ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## mu = 0:0.2:1; ## sigma = 0.2:0.2:1.2; ## [m, v] = lognstat (mu, sigma) ## @end group ## ## @group ## [m, v] = lognstat (0, sigma) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the lognormal distribution function [m, v] = lognstat (mu, sigma) # Check arguments if (nargin != 2) print_usage (); endif if (! isempty (mu) && ! ismatrix (mu)) error ("lognstat: mu must be a numeric matrix"); endif if (! isempty (sigma) && ! ismatrix (sigma)) error ("lognstat: sigma must be a numeric matrix"); endif if (! isscalar (mu) || ! isscalar (sigma)) [retval, mu, sigma] = common_size (mu, sigma); if (retval > 0) error ("lognstat: mu and sigma must be of common size or scalar"); endif endif # Calculate moments m = exp (mu + (sigma .^ 2) ./ 2); v = (exp (sigma .^ 2) - 1) .* exp (2 .* mu + sigma .^ 2); # Continue argument check k = find (! (sigma >= 0) | ! (sigma < Inf)); if (any (k)) m(k) = NaN; v(k) = NaN; endif endfunction %!test %! mu = 0:0.2:1; %! sigma = 0.2:0.2:1.2; %! [m, v] = lognstat (mu, sigma); %! expected_m = [1.0202, 1.3231, 1.7860, 2.5093, 3.6693, 5.5845]; %! expected_v = [0.0425, 0.3038, 1.3823, 5.6447, 23.1345, 100.4437]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); %!test %! sigma = 0.2:0.2:1.2; %! [m, v] = lognstat (0, sigma); %! expected_m = [1.0202, 1.0833, 1.1972, 1.3771, 1.6487, 2.0544]; %! expected_v = [0.0425, 0.2036, 0.6211, 1.7002, 4.6708, 13.5936]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); statistics-1.4.3/inst/mahal.m0000644000000000000000000000525614153320774014332 0ustar0000000000000000## Copyright (C) 2015 Lachlan Andrew ## ## This program is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## This program, is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {Function File} {} mahal (@var{y}, @var{x}) ## Mahalanobis' D-square distance. ## ## Return the Mahalanobis' D-square distance of the points in ## @var{y} from the distribution implied by points @var{x}. ## ## Specifically, it uses a Cholesky decomposition to set ## ## @example ## answer(i) = (@var{y}(i,:) - mean (@var{x})) * inv (A) * (@var{y}(i,:)-mean (@var{x}))' ## @end example ## ## where A is the covariance of @var{x}. ## ## The data @var{x} and @var{y} must have the same number of components ## (columns), but may have a different number of observations (rows). ## ## @end deftypefn ## Author: Lachlan Andrew ## Created: September 2015 ## Based on function mahalanobis by Friedrich Leisch function retval = mahal (y, x) if (nargin != 2) print_usage (); endif if (! (isnumeric (x) || islogical (x)) || ! (isnumeric (y) || islogical (y))) error ("mahal: X and Y must be numeric matrices or vectors"); endif if (! ismatrix (x) || ! ismatrix (y)) error ("mahal: X and Y must be 2-D matrices or vectors"); endif [xr, xc] = size (x); [yr, yc] = size (y); if (xc != yc) error ("mahal: X and Y must have the same number of columns"); endif if (isinteger (x)) x = double (x); endif xm = mean (x, 1); ## Center data by subtracting mean of x x = bsxfun (@minus, x, xm); y = bsxfun (@minus, y, xm); w = (x' * x) / (xr - 1); retval = sumsq (y / chol (w), 2); endfunction ## Test input validation %!error mahal () %!error mahal (1, 2, 3) %!error mahal ("A", "B") %!error mahal ([1, 2], ["A", "B"]) %!error mahal (ones (2, 2, 2)) %!error mahal (ones (2, 2), ones (2, 2, 2)) %!error mahal (ones (2, 2), ones (2, 3)) %!test %! X = [1 0; 0 1; 1 1; 0 0]; %! assert (mahal (X, X), [1.5; 1.5; 1.5; 1.5], 10*eps) %! assert (mahal (X, X+1), [7.5; 7.5; 1.5; 13.5], 10*eps) %!assert (mahal ([true; true], [false; true]), [0.5; 0.5], eps) statistics-1.4.3/inst/mhsample.m0000644000000000000000000002710414153320774015052 0ustar0000000000000000######################################################################## ## ## Copyright (C) 1993-2021 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or . ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {[@var{smpl}, @var{accept}] =} mhsample (@var{start}, @var{nsamples}, @var{property}, @var{value}, ...) ## Draws @var{nsamples} samples from a target stationary distribution @var{pdf} ## using Metropolis-Hastings algorithm. ## ## Inputs: ## ## @itemize ## @item ## @var{start} is a @var{nchain} by @var{dim} matrix of starting points for each ## Markov chain. Each row is the starting point of a different chain and each ## column corresponds to a different dimension. ## ## @item ## @var{nsamples} is the number of samples, the length of each Markov chain. ## @end itemize ## ## Some property-value pairs can or must be specified, they are: ## ## (Required) One of: ## ## @itemize ## @item ## "pdf" @var{pdf}: a function handle of the target stationary distribution to ## be sampled. The function should accept different locations in each row and ## each column corresponds to a different dimension. ## ## or ## ## @item ## "logpdf" @var{logpdf}: a function handle of the log of the target stationary ## distribution to be sampled. The function should accept different locations ## in each row and each column corresponds to a different dimension. ## @end itemize ## ## In case optional argument @var{symmetric} is set to false (the default), one ## of: ## ## @itemize ## @item ## "proppdf" @var{proppdf}: a function handle of the proposal distribution that ## is sampled from with @var{proprnd} to give the next point in the chain. The ## function should accept two inputs, the random variable and the current ## location each input should accept different locations in each row and each ## column corresponds to a different dimension. ## ## or ## ## @item ## "logproppdf" @var{logproppdf}: the log of "proppdf". ## @end itemize ## ## The following input property/pair values may be needed depending on the ## desired outut: ## ## @itemize ## @item ## "proprnd" @var{proprnd}: (Required) a function handle which generates random ## numbers from @var{proppdf}. The function should accept different locations ## in each row and each column corresponds to a different dimension ## corresponding with the current location. ## ## @item ## "symmetric" @var{symmetric}: true or false based on whether @var{proppdf} is ## a symmetric distribution. If true, @var{proppdf} (or @var{logproppdf}) need ## not be specified. The default is false. ## ## @item ## "burnin" @var{burnin} the number of points to discard at the beginning, the ## default is 0. ## ## @item ## "thin" @var{thin}: omits @var{thin}-1 of every @var{thin} points in the ## generated Markov chain. The default is 1. ## ## @item ## "nchain" @var{nchain}: the number of Markov chains to generate. The default ## is 1. ## @end itemize ## ## Outputs: ## ## @itemize ## @item ## @var{smpl}: a @var{nsamples} x @var{dim} x @var{nchain} tensor of random ## values drawn from @var{pdf}, where the rows are different random values, the ## columns correspond to the dimensions of @var{pdf}, and the third dimension ## corresponds to different Markov chains. ## ## @item ## @var{accept} is a vector of the acceptance rate for each chain. ## @end itemize ## ## Example : Sampling from a normal distribution ## ## @example ## @group ## start = 1; ## nsamples = 1e3; ## pdf = @@(x) exp (-.5 * x .^ 2) / (pi ^ .5 * 2 ^ .5); ## proppdf = @@(x,y) 1 / 6; ## proprnd = @@(x) 6 * (rand (size (x)) - .5) + x; ## [smpl, accept] = mhsample (start, nsamples, "pdf", pdf, "proppdf", ... ## proppdf, "proprnd", proprnd, "thin", 4); ## histfit (smpl); ## @end group ## @end example ## ## @seealso{rand, slicesample} ## @end deftypefn function [smpl, accept] = mhsample (start, nsamples, varargin) if (nargin < 6) print_usage (); endif sizestart = size (start); pdf = []; proppdf = []; logpdf = []; logproppdf = []; proprnd = []; sym = false; K = 0; # burnin m = 1; # thin nchain = 1; for k = 1:2:length (varargin) if (ischar (varargin{k})) switch lower(varargin{k}) case "pdf" if (isa (varargin{k+1}, "function_handle")) pdf = varargin{k+1}; else error ("mhsample: pdf must be a function handle"); endif case "proppdf" if (isa (varargin{k+1}, "function_handle")) proppdf = varargin{k+1}; else error ("mhsample: proppdf must be a function handle"); endif case "logpdf" if (isa (varargin{k+1}, "function_handle")) pdf = varargin{k+1}; else error ("mhsample: logpdf must be a function handle"); endif case "logproppdf" if (isa (varargin{k+1}, "function_handle")) proppdf = varargin{k+1}; else error ("mhsample: logproppdf must be a function handle"); endif case "proprnd" if (isa (varargin{k+1}, "function_handle")) proprnd = varargin{k+1}; else error ("mhsample: proprnd must be a function handle"); endif case "symmetric" if (isa (varargin{k+1}, "logical")) sym = varargin{k+1}; else error ("mhsample: sym must be true or false"); endif case "burnin" if (varargin{k+1}>=0) K = varargin{k+1}; else error ("mhsample: K must be greater than or equal to 0"); endif case "thin" if (varargin{k+1} >= 1) m = varargin{k+1}; else error ("mhsample: m must be greater than or equal to 1"); endif case "nchain" if (varargin{k+1} >= 1) nchain = varargin{k+1}; else error ("mhsample: nchain must be greater than or equal to 1"); endif otherwise warning (["mhsample: Ignoring unknown option " varargin{k}]); endswitch else error (["mhsample: " varargin{k} " is not a valid property."]); endif endfor if (! isempty (pdf) && isempty (logpdf)) logpdf=@(x) rloge (pdf (x)); elseif (isempty (pdf) && isempty (logpdf)) error ("mhsample: pdf or logpdf must be input."); endif if (! isempty (proppdf) && isempty (logproppdf)) logproppdf = @(x, y) rloge (proppdf (x, y)); elseif (isempty (proppdf) && isempty (logproppdf) && ! sym) error ("mhsample: proppdf or logproppdf must be input unless 'symetrical' is true."); endif if (! isa (proprnd, "function_handle")) error ("mhsample: proprnd must be a function handle."); endif if (length (sizestart) == 2) sizestart = [sizestart 0]; end smpl = zeros (nsamples, sizestart(2), nchain); if (all (sizestart([1 3]) == [1 nchain])) ## Could remove, not Matlab compatable but allows continuing chains smpl(1, :, :) = start; elseif (all (sizestart([1 3]) == [nchain 0])) smpl(1, :, :) = permute (start, [3, 2, 1]); elseif (all (sizestart([1 3]) == [1 0])) ## Could remove, not Matlab compatable but allows all chains to start ## at the same location smpl(1, :, :) = repmat (start,[1, 1, nchain]); else error ("mhsample: start must be a nchain by dim matrix."); endif cx = permute (smpl(1, :, :),[3, 2, 1]); accept = zeros (nchain, 1); i = 1; rnd = log (rand (nchain, nsamples*m+K)); for k = 1:nsamples*m+K canacc = rem (k-K, m) == 0; px = proprnd (cx); if (sym) A = logpdf (px) - logpdf(cx); else A = (logpdf (px) + logproppdf (cx, px)) - (logpdf (cx) + logproppdf (px, cx)); endif ac = rnd(:, k) < min (A, 0); cx(ac, :) = px(ac, :); accept(ac)++; if (canacc) smpl(i, :, :) = permute (cx, [3, 2, 1]); end if (k > K && canacc) i++; endif endfor accept ./= (nsamples * m + K); endfunction function y = rloge (x) y = -inf (size (x)); xg0 = x > 0; y(xg0) = log (x(xg0)); endfunction %!demo %! ## Define function to sample %! d = 2; %! mu = [-1; 2]; %! Sigma = rand (d); %! Sigma = (Sigma + Sigma'); %! Sigma += eye (d) * abs (eigs (Sigma, 1, "sa")) * 1.1; %! pdf = @(x)(2*pi)^(-d/2)*det(Sigma)^-.5*exp(-.5*sum((x.'-mu).*(Sigma\(x.'-mu)),1)); %! ## Inputs %! start = ones (1, 2); %! nsamples = 500; %! sym = true; %! K = 500; %! m = 10; %! proprnd = @(x) (rand (size (x)) - .5) * 3 + x; %! [smpl, accept] = mhsample (start, nsamples, "pdf", pdf, "proprnd", proprnd, ... %! "symmetric", sym, "burnin", K, "thin", m); %! figure; %! hold on; %! plot (smpl(:, 1), smpl(:, 2), 'x'); %! [x, y] = meshgrid (linspace (-6, 4), linspace(-3, 7)); %! z = reshape (pdf ([x(:), y(:)]), size(x)); %! mesh (x, y, z, "facecolor", "None"); %! ## Using sample points to find the volume of half a sphere with radius of .5 %! f = @(x) ((.25-(x(:,1)+1).^2-(x(:,2)-2).^2).^.5.*(((x(:,1)+1).^2+(x(:,2)-2).^2)<.25)).'; %! int = mean (f (smpl) ./ pdf (smpl)); %! errest = std (f (smpl) ./ pdf (smpl)) / nsamples ^ .5; %! trueerr = abs (2 / 3 * pi * .25 ^ (3 / 2) - int); %! printf ("Monte Carlo integral estimate int f(x) dx = %f\n", int); %! printf ("Monte Carlo integral error estimate %f\n", errest); %! printf ("The actual error %f\n", trueerr); %! mesh (x, y, reshape (f([x(:), y(:)]), size(x)), "facecolor", "None"); %!demo %! ## Integrate truncated normal distribution to find normilization constant %! pdf = @(x) exp (-.5*x.^2)/(pi^.5*2^.5); %! nsamples = 1e3; %! proprnd = @(x) (rand (size (x)) - .5) * 3 + x; %! [smpl, accept] = mhsample (1, nsamples, "pdf", pdf, "proprnd", proprnd, ... %! "symmetric", true, "thin", 4); %! f = @(x) exp(-.5 * x .^ 2) .* (x >= -2 & x <= 2); %! x = linspace (-3, 3, 1000); %! area(x, f(x)); %! xlabel ('x'); %! ylabel ('f(x)'); %! int = mean (f (smpl) ./ pdf (smpl)); %! errest = std (f (smpl) ./ pdf (smpl)) / nsamples^ .5; %! trueerr = abs (erf (2 ^ .5) * 2 ^ .5 * pi ^ .5 - int); %! printf ("Monte Carlo integral estimate int f(x) dx = %f\n", int); %! printf ("Monte Carlo integral error estimate %f\n", errest); %! printf ("The actual error %f\n", trueerr); %!test %! nchain = 1e4; %! start = rand (nchain, 1); %! nsamples = 1e3; %! pdf = @(x) exp (-.5*(x-1).^2)/(2*pi)^.5; %! proppdf = @(x, y) 1/3; %! proprnd = @(x) 3 * (rand (size (x)) - .5) + x; %! [smpl, accept] = mhsample (start, nsamples, "pdf", pdf, "proppdf", proppdf, ... %! "proprnd", proprnd, "thin", 2, "nchain", nchain, ... %! "burnin", 0); %! assert (mean (mean (smpl, 1), 3), 1, .01); %! assert (mean (var (smpl, 1), 3), 1, .01) %!error mhsample (); %!error mhsample (1); %!error mhsample (1, 1); %!error mhsample (1, 1, "pdf", @(x)x); %!error mhsample (1, 1, "pdf", @(x)x, "proprnd", @(x)x+rand(size(x))); statistics-1.4.3/inst/mnpdf.m0000644000000000000000000000776614153320774014364 0ustar0000000000000000## Copyright (C) 2012 Arno Onken ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} mnpdf (@var{x}, @var{p}) ## Compute the probability density function of the multinomial distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{x} is vector with a single sample of a multinomial distribution with ## parameter @var{p} or a matrix of random samples from multinomial ## distributions. In the latter case, each row of @var{x} is a sample from a ## multinomial distribution with the corresponding row of @var{p} being its ## parameter. ## ## @item ## @var{p} is a vector with the probabilities of the categories or a matrix ## with each row containing the probabilities of a multinomial sample. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{y} is a vector of probabilites of the random samples @var{x} from the ## multinomial distribution with corresponding parameter @var{p}. The parameter ## @var{n} of the multinomial distribution is the sum of the elements of each ## row of @var{x}. The length of @var{y} is the number of columns of @var{x}. ## If a row of @var{p} does not sum to @code{1}, then the corresponding element ## of @var{y} will be @code{NaN}. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## x = [1, 4, 2]; ## p = [0.2, 0.5, 0.3]; ## y = mnpdf (x, p); ## @end group ## ## @group ## x = [1, 4, 2; 1, 0, 9]; ## p = [0.2, 0.5, 0.3; 0.1, 0.1, 0.8]; ## y = mnpdf (x, p); ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, 2001. ## ## @item ## Merran Evans, Nicholas Hastings and Brian Peacock. @cite{Statistical ## Distributions}. pages 134-136, Wiley, New York, third edition, 2000. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: PDF of the multinomial distribution function y = mnpdf (x, p) # Check arguments if (nargin != 2) print_usage (); endif if (! ismatrix (x) || any (x(:) < 0 | round (x(:) != x(:)))) error ("mnpdf: x must be a matrix of non-negative integer values"); endif if (! ismatrix (p) || any (p(:) < 0)) error ("mnpdf: p must be a non-empty matrix with rows of probabilities"); endif # Adjust input sizes if (! isvector (x) || ! isvector (p)) if (isvector (x)) x = x(:)'; endif if (isvector (p)) p = p(:)'; endif if (size (x, 1) == 1 && size (p, 1) > 1) x = repmat (x, size (p, 1), 1); elseif (size (x, 1) > 1 && size (p, 1) == 1) p = repmat (p, size (x, 1), 1); endif endif # Continue argument check if (any (size (x) != size (p))) error ("mnpdf: x and p must have compatible sizes"); endif # Count total number of elements of each multinomial sample n = sum (x, 2); # Compute probability density function of the multinomial distribution t = x .* log (p); t(x == 0) = 0; y = exp (gammaln (n+1) - sum (gammaln (x+1), 2) + sum (t, 2)); # Set invalid rows to NaN k = (abs (sum (p, 2) - 1) > 1e-6); y(k) = NaN; endfunction %!test %! x = [1, 4, 2]; %! p = [0.2, 0.5, 0.3]; %! y = mnpdf (x, p); %! assert (y, 0.11812, 0.001); %!test %! x = [1, 4, 2; 1, 0, 9]; %! p = [0.2, 0.5, 0.3; 0.1, 0.1, 0.8]; %! y = mnpdf (x, p); %! assert (y, [0.11812; 0.13422], 0.001); statistics-1.4.3/inst/mnrnd.m0000644000000000000000000001334614153320774014365 0ustar0000000000000000## Copyright (C) 2012 Arno Onken ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{x} =} mnrnd (@var{n}, @var{p}) ## @deftypefnx {Function File} {@var{x} =} mnrnd (@var{n}, @var{p}, @var{s}) ## Generate random samples from the multinomial distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{n} is the first parameter of the multinomial distribution. @var{n} can ## be scalar or a vector containing the number of trials of each multinomial ## sample. The elements of @var{n} must be non-negative integers. ## ## @item ## @var{p} is the second parameter of the multinomial distribution. @var{p} can ## be a vector with the probabilities of the categories or a matrix with each ## row containing the probabilities of a multinomial sample. If @var{p} has ## more than one row and @var{n} is non-scalar, then the number of rows of ## @var{p} must match the number of elements of @var{n}. ## ## @item ## @var{s} is the number of multinomial samples to be generated. @var{s} must ## be a non-negative integer. If @var{s} is specified, then @var{n} must be ## scalar and @var{p} must be a vector. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{x} is a matrix of random samples from the multinomial distribution with ## corresponding parameters @var{n} and @var{p}. Each row corresponds to one ## multinomial sample. The number of columns, therefore, corresponds to the ## number of columns of @var{p}. If @var{s} is not specified, then the number ## of rows of @var{x} is the maximum of the number of elements of @var{n} and ## the number of rows of @var{p}. If a row of @var{p} does not sum to @code{1}, ## then the corresponding row of @var{x} will contain only @code{NaN} values. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## n = 10; ## p = [0.2, 0.5, 0.3]; ## x = mnrnd (n, p); ## @end group ## ## @group ## n = 10 * ones (3, 1); ## p = [0.2, 0.5, 0.3]; ## x = mnrnd (n, p); ## @end group ## ## @group ## n = (1:2)'; ## p = [0.2, 0.5, 0.3; 0.1, 0.1, 0.8]; ## x = mnrnd (n, p); ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, 2001. ## ## @item ## Merran Evans, Nicholas Hastings and Brian Peacock. @cite{Statistical ## Distributions}. pages 134-136, Wiley, New York, third edition, 2000. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Random samples from the multinomial distribution function x = mnrnd (n, p, s) # Check arguments if (nargin == 3) if (! isscalar (n) || n < 0 || round (n) != n) error ("mnrnd: n must be a non-negative integer"); endif if (! isvector (p) || any (p < 0 | p > 1)) error ("mnrnd: p must be a vector of probabilities"); endif if (! isscalar (s) || s < 0 || round (s) != s) error ("mnrnd: s must be a non-negative integer"); endif elseif (nargin == 2) if (isvector (p) && size (p, 1) > 1) p = p'; endif if (! isvector (n) || any (n < 0 | round (n) != n) || size (n, 2) > 1) error ("mnrnd: n must be a non-negative integer column vector"); endif if (! ismatrix (p) || isempty (p) || any (p < 0 | p > 1)) error ("mnrnd: p must be a non-empty matrix with rows of probabilities"); endif if (! isscalar (n) && size (p, 1) > 1 && length (n) != size (p, 1)) error ("mnrnd: the length of n must match the number of rows of p"); endif else print_usage (); endif # Adjust input sizes if (nargin == 3) n = n * ones (s, 1); p = repmat (p(:)', s, 1); elseif (nargin == 2) if (isscalar (n) && size (p, 1) > 1) n = n * ones (size (p, 1), 1); elseif (size (p, 1) == 1) p = repmat (p, length (n), 1); endif endif sz = size (p); # Upper bounds of categories ub = cumsum (p, 2); # Make sure that the greatest upper bound is 1 gub = ub(:, end); ub(:, end) = 1; # Lower bounds of categories lb = [zeros(sz(1), 1) ub(:, 1:(end-1))]; # Draw multinomial samples x = zeros (sz); for i = 1:sz(1) # Draw uniform random numbers r = repmat (rand (n(i), 1), 1, sz(2)); # Compare the random numbers of r to the cumulated probabilities of p and # count the number of samples for each category x(i, :) = sum (r <= repmat (ub(i, :), n(i), 1) & r > repmat (lb(i, :), n(i), 1), 1); endfor # Set invalid rows to NaN k = (abs (gub - 1) > 1e-6); x(k, :) = NaN; endfunction %!test %! n = 10; %! p = [0.2, 0.5, 0.3]; %! x = mnrnd (n, p); %! assert (size (x), size (p)); %! assert (all (x >= 0)); %! assert (all (round (x) == x)); %! assert (sum (x) == n); %!test %! n = 10 * ones (3, 1); %! p = [0.2, 0.5, 0.3]; %! x = mnrnd (n, p); %! assert (size (x), [length(n), length(p)]); %! assert (all (x >= 0)); %! assert (all (round (x) == x)); %! assert (all (sum (x, 2) == n)); %!test %! n = (1:2)'; %! p = [0.2, 0.5, 0.3; 0.1, 0.1, 0.8]; %! x = mnrnd (n, p); %! assert (size (x), size (p)); %! assert (all (x >= 0)); %! assert (all (round (x) == x)); %! assert (all (sum (x, 2) == n)); statistics-1.4.3/inst/monotone_smooth.m0000644000000000000000000001246114153320774016473 0ustar0000000000000000## Copyright (C) 2011 Nir Krakauer ## Copyright (C) 2011 CarnĂ« Draug ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{yy} =} monotone_smooth (@var{x}, @var{y}, @var{h}) ## Produce a smooth monotone increasing approximation to a sampled functional ## dependence ## ## A kernel method is used (an Epanechnikov smoothing kernel is ## applied to y(x); this is integrated to yield the monotone increasing form. ## See Reference 1 for details.) ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{x} is a vector of values of the independent variable. ## ## @item ## @var{y} is a vector of values of the dependent variable, of the same size as ## @var{x}. For best performance, it is recommended that the @var{y} already be ## fairly smooth, e.g. by applying a kernel smoothing to the original values if ## they are noisy. ## ## @item ## @var{h} is the kernel bandwidth to use. If @var{h} is not given, a "reasonable" ## value is computed. ## ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{yy} is the vector of smooth monotone increasing function values at @var{x}. ## ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## x = 0:0.1:10; ## y = (x .^ 2) + 3 * randn(size(x)); %typically non-monotonic from the added noise ## ys = ([y(1) y(1:(end-1))] + y + [y(2:end) y(end)])/3; %crudely smoothed via ## moving average, but still typically non-monotonic ## yy = monotone_smooth(x, ys); %yy is monotone increasing in x ## plot(x, y, '+', x, ys, x, yy) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Holger Dette, Natalie Neumeyer and Kay F. Pilz (2006), A simple nonparametric ## estimator of a strictly monotone regression function, @cite{Bernoulli}, 12:469-490 ## @item ## Regine Scheder (2007), R Package 'monoProc', Version 1.0-6, ## @url{http://cran.r-project.org/web/packages/monoProc/monoProc.pdf} (The ## implementation here is based on the monoProc function mono.1d) ## @end enumerate ## @end deftypefn ## Author: Nir Krakauer ## Description: Nonparametric monotone increasing regression function yy = monotone_smooth (x, y, h) if (nargin < 2 || nargin > 3) print_usage (); elseif (!isnumeric (x) || !isvector (x)) error ("first argument x must be a numeric vector") elseif (!isnumeric (y) || !isvector (y)) error ("second argument y must be a numeric vector") elseif (numel (x) != numel (y)) error ("x and y must have the same number of elements") elseif (nargin == 3 && (!isscalar (h) || !isnumeric (h))) error ("third argument 'h' (kernel bandwith) must a numeric scalar") endif n = numel(x); %set filter bandwidth at a reasonable default value, if not specified if (nargin != 3) s = std(x); h = s / (n^0.2); end x_min = min(x); x_max = max(x); y_min = min(y); y_max = max(y); %transform range of x to [0, 1] xl = (x - x_min) / (x_max - x_min); yy = ones(size(y)); %Epanechnikov smoothing kernel (with finite support) %K_epanech_kernel = @(z) (3/4) * ((1 - z).^2) .* (abs(z) < 1); K_epanech_int = @(z) mean(((abs(z) < 1)/2) - (3/4) * (z .* (abs(z) < 1) - (1/3) * (z.^3) .* (abs(z) < 1)) + (z < -1)); %integral of kernels up to t monotone_inverse = @(t) K_epanech_int((y - t) / h); %find the value of the monotone smooth function at each point in x niter_max = 150; %maximum number of iterations for estimating each value (should not be reached in most cases) for l = 1:n tmax = y_max; tmin = y_min; wmin = monotone_inverse(tmin); wmax = monotone_inverse(tmax); if (wmax == wmin) yy(l) = tmin; else wt = xl(l); iter_max_reached = 1; for i = 1:niter_max wt_scaled = (wt - wmin) / (wmax - wmin); tn = tmin + wt_scaled * (tmax - tmin) ; wn = monotone_inverse(tn); wn_scaled = (wn - wmin) / (wmax - wmin); %if (abs(wt-wn) < 1E-4) || (tn < (y_min-0.1)) || (tn > (y_max+0.1)) %% criterion for break in the R code -- replaced by the following line to %% hopefully be less dependent on the scale of y if (abs(wt_scaled-wn_scaled) < 1E-4) || (wt_scaled < -0.1) || (wt_scaled > 1.1) iter_max_reached = 0; break endif if wn > wt tmax = tn; wmax = wn; else tmin = tn; wmin = wn; endif endfor if iter_max_reached warning("at x = %g, maximum number of iterations %d reached without convergence; approximation may not be optimal", x(l), niter_max) endif yy(l) = tmin + (wt - wmin) * (tmax - tmin) / (wmax - wmin); endif endfor endfunction statistics-1.4.3/inst/mvncdf.m0000644000000000000000000001115014153320774014513 0ustar0000000000000000## Copyright (C) 2008 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} =} mvncdf (@var{x}, @var{mu}, @var{sigma}) ## @deftypefnx {Function File} {} mvncdf (@var{a}, @var{x}, @var{mu}, @var{sigma}) ## @deftypefnx {Function File} {[@var{p}, @var{err}] =} mvncdf (@dots{}) ## Compute the cumulative distribution function of the multivariate ## normal distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{x} is the upper limit for integration where each row corresponds ## to an observation. ## ## @item ## @var{mu} is the mean. ## ## @item ## @var{sigma} is the correlation matrix. ## ## @item ## @var{a} is the lower limit for integration where each row corresponds ## to an observation. @var{a} must have the same size as @var{x}. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{p} is the cumulative distribution at each row of @var{x} and ## @var{a}. ## ## @item ## @var{err} is the estimated error. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## x = [1 2]; ## mu = [0.5 1.5]; ## sigma = [1.0 0.5; 0.5 1.0]; ## p = mvncdf (x, mu, sigma) ## @end group ## ## @group ## a = [-inf 0]; ## p = mvncdf (a, x, mu, sigma) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Alan Genz and Frank Bretz. Numerical Computation of Multivariate ## t-Probabilities with Application to Power Calculation of Multiple ## Constrasts. @cite{Journal of Statistical Computation and Simulation}, ## 63, pages 361-378, 1999. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: CDF of the multivariate normal distribution function [p, err] = mvncdf (varargin) # Monte-Carlo confidence factor for the standard error: 99 % gamma = 2.5; # Tolerance err_eps = 1e-3; if (length (varargin) == 1) x = varargin{1}; mu = []; sigma = eye (size (x, 2)); a = -Inf .* ones (size (x)); elseif (length (varargin) == 3) x = varargin{1}; mu = varargin{2}; sigma = varargin{3}; a = -Inf .* ones (size (x)); elseif (length (varargin) == 4) a = varargin{1}; x = varargin{2}; mu = varargin{3}; sigma = varargin{4}; else print_usage (); endif # Dimension q = size (sigma, 1); cases = size (x, 1); # Default value for mu if (isempty (mu)) mu = zeros (1, q); endif # Check parameters if (size (x, 2) != q) error ("mvncdf: x must have the same number of columns as sigma"); endif if (any (size (x) != size (a))) error ("mvncdf: a must have the same size as x"); endif if (isscalar (mu)) mu = ones (1, q) .* mu; elseif (! isvector (mu) || size (mu, 2) != q) error ("mvncdf: mu must be a scalar or a vector with the same number of columns as x"); endif x = x - repmat (mu, cases, 1); if (q < 1 || size (sigma, 2) != q || any (any (sigma != sigma')) || min (eig (sigma)) <= 0) error ("mvncdf: sigma must be nonempty symmetric positive definite"); endif c = chol (sigma)'; # Number of integral transformations n = 1; p = zeros (cases, 1); varsum = zeros (cases, 1); err = ones (cases, 1) .* err_eps; # Apply crude Monte-Carlo estimation while any (err >= err_eps) # Sample from q-1 dimensional unit hypercube w = rand (cases, q - 1); # Transformation of the multivariate normal integral dvev = normcdf ([a(:, 1) / c(1, 1), x(:, 1) / c(1, 1)]); dv = dvev(:, 1); ev = dvev(:, 2); fv = ev - dv; y = zeros (cases, q - 1); for i = 1:(q - 1) y(:, i) = norminv (dv + w(:, i) .* (ev - dv)); dvev = normcdf ([(a(:, i + 1) - c(i + 1, 1:i) .* y(:, 1:i)) ./ c(i + 1, i + 1), (x(:, i + 1) - c(i + 1, 1:i) .* y(:, 1:i)) ./ c(i + 1, i + 1)]); dv = dvev(:, 1); ev = dvev(:, 2); fv = (ev - dv) .* fv; endfor n++; # Estimate standard error varsum += (n - 1) .* ((fv - p) .^ 2) ./ n; err = gamma .* sqrt (varsum ./ (n .* (n - 1))); p += (fv - p) ./ n; endwhile endfunction statistics-1.4.3/inst/mvnpdf.m0000644000000000000000000000743514153320774014543 0ustar0000000000000000## Author: Paul Kienzle ## This program is granted to the public domain. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} mvnpdf (@var{x}) ## @deftypefnx{Function File} {@var{y} =} mvnpdf (@var{x}, @var{mu}) ## @deftypefnx{Function File} {@var{y} =} mvnpdf (@var{x}, @var{mu}, @var{sigma}) ## Compute multivariate normal pdf for @var{x} given mean @var{mu} and covariance matrix ## @var{sigma}. The dimension of @var{x} is @var{d} x @var{p}, @var{mu} is ## @var{1} x @var{p} and @var{sigma} is @var{p} x @var{p}. The normal pdf is ## defined as ## ## @example ## @iftex ## @tex ## $$ 1/y^2 = (2 pi)^p |\Sigma| \exp \{ (x-\mu)^T \Sigma^{-1} (x-\mu) \} $$ ## @end tex ## @end iftex ## @ifnottex ## 1/@var{y}^2 = (2 pi)^@var{p} |@var{Sigma}| exp @{ (@var{x}-@var{mu})' inv(@var{Sigma})@ ## (@var{x}-@var{mu}) @} ## @end ifnottex ## @end example ## ## @strong{References} ## ## NIST Engineering Statistics Handbook 6.5.4.2 ## http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc542.htm ## ## @strong{Algorithm} ## ## Using Cholesky factorization on the positive definite covariance matrix: ## ## @example ## @var{r} = chol (@var{sigma}); ## @end example ## ## where @var{r}'*@var{r} = @var{sigma}. Being upper triangular, the determinant ## of @var{r} is trivially the product of the diagonal, and the determinant of ## @var{sigma} is the square of this: ## ## @example ## @var{det} = prod (diag (@var{r}))^2; ## @end example ## ## The formula asks for the square root of the determinant, so no need to ## square it. ## ## The exponential argument @var{A} = @var{x}' * inv (@var{sigma}) * @var{x} ## ## @example ## @var{A} = @var{x}' * inv (@var{sigma}) * @var{x} ## = @var{x}' * inv (@var{r}' * @var{r}) * @var{x} ## = @var{x}' * inv (@var{r}) * inv(@var{r}') * @var{x} ## @end example ## ## Given that inv (@var{r}') == inv(@var{r})', at least in theory if not numerically, ## ## @example ## @var{A} = (@var{x}' / @var{r}) * (@var{x}'/@var{r})' = sumsq (@var{x}'/@var{r}) ## @end example ## ## The interface takes the parameters to the multivariate normal in columns rather than ## rows, so we are actually dealing with the transpose: ## ## @example ## @var{A} = sumsq (@var{x}/r) ## @end example ## ## and the final result is: ## ## @example ## @var{r} = chol (@var{sigma}) ## @var{y} = (2*pi)^(-@var{p}/2) * exp (-sumsq ((@var{x}-@var{mu})/@var{r}, 2)/2) / prod (diag (@var{r})) ## @end example ## ## @seealso{mvncdf, mvnrnd} ## @end deftypefn function pdf = mvnpdf (x, mu = 0, sigma = 1) ## Check input if (!ismatrix (x)) error ("mvnpdf: first input must be a matrix"); endif if (!isvector (mu) && !isscalar (mu)) error ("mvnpdf: second input must be a real scalar or vector"); endif if (!ismatrix (sigma) || !issquare (sigma)) error ("mvnpdf: third input must be a square matrix"); endif [ps, ps] = size (sigma); [d, p] = size (x); if (p != ps) error ("mvnpdf: dimensions of data and covariance matrix does not match"); endif if (numel (mu) != p && numel (mu) != 1) error ("mvnpdf: dimensions of data does not match dimensions of mean value"); endif mu = mu (:).'; if (all (size (mu) == [1, p])) mu = repmat (mu, [d, 1]); endif if (nargin < 3) pdf = (2*pi)^(-p/2) * exp (-sumsq (x-mu, 2)/2); else r = chol (sigma); pdf = (2*pi)^(-p/2) * exp (-sumsq ((x-mu)/r, 2)/2) / prod (diag (r)); endif endfunction %!demo %! mu = [0, 0]; %! sigma = [1, 0.1; 0.1, 0.5]; %! [X, Y] = meshgrid (linspace (-3, 3, 25)); %! XY = [X(:), Y(:)]; %! Z = mvnpdf (XY, mu, sigma); %! mesh (X, Y, reshape (Z, size (X))); %! colormap jet %!test %! mu = [1,-1]; %! sigma = [.9 .4; .4 .3]; %! x = [ 0.5 -1.2; -0.5 -1.4; 0 -1.5]; %! p = [ 0.41680003660313; 0.10278162359708; 0.27187267524566 ]; %! q = mvnpdf (x, mu, sigma); %! assert (p, q, 10*eps); statistics-1.4.3/inst/mvnrnd.m0000644000000000000000000001332714153320774014552 0ustar0000000000000000## Copyright (C) 2003 Iain Murray ## ## This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License along with this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{s} = mvnrnd (@var{mu}, @var{Sigma}) ## @deftypefnx{Function File} @var{s} = mvnrnd (@var{mu}, @var{Sigma}, @var{n}) ## @deftypefnx{Function File} @var{s} = mvnrnd (@dots{}, @var{tol}) ## Draw @var{n} random @var{d}-dimensional vectors from a multivariate Gaussian distribution with mean @var{mu}(@var{n}x@var{d}) and covariance matrix ## @var{Sigma}(@var{d}x@var{d}). ## ## @var{mu} must be @var{n}-by-@var{d} (or 1-by-@var{d} if @var{n} is given) or a scalar. ## ## If the argument @var{tol} is given the eigenvalues of @var{Sigma} are checked for positivity against -100*tol. The default value of tol is @code{eps*norm (Sigma, "fro")}. ## ## @end deftypefn function s = mvnrnd (mu, Sigma, K, tol=eps*norm (Sigma, "fro")) % Iain Murray 2003 -- I got sick of this simple thing not being in Octave and locking up a stats-toolbox license in Matlab for no good reason. % May 2004 take a third arg, cases. Makes it more compatible with Matlab's. % Paul Kienzle % * Add GPL notice. % * Add docs for argument K % 2012 Juan Pablo Carbajal % * Uses Octave 3.6.2 broadcast. % * Stabilizes chol by perturbing Sigma with a epsilon multiple of the identity. % The effect on the generated samples is to add additional independent noise of variance epsilon. Ref: GPML Rasmussen & Williams. 2006. pp 200-201 % * Improved doc. % * Added tolerance to the positive definite check % * Used chol with option 'upper'. % 2014 Nir Krakauer % * Add tests. % * Allow mu to be scalar, in which case it's assumed that all elements share this mean. %perform some input checking if ~issquare (Sigma) error ('Sigma must be a square covariance matrix.'); end d = size(Sigma, 1); % If mu is column vector and Sigma not a scalar then assume user didn't read help but let them off and flip mu. Don't be more liberal than this or it will encourage errors (eg what should you do if mu is square?). if (size (mu, 2) == 1) && (d != 1) mu = mu'; end if nargin >= 3 n = K; else n = size(mu, 1); %1 if mu is scalar end if (~isscalar (mu)) && any(size (mu) != [1,d]) && any(size (mu) != [n,d]) error ('mu must be nxd, 1xd, or scalar, where Sigma has dimensions dxd.'); end warning ("off", "Octave:broadcast","local"); try U = chol (Sigma + tol*eye (d),"upper"); catch [E , Lambda] = eig (Sigma); if min (diag (Lambda)) < -100*tol error('Sigma must be positive semi-definite. Lowest eigenvalue %g', ... min (diag (Lambda))); else Lambda(Lambda<0) = 0; end warning ("mvnrnd:InvalidInput","Cholesky factorization failed. Using diagonalized matrix.") U = sqrt (Lambda) * E'; end s = randn(n,d)*U + mu; warning ("on", "Octave:broadcast"); endfunction % {{{ END OF CODE --- Guess I should provide an explanation: % % We can draw from axis aligned unit Gaussians with randn(d) % x ~ A*exp(-0.5*x'*x) % We can then rotate this distribution using % y = U'*x % Note that % x = inv(U')*y % Our new variable y is distributed according to: % y ~ B*exp(-0.5*y'*inv(U'*U)*y) % or % y ~ N(0,Sigma) % where % Sigma = U'*U % For a given Sigma we can use the chol function to find the corresponding U, % draw x and find y. We can adjust for a non-zero mean by just adding it on. % % But the Cholsky decomposition function doesn't always work... % Consider Sigma=[1 1;1 1]. Now inv(Sigma) doesn't actually exist, but Matlab's % mvnrnd provides samples with this covariance st x(1)~N(0,1) x(2)=x(1). The % fast way to deal with this would do something similar to chol but be clever % when the rows aren't linearly independent. However, I can't be bothered, so % another way of doing the decomposition is by diagonalising Sigma (which is % slower but works). % if % [E,Lambda]=eig(Sigma) % then % Sigma = E*Lambda*E' % so % U = sqrt(Lambda)*E' % If any Lambdas are negative then Sigma just isn't even positive semi-definite % so we can give up. % % Paul Kienzle adds: % Where it exists, chol(Sigma) is numerically well behaved. chol(hilb(12)) for doubles and for 100 digit floating point differ in the last digit. % Where chol(Sigma) doesn't exist, X*sqrt(Lambda)*E' will be somewhat accurate. For example, the elements of sqrt(Lambda)*E' for hilb(12), hilb(55) and hilb(120) are accurate to around 1e-8 or better. This was tested using the TNT+JAMA for eig and chol templates, and qlib for 100 digit precision. % }}} %!shared m, n, C, rho %! m = 10; n = 3; rho = 0.4; C = rho*ones(n, n) + (1 - rho)*eye(n); %!assert(size(mvnrnd(0, C, m)), [m n]) %!assert(size(mvnrnd(zeros(1, n), C, m)), [m n]) %!assert(size(mvnrnd(zeros(n, 1), C, m)), [m n]) %!assert(size(mvnrnd(zeros(m, n), C, m)), [m n]) %!assert(size(mvnrnd(zeros(m, n), C)), [m n]) %!assert(size(mvnrnd(zeros(1, n), C)), [1 n]) %!assert(size(mvnrnd(zeros(n, 1), C)), [1 n]) %!error(mvnrnd(zeros(m+1, n), C, m)) %!error(mvnrnd(zeros(1, n+1), C, m)) %!error(mvnrnd(zeros(n+1, 1), C, m)) %!error(mvnrnd(zeros(m, n), eye(n+1), m)) %!error(mvnrnd(zeros(m, n), eye(n+1, n), m)) statistics-1.4.3/inst/mvtcdf.m0000644000000000000000000001123414153320774014524 0ustar0000000000000000## Copyright (C) 2008 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} =} mvtcdf (@var{x}, @var{sigma}, @var{nu}) ## @deftypefnx {Function File} {} mvtcdf (@var{a}, @var{x}, @var{sigma}, @var{nu}) ## @deftypefnx {Function File} {[@var{p}, @var{err}] =} mvtcdf (@dots{}) ## Compute the cumulative distribution function of the multivariate ## Student's t distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{x} is the upper limit for integration where each row corresponds ## to an observation. ## ## @item ## @var{sigma} is the correlation matrix. ## ## @item ## @var{nu} is the degrees of freedom. ## ## @item ## @var{a} is the lower limit for integration where each row corresponds ## to an observation. @var{a} must have the same size as @var{x}. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{p} is the cumulative distribution at each row of @var{x} and ## @var{a}. ## ## @item ## @var{err} is the estimated error. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## x = [1 2]; ## sigma = [1.0 0.5; 0.5 1.0]; ## nu = 4; ## p = mvtcdf (x, sigma, nu) ## @end group ## ## @group ## a = [-inf 0]; ## p = mvtcdf (a, x, sigma, nu) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Alan Genz and Frank Bretz. Numerical Computation of Multivariate ## t-Probabilities with Application to Power Calculation of Multiple ## Constrasts. @cite{Journal of Statistical Computation and Simulation}, ## 63, pages 361-378, 1999. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: CDF of the multivariate Student's t distribution function [p, err] = mvtcdf (varargin) # Monte-Carlo confidence factor for the standard error: 99 % gamma = 2.5; # Tolerance err_eps = 1e-3; if (length (varargin) == 3) x = varargin{1}; sigma = varargin{2}; nu = varargin{3}; a = -Inf .* ones (size (x)); elseif (length (varargin) == 4) a = varargin{1}; x = varargin{2}; sigma = varargin{3}; nu = varargin{4}; else print_usage (); endif # Dimension q = size (sigma, 1); cases = size (x, 1); # Check parameters if (size (x, 2) != q) error ("mvtcdf: x must have the same number of columns as sigma"); endif if (any (size (x) != size (a))) error ("mvtcdf: a must have the same size as x"); endif if (! isscalar (nu) && (! isvector (nu) || length (nu) != cases)) error ("mvtcdf: nu must be a scalar or a vector with the same number of rows as x"); endif # Convert to correlation matrix if necessary if (any (diag (sigma) != 1)) svar = repmat (diag (sigma), 1, q); sigma = sigma ./ sqrt (svar .* svar'); endif if (q < 1 || size (sigma, 2) != q || any (any (sigma != sigma')) || min (eig (sigma)) <= 0) error ("mvtcdf: sigma must be nonempty symmetric positive definite"); endif nu = nu(:); c = chol (sigma)'; # Number of integral transformations n = 1; p = zeros (cases, 1); varsum = zeros (cases, 1); err = ones (cases, 1) .* err_eps; # Apply crude Monte-Carlo estimation while any (err >= err_eps) # Sample from q-1 dimensional unit hypercube w = rand (cases, q - 1); # Transformation of the multivariate t-integral dvev = tcdf ([a(:, 1) / c(1, 1), x(:, 1) / c(1, 1)], nu); dv = dvev(:, 1); ev = dvev(:, 2); fv = ev - dv; y = zeros (cases, q - 1); for i = 1:(q - 1) y(:, i) = tinv (dv + w(:, i) .* (ev - dv), nu + i - 1) .* sqrt ((nu + sum (y(:, 1:(i-1)) .^ 2, 2)) ./ (nu + i - 1)); tf = (sqrt ((nu + i) ./ (nu + sum (y(:, 1:i) .^ 2, 2)))) ./ c(i + 1, i + 1); dvev = tcdf ([(a(:, i + 1) - c(i + 1, 1:i) .* y(:, 1:i)) .* tf, (x(:, i + 1) - c(i + 1, 1:i) .* y(:, 1:i)) .* tf], nu + i); dv = dvev(:, 1); ev = dvev(:, 2); fv = (ev - dv) .* fv; endfor n++; # Estimate standard error varsum += (n - 1) .* ((fv - p) .^ 2) ./ n; err = gamma .* sqrt (varsum ./ (n .* (n - 1))); p += (fv - p) ./ n; endwhile endfunction statistics-1.4.3/inst/mvtpdf.m0000644000000000000000000000746214153320774014551 0ustar0000000000000000## Copyright (C) 2015 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} =} mvtpdf (@var{x}, @var{sigma}, @var{nu}) ## Compute the probability density function of the multivariate Student's t distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{x} are the points at which to find the probability, where each row corresponds ## to an observation. (@var{n} by @var{d} matrix) ## ## @item ## @var{sigma} is the scale matrix. (@var{d} by @var{d} symmetric positive definite matrix) ## ## @item ## @var{nu} is the degrees of freedom. (scalar or @var{n} vector) ## ## @end itemize ## ## The distribution is assumed to be centered (zero mean). ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{p} is the probability density for each row of @var{x}. (@var{n} by 1 vector) ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## x = [1 2]; ## sigma = [1.0 0.5; 0.5 1.0]; ## nu = 4; ## p = mvtpdf (x, sigma, nu) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Michael Roth, On the Multivariate t Distribution, Technical report from Automatic Control at Linkoepings universitet, @url{http://users.isy.liu.se/en/rt/roth/student.pdf} ## @end enumerate ## @end deftypefn ## Author: Nir Krakauer ## Description: PDF of the multivariate Student's t distribution function [p] = mvtpdf (x, sigma, nu) if (nargin != 3) print_usage (); endif # Dimensions d = size (sigma, 1); n = size (x, 1); # Check parameters if (size (x, 2) != d) error ("mvtpdf: x must have the same number of columns as sigma"); endif if (! isscalar (nu) && (! isvector (nu) || numel (nu) != n)) error ("mvtpdf: nu must be a scalar or a vector with the same number of rows as x"); endif if (d < 1 || size (sigma, 2) != d || ! issymmetric (sigma)) error ("mvtpdf: sigma must be nonempty and symmetric"); endif try U = chol (sigma); catch error ("mvtpdf: sigma must be positive definite"); end_try_catch nu = nu(:); sqrt_det_sigma = prod(diag(U)); #square root of determinant of sigma c = (gamma((nu+d)/2) ./ gamma(nu/2)) ./ (sqrt_det_sigma * (nu*pi).^(d/2)); #scale factor for PDF p = c ./ ((1 + sumsq(U' \ x') ./ nu') .^ ((nu' + d)/2))'; #note: sumsq(U' \ x') is equivalent to the quadratic form x*inv(sigma)*x' endfunction #test results verified with R mvtnorm package dmvt function %!assert (mvtpdf ([0 0], eye(2), 1), 0.1591549, 1E-7) #dmvt(x = c(0,0), sigma = diag(2), log = FALSE) %!assert (mvtpdf ([1 0], [1 0.5; 0.5 1], 2), 0.06615947, 1E-7) #dmvt(x = c(1,0), sigma = matrix(c(1, 0.5, 0.5, 1), nrow=2, ncol=2), df = 2, log = FALSE) %!assert (mvtpdf ([1 0.4 0; 1.2 0.5 0.5; 1.4 0.6 1], [1 0.5 0.3; 0.5 1 0.6; 0.3 0.6 1], [5 6 7]), [0.04713313 0.03722421 0.02069011]', 1E-7) #dmvt(x = c(1,0.4,0), sigma = matrix(c(1, 0.5, 0.3, 0.5, 1, 0.6, 0.3, 0.6, 1), nrow=3, ncol=3), df = 5, log = FALSE); dmvt(x = c(1.2,0.5,0.5), sigma = matrix(c(1, 0.5, 0.3, 0.5, 1, 0.6, 0.3, 0.6, 1), nrow=3, ncol=3), df = 6, log = FALSE); dmvt(x = c(1.4,0.6,1), sigma = matrix(c(1, 0.5, 0.3, 0.5, 1, 0.6, 0.3, 0.6, 1), nrow=3, ncol=3), df = 7, log = FALSE) statistics-1.4.3/inst/mvtrnd.m0000644000000000000000000001032214153320774014550 0ustar0000000000000000## Copyright (C) 2012 Arno Onken , Iñigo Urteaga ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{x} =} mvtrnd (@var{sigma}, @var{nu}) ## @deftypefnx {Function File} {@var{x} =} mvtrnd (@var{sigma}, @var{nu}, @var{n}) ## Generate random samples from the multivariate t-distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{sigma} is the matrix of correlation coefficients. If there are any ## non-unit diagonal elements then @var{sigma} will be normalized, so that the ## resulting covariance of the obtained samples @var{x} follows: ## @code{cov (x) = nu/(nu-2) * sigma ./ (sqrt (diag (sigma) * diag (sigma)))}. ## In order to obtain samples distributed according to a standard multivariate ## t-distribution, @var{sigma} must be equal to the identity matrix. To generate ## multivariate t-distribution samples @var{x} with arbitrary covariance matrix ## @var{sigma}, the following scaling might be used: ## @code{x = mvtrnd (sigma, nu, n) * diag (sqrt (diag (sigma)))}. ## ## @item ## @var{nu} is the degrees of freedom for the multivariate t-distribution. ## @var{nu} must be a vector with the same number of elements as samples to be ## generated or be scalar. ## ## @item ## @var{n} is the number of rows of the matrix to be generated. @var{n} must be ## a non-negative integer and corresponds to the number of samples to be ## generated. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{x} is a matrix of random samples from the multivariate t-distribution ## with @var{n} row samples. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## sigma = [1, 0.5; 0.5, 1]; ## nu = 3; ## n = 10; ## x = mvtrnd (sigma, nu, n); ## @end group ## ## @group ## sigma = [1, 0.5; 0.5, 1]; ## nu = [2; 3]; ## n = 2; ## x = mvtrnd (sigma, nu, 2); ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, 2001. ## ## @item ## Samuel Kotz and Saralees Nadarajah. @cite{Multivariate t Distributions and ## Their Applications}. Cambridge University Press, Cambridge, 2004. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Random samples from the multivariate t-distribution function x = mvtrnd (sigma, nu, n) # Check arguments if (nargin < 2) print_usage (); endif if (! ismatrix (sigma) || any (any (sigma != sigma')) || min (eig (sigma)) <= 0) error ("mvtrnd: sigma must be a positive definite matrix"); endif if (!isvector (nu) || any (nu <= 0)) error ("mvtrnd: nu must be a positive scalar or vector"); endif nu = nu(:); if (nargin > 2) if (! isscalar (n) || n < 0 | round (n) != n) error ("mvtrnd: n must be a non-negative integer") endif if (isscalar (nu)) nu = nu * ones (n, 1); else if (length (nu) != n) error ("mvtrnd: n must match the length of nu") endif endif else n = length (nu); endif # Normalize sigma if (any (diag (sigma) != 1)) sigma = sigma ./ sqrt (diag (sigma) * diag (sigma)'); endif # Dimension d = size (sigma, 1); # Draw samples y = mvnrnd (zeros (1, d), sigma, n); u = repmat (chi2rnd (nu), 1, d); x = y .* sqrt (repmat (nu, 1, d) ./ u); endfunction %!test %! sigma = [1, 0.5; 0.5, 1]; %! nu = 3; %! n = 10; %! x = mvtrnd (sigma, nu, n); %! assert (size (x), [10, 2]); %!test %! sigma = [1, 0.5; 0.5, 1]; %! nu = [2; 3]; %! n = 2; %! x = mvtrnd (sigma, nu, 2); %! assert (size (x), [2, 2]); statistics-1.4.3/inst/nakacdf.m0000644000000000000000000000631014153320774014627 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} nakacdf (@var{x}, @var{m}, @var{w}) ## For each element of @var{x}, compute the cumulative distribution function ## (CDF) at @var{x} of the Nakagami distribution with shape parameter @var{m} ## and scale parameter @var{w}. ## ## @end deftypefn ## Author: Dag Lyberg ## Description: CDF of the Nakagami distribution function cdf = nakacdf (x, m, w) if (nargin != 3) print_usage (); endif if (! isscalar (m) || ! isscalar (w)) [retval, x, m, w] = common_size (x, m, w); if (retval > 0) error ("nakacdf: X, M and W must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (m) || iscomplex (w)) error ("nakacdf: X, M and W must not be complex"); endif if (isa (x, "single") || isa (m, "single") || isa (w, "single")) inv = zeros (size (x), "single"); else inv = zeros (size (x)); endif k = isnan (x) | ! (m > 0) | ! (w > 0); cdf(k) = NaN; k = (x == Inf) & (0 < m) & (m < Inf) & (0 < w) & (w < Inf); cdf(k) = 1; k = (0 < x) & (x < Inf) & (0 < m) & (m < Inf) & (0 < w) & (w < Inf); if (isscalar(x) && isscalar (m) && isscalar(w)) left = m; right = (m/w) * x^2; cdf(k) = gammainc(right, left); elseif (isscalar (m) && isscalar(w)) left = m * ones(size(x)); right = (m/w) * x.^2; cdf(k) = gammainc(right(k), left(k)); else left = m .* ones(size(x)); right = (m./w) .* x.^2; cdf(k) = gammainc(right(k), left(k)); endif endfunction %!shared x,y %! x = [-1, 0, 1, 2, Inf]; %! y = [0, 0, 0.63212055882855778, 0.98168436111126578, 1]; %!assert (nakacdf (x, ones (1,5), ones (1,5)), y, eps) %!assert (nakacdf (x, 1, 1), y, eps) %!assert (nakacdf (x, [1, 1, NaN, 1, 1], 1), [y(1:2), NaN, y(4:5)]) %!assert (nakacdf (x, 1, [1, 1, NaN, 1, 1]), [y(1:2), NaN, y(4:5)]) %!assert (nakacdf ([x, NaN], 1, 1), [y, NaN], eps) ## Test class of input preserved %!assert (nakacdf (single ([x, NaN]), 1, 1), single ([y, NaN]), eps('single')) %!assert (nakacdf ([x, NaN], single (1), 1), single ([y, NaN]), eps('single')) %!assert (nakacdf ([x, NaN], 1, single (1)), single ([y, NaN]), eps('single')) ## Test input validation %!error nakacdf () %!error nakacdf (1) %!error nakacdf (1,2) %!error nakacdf (1,2,3,4) %!error nakacdf (ones (3), ones (2), ones(2)) %!error nakacdf (ones (2), ones (3), ones(2)) %!error nakacdf (ones (2), ones (2), ones(3)) %!error nakacdf (i, 2, 2) %!error nakacdf (2, i, 2) %!error nakacdf (2, 2, i) statistics-1.4.3/inst/nakainv.m0000644000000000000000000000623314153320774014673 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} nakainv (@var{x}, @var{m}, @var{w}) ## For each element of @var{x}, compute the quantile (the inverse of the CDF) ## at @var{x} of the Nakagami distribution with shape parameter @var{m} and ## scale parameter @var{w}. ## ## @end deftypefn ## Author: Dag Lyberg ## Description: Quantile function of the Nakagami distribution function inv = nakainv (x, m, w) if (nargin != 3) print_usage (); endif if (! isscalar (m) || ! isscalar (w)) [retval, x, m, w] = common_size (x, m, w); if (retval > 0) error ("nakainv: X, M and W must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (m) || iscomplex (w)) error ("nakainv: X, M, and W must not be complex"); endif if (isa (x, "single") || isa (m, "single") || isa (w, "single")) inv = zeros (size (x), "single"); else inv = zeros (size (x)); endif k = isnan (x) | ! (0 <= x) | ! (x <= 1) | ! (-Inf < m) | ! (m < Inf) ... | ! (0 < w) | ! (w < Inf); inv(k) = NaN; k = (x == 1) & (-Inf < m) & (m < Inf) & (0 < w) & (w < Inf); inv(k) = Inf; k = (0 < x) & (x < 1) & (0 < m) & (m < Inf) & (0 < w) & (w < Inf); if (isscalar (m) && isscalar(w)) m_gamma = m; w_gamma = w/m; inv(k) = gaminv(x(k), m_gamma, w_gamma); inv(k) = sqrt(inv(k)); else m_gamma = m; w_gamma = w./m; inv(k) = gaminv(x(k), m_gamma(k), w_gamma(k)); inv(k) = sqrt(inv(k)); endif endfunction %!shared x,y %! x = [-Inf, -1, 0, 1/2, 1, 2, Inf]; %! y = [NaN, NaN, 0, 0.83255461115769769, Inf, NaN, NaN]; %!assert (nakainv (x, ones (1,7), ones (1,7)), y, eps) %!assert (nakainv (x, 1, 1), y, eps) %!assert (nakainv (x, [1, 1, 1, NaN, 1, 1, 1], 1), [y(1:3), NaN, y(5:7)], eps) %!assert (nakainv (x, 1, [1, 1, 1, NaN, 1, 1, 1]), [y(1:3), NaN, y(5:7)], eps) %!assert (nakainv ([x, NaN], 1, 1), [y, NaN], eps) ## Test class of input preserved %!assert (nakainv (single ([x, NaN]), 1, 1), single ([y, NaN])) %!assert (nakainv ([x, NaN], single (1), 1), single ([y, NaN])) %!assert (nakainv ([x, NaN], 1, single (1)), single ([y, NaN])) ## Test input validation %!error nakainv () %!error nakainv (1) %!error nakainv (1,2) %!error nakainv (1,2,3,4) %!error nakainv (ones (3), ones (2), ones(2)) %!error nakainv (ones (2), ones (3), ones(2)) %!error nakainv (ones (2), ones (2), ones(3)) %!error nakainv (i, 2, 2) %!error nakainv (2, i, 2) %!error nakainv (2, 2, i) statistics-1.4.3/inst/nakapdf.m0000644000000000000000000000611714153320774014651 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} nakapdf (@var{x}, @var{m}, @var{w}) ## For each element of @var{x}, compute the probability density function (PDF) ## at @var{x} of the Nakagami distribution with shape parameter @var{m} and ## scale parameter @var{w}. ## @end deftypefn ## Author: Dag Lyberg ## Description: PDF of the Nakagami distribution function pdf = nakapdf (x, m, w) if (nargin != 3) print_usage (); endif if (! isscalar (m) || ! isscalar (w)) [retval, x, m, w] = common_size (x, m, w); if (retval > 0) error ("nakapdf: X, M and W must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (m) || iscomplex (w)) error ("nakapdf: X, M and W must not be complex"); endif if (isa (x, "single") || isa (m, "single") || isa (w, "single")) pdf = zeros (size (x), "single"); else pdf = zeros (size (x)); endif k = isnan (x) | ! (m > 0.5) | ! (w > 0); pdf(k) = NaN; k = (0 < x) & (x < Inf) & (0 < m) & (m < Inf) & (0 < w) & (w < Inf); if (isscalar (m) && isscalar(w)) pdf(k) = exp (log (2) + m*log (m) - log (gamma (m)) - ... m*log (w) + (2*m-1) * ... log (x(k)) - (m/w) * x(k).^2); else pdf(k) = exp(log(2) + m(k).*log (m(k)) - log (gamma (m(k))) - ... m(k).*log (w(k)) + (2*m(k)-1) ... .* log (x(k)) - (m(k)./w(k)) .* x(k).^2); endif endfunction %!shared x,y %! x = [-1, 0, 1, 2, Inf]; %! y = [0, 0, 0.73575888234288467, 0.073262555554936715, 0]; %!assert (nakapdf (x, ones (1,5), ones (1,5)), y, eps) %!assert (nakapdf (x, 1, 1), y, eps) %!assert (nakapdf (x, [1, 1, NaN, 1, 1], 1), [y(1:2), NaN, y(4:5)], eps) %!assert (nakapdf (x, 1, [1, 1, NaN, 1, 1]), [y(1:2), NaN, y(4:5)], eps) %!assert (nakapdf ([x, NaN], 1, 1), [y, NaN], eps) ## Test class of input preserved %!assert (nakapdf (single ([x, NaN]), 1, 1), single ([y, NaN])) %!assert (nakapdf ([x, NaN], single (1), 1), single ([y, NaN])) %!assert (nakapdf ([x, NaN], 1, single (1)), single ([y, NaN])) ## Test input validation %!error nakapdf () %!error nakapdf (1) %!error nakapdf (1,2) %!error nakapdf (1,2,3,4) %!error nakapdf (ones (3), ones (2), ones(2)) %!error nakapdf (ones (2), ones (3), ones(2)) %!error nakapdf (ones (2), ones (2), ones(3)) %!error nakapdf (i, 2, 2) %!error nakapdf (2, i, 2) %!error nakapdf (2, 2, i) statistics-1.4.3/inst/nakarnd.m0000644000000000000000000001055114153320774014660 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} nakarnd (@var{m}, @var{w}) ## @deftypefnx {} {} nakarnd (@var{m}, @var{w}, @var{r}) ## @deftypefnx {} {} nakarnd (@var{m}, @var{w}, @var{r}, @var{c}, @dots{}) ## @deftypefnx {} {} nakarnd (@var{m}, @var{w}, [@var{sz}]) ## Return a matrix of random samples from the Nakagami distribution with ## shape parameter @var{m} and scale @var{w}. ## ## When called with a single size argument, return a square matrix with ## the dimension specified. When called with more than one scalar argument the ## first two arguments are taken as the number of rows and columns and any ## further arguments specify additional matrix dimensions. The size may also ## be specified with a vector of dimensions @var{sz}. ## ## If no size arguments are given then the result matrix is the common size of ## @var{m} and @var{w}. ## @end deftypefn ## Author: Dag Lyberg ## Description: Random deviates from the Nakagami distribution function rnd = nakarnd (m, w, varargin) if (nargin < 2) print_usage (); endif if (! isscalar (m) || ! isscalar (w)) [retval, m, w] = common_size (m, w); if (retval > 0) error ("nakarnd: M and W must be of common size or scalars"); endif endif if (iscomplex (m) || iscomplex (w)) error ("nakarnd: M and W must not be complex"); endif if (nargin == 2) sz = size (m); elseif (nargin == 3) if (isscalar (varargin{1}) && varargin{1} >= 0) sz = [varargin{1}, varargin{1}]; elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) sz = varargin{1}; else error ("nakarnd: dimension vector must be row vector of non-negative integers"); endif elseif (nargin > 3) if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) error ("nakarnd: dimensions must be non-negative integers"); endif sz = [varargin{:}]; endif if (! isscalar (m) && ! isequal (size (w), sz)) error ("nakagrnd: M and W must be scalar or of size SZ"); endif if (isa (m, "single") || isa (w, "single")) cls = "single"; else cls = "double"; endif if (isscalar (m) && isscalar (w)) if ((0 < m) && (m < Inf) && (0 < w) && (w < Inf)) m_gamma = m; w_gamma = w/m; rnd = gamrnd(m_gamma, w_gamma, sz); rnd = sqrt(rnd); else rnd = NaN (sz, cls); endif else rnd = NaN (sz, cls); k = (0 < m) & (m < Inf) & (0 < w) & (w < Inf); m_gamma = m; w_gamma = w./m; rnd(k) = gamrnd(m_gamma(k), w_gamma(k)); rnd(k) = sqrt(rnd(k)); endif endfunction %!assert (size (nakarnd (1,1)), [1, 1]) %!assert (size (nakarnd (ones (2,1), 1)), [2, 1]) %!assert (size (nakarnd (ones (2,2), 1)), [2, 2]) %!assert (size (nakarnd (1, ones (2,1))), [2, 1]) %!assert (size (nakarnd (1, ones (2,2))), [2, 2]) %!assert (size (nakarnd (1,1, 3)), [3, 3]) %!assert (size (nakarnd (1,1, [4 1])), [4, 1]) %!assert (size (nakarnd (1,1, 4, 1)), [4, 1]) ## Test class of input preserved %!assert (class (nakarnd (1,1)), "double") %!assert (class (nakarnd (single (1),1)), "single") %!assert (class (nakarnd (single ([1 1]),1)), "single") %!assert (class (nakarnd (1,single (1))), "single") %!assert (class (nakarnd (1,single ([1 1]))), "single") ## Test input validation %!error nakarnd () %!error nakarnd (1) %!error nakarnd (zeros (3), ones (2)) %!error nakarnd (zeros (2), ones (3)) %!error nakarnd (i, 2) %!error nakarnd (1, i) %!error nakarnd (1,2, -1) %!error nakarnd (1,2, ones (2)) %!error nakarnd (1, 2, [2 -1 2]) %!error nakarnd (1,2, 1, ones (2)) %!error nakarnd (1,2, 1, -1) %!error nakarnd (ones (2,2), 2, 3) %!error nakarnd (ones (2,2), 2, [3, 2]) %!error nakarnd (ones (2,2), 2, 2, 3) statistics-1.4.3/inst/nanmax.m0000644000000000000000000000342314153320774014524 0ustar0000000000000000## Copyright (C) 2001 Paul Kienzle ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{v}, @var{idx}] =} nanmax (@var{X}) ## @deftypefnx{Function File} {[@var{v}, @var{idx}] =} nanmax (@var{X}, @var{Y}) ## Find the maximal element while ignoring NaN values. ## ## @code{nanmax} is identical to the @code{max} function except that NaN values ## are ignored. If all values in a column are NaN, the maximum is ## returned as NaN rather than []. ## ## @seealso{max, nansum, nanmin, nanmean, nanmedian} ## @end deftypefn function [v, idx] = nanmax (X, Y, DIM) if nargin < 1 || nargin > 3 print_usage; elseif nargin == 1 || (nargin == 2 && isempty(Y)) nanvals = isnan(X); X(nanvals) = -Inf; [v, idx] = max (X); v(all(nanvals)) = NaN; elseif (nargin == 3 && isempty(Y)) nanvals = isnan(X); X(nanvals) = -Inf; [v, idx] = max (X,[],DIM); v(all(nanvals,DIM)) = NaN; else Xnan = isnan(X); Ynan = isnan(Y); X(Xnan) = -Inf; Y(Ynan) = -Inf; if (nargin == 3) [v, idx] = max(X,Y,DIM); else [v, idx] = max(X,Y); endif v(Xnan & Ynan) = NaN; endif endfunction statistics-1.4.3/inst/nanmean.m0000644000000000000000000000250714153320774014661 0ustar0000000000000000## Copyright (C) 2001 Paul Kienzle ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{v} =} nanmean (@var{X}) ## @deftypefnx{Function File} {@var{v} =} nanmean (@var{X}, @var{dim}) ## Compute the mean value while ignoring NaN values. ## ## @code{nanmean} is identical to the @code{mean} function except that NaN values ## are ignored. If all values are NaN, the mean is returned as NaN. ## ## @seealso{mean, nanmin, nanmax, nansum, nanmedian} ## @end deftypefn function v = nanmean (X, varargin) if nargin < 1 print_usage; else n = sum (!isnan(X), varargin{:}); n(n == 0) = NaN; X(isnan(X)) = 0; v = sum (X, varargin{:}) ./ n; endif endfunction statistics-1.4.3/inst/nanmedian.m0000644000000000000000000000522514153320774015176 0ustar0000000000000000## Copyright (C) 2001 Paul Kienzle ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{v} = nanmedian (@var{x}) ## @deftypefnx{Function File} @var{v} = nanmedian (@var{x}, @var{dim}) ## Compute the median of data while ignoring NaN values. ## ## This function is identical to the @code{median} function except that NaN values ## are ignored. If all values are NaN, the median is returned as NaN. ## ## @seealso{median, nanmin, nanmax, nansum, nanmean} ## @end deftypefn function v = nanmedian (X, varargin) if nargin < 1 || nargin > 2 print_usage; endif if nargin < 2 dim = min(find(size(X)>1)); if isempty(dim), dim=1; endif; else dim = varargin{:}; endif sz = size (X); if (prod (sz) > 1) ## Find lengths of datasets after excluding NaNs; valid datasets ## are those that are not empty after you remove all the NaNs n = sz(dim) - sum (isnan(X),varargin{:}); ## When n is equal to zero, force it to one, so that median ## picks up a NaN value below n (n==0) = 1; ## Sort the datasets, with the NaN going to the end of the data X = sort (X, varargin{:}); ## Determine the offset for each column in single index mode colidx = reshape((0:(prod(sz) / sz(dim) - 1)), size(n)); colidx = floor(colidx / prod(sz(1:dim-1))) * prod(sz(1:dim)) + ... mod(colidx,prod(sz(1:dim-1))); stride = prod(sz(1:dim-1)); ## Average the two central values of the sorted list to compute ## the median, but only do so for valid rows. If the dataset ## is odd length, the single central value will be used twice. ## E.g., ## for n==5, ceil(2.5+0.5) is 3 and floor(2.5+0.5) is also 3 ## for n==6, ceil(3.0+0.5) is 4 and floor(3.0+0.5) is 3 ## correction made for stride of data "stride*ceil(2.5-0.5)+1" v = (X(colidx + stride*ceil(n./2-0.5) + 1) + ... X(colidx + stride*floor(n./2-0.5) + 1)) ./ 2; else error ("nanmedian: invalid matrix argument"); endif endfunction statistics-1.4.3/inst/nanmin.m0000644000000000000000000000352014153320774014520 0ustar0000000000000000## Copyright (C) 2001 Paul Kienzle ## Copyright (C) 2003 Alois Schloegl ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{v}, @var{idx}] =} nanmin (@var{X}) ## @deftypefnx{Function File} {[@var{v}, @var{idx}] =} nanmin (@var{X}, @var{Y}) ## Find the minimal element while ignoring NaN values. ## ## @code{nanmin} is identical to the @code{min} function except that NaN values ## are ignored. If all values in a column are NaN, the minimum is ## returned as NaN rather than []. ## ## @seealso{min, nansum, nanmax, nanmean, nanmedian} ## @end deftypefn function [v, idx] = nanmin (X, Y, DIM) if nargin < 1 || nargin > 3 print_usage; elseif nargin == 1 || (nargin == 2 && isempty(Y)) nanvals = isnan(X); X(nanvals) = Inf; [v, idx] = min (X); v(all(nanvals)) = NaN; elseif (nargin == 3 && isempty(Y)) nanvals = isnan(X); X(nanvals) = Inf; [v, idx] = min (X,[],DIM); v(all(nanvals,DIM)) = NaN; else Xnan = isnan(X); Ynan = isnan(Y); X(Xnan) = Inf; Y(Ynan) = Inf; if (nargin == 3) [v, idx] = min(X,Y,DIM); else [v, idx] = min(X,Y); endif v(Xnan & Ynan) = NaN; endif endfunction statistics-1.4.3/inst/nanstd.m0000644000000000000000000000614214153320774014532 0ustar0000000000000000## Copyright (C) 2001 Paul Kienzle ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{v} =} nanstd (@var{X}) ## @deftypefnx{Function File} {@var{v} =} nanstd (@var{X}, @var{opt}) ## @deftypefnx{Function File} {@var{v} =} nanstd (@var{X}, @var{opt}, @var{dim}) ## Compute the standard deviation while ignoring NaN values. ## ## @code{nanstd} is identical to the @code{std} function except that NaN values are ## ignored. If all values are NaN, the standard deviation is returned as NaN. ## If there is only a single non-NaN value, the deviation is returned as 0. ## ## The argument @var{opt} determines the type of normalization to use. Valid values ## are ## ## @table @asis ## @item 0: ## normalizes with @math{N-1}, provides the square root of best unbiased estimator of ## the variance [default] ## @item 1: ## normalizes with @math{N}, this provides the square root of the second moment around ## the mean ## @end table ## ## The third argument @var{dim} determines the dimension along which the standard ## deviation is calculated. ## ## @seealso{std, nanmin, nanmax, nansum, nanmedian, nanmean} ## @end deftypefn function v = nanstd (X, opt, varargin) if nargin < 1 print_usage; else if nargin < 3 dim = min(find(size(X)>1)); if isempty(dim), dim=1; endif; else dim = varargin{1}; endif if ((nargin < 2) || isempty(opt)) opt = 0; endif ## determine the number of non-missing points in each data set n = sum (!isnan(X), varargin{:}); ## replace missing data with zero and compute the mean X(isnan(X)) = 0; meanX = sum (X, varargin{:}) ./ n; ## subtract the mean from the data and compute the sum squared sz = ones(1,length(size(X))); sz(dim) = size(X,dim); v = sumsq (X - repmat(meanX,sz), varargin{:}); ## because the missing data was set to zero each missing data ## point will contribute (-meanX)^2 to sumsq, so remove these v = v - (meanX .^ 2) .* (size(X,dim) - n); if (opt == 0) ## compute the standard deviation from the corrected sumsq using ## max(n-1,1) in the denominator so that the std for a single point is 0 v = sqrt ( v ./ max(n - 1, 1) ); elseif (opt == 1) ## compute the standard deviation from the corrected sumsq v = sqrt ( v ./ n ); else error ("std: unrecognized normalization type"); endif ## make sure that we return a real number v = real (v); endif endfunction statistics-1.4.3/inst/nansum.m0000644000000000000000000000402414153320774014541 0ustar0000000000000000## Copyright (C) 2001 Paul Kienzle ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Built-in Function} {} nansum (@var{x}) ## @deftypefnx {Built-in Function} {} nansum (@var{x}, @var{dim}) ## @deftypefnx {Built-in Function} {} nansum (@dots{}, @qcode{"native"}) ## @deftypefnx {Built-in Function} {} nansum (@dots{}, @qcode{"double"}) ## @deftypefnx {Built-in Function} {} nansum (@dots{}, @qcode{"extra"}) ## Compute the sum while ignoring NaN values. ## ## @code{nansum} is identical to the @code{sum} function except that NaN ## values are treated as 0 and so ignored. If all values are NaN, the sum is ## returned as 0. ## ## See help text of @code{sum} for details on the options. ## ## @seealso{sum, nanmin, nanmax, nanmean, nanmedian} ## @end deftypefn function v = nansum (X, varargin) if (nargin < 1) print_usage (); else X(isnan (X)) = 0; v = sum (X, varargin{:}); endif endfunction %!assert (nansum ([2 4 NaN 7]), 13) %!assert (nansum ([2 4 NaN Inf]), Inf) %!assert (nansum ([1 NaN 3; NaN 5 6; 7 8 NaN]), [8 13 9]) %!assert (nansum ([1 NaN 3; NaN 5 6; 7 8 NaN], 2), [4; 11; 15]) %!assert (nansum (single ([1 NaN 3; NaN 5 6; 7 8 NaN])), single ([8 13 9])) %!assert (nansum (single ([1 NaN 3; NaN 5 6; 7 8 NaN]), "double"), [8 13 9]) %!assert (nansum (uint8 ([2 4 1 7])), 14) %!assert (nansum (uint8 ([2 4 1 7]), "native"), uint8 (14)) %!assert (nansum (uint8 ([2 4 1 7])), 14) statistics-1.4.3/inst/nanvar.m0000644000000000000000000000400014153320774014517 0ustar0000000000000000# Copyright (C) 2008 Sylvain Pelissier ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} nanvar (@var{x}) ## @deftypefnx{Function File} {@var{v} =} nanvar (@var{X}, @var{opt}) ## @deftypefnx{Function File} {@var{v} =} nanvar (@var{X}, @var{opt}, @var{dim}) ## Compute the variance while ignoring NaN values. ## ## For vector arguments, return the (real) variance of the values. ## For matrix arguments, return a row vector containing the variance for ## each column. ## ## The argument @var{opt} determines the type of normalization to use. ## Valid values are ## ## @table @asis ## @item 0: ## Normalizes with @math{N-1}, provides the best unbiased estimator of the ## variance [default]. ## @item 1: ## Normalizes with @math{N}, this provides the second moment around the mean. ## @end table ## ## The third argument @var{dim} determines the dimension along which the ## variance is calculated. ## ## @seealso{var, nanmean, nanstd, nanmax, nanmin} ## @end deftypefn function y = nanvar(x,w,dim) if nargin < 1 print_usage (); else if ((nargin < 2) || isempty(w)) w = 0; endif if nargin < 3 dim = min(find(size(x)>1)); if isempty(dim) dim=1; endif endif y = nanstd(x,w,dim).^2; endif endfunction ## Tests %!shared x %! x = [1 2 nan 3 4 5]; %!assert (nanvar (x), var (x(! isnan (x))), 10*eps) statistics-1.4.3/inst/nbinstat.m0000644000000000000000000000643014153320774015065 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} nbinstat (@var{n}, @var{p}) ## Compute mean and variance of the negative binomial distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{n} is the first parameter of the negative binomial distribution. The elements ## of @var{n} must be natural numbers ## ## @item ## @var{p} is the second parameter of the negative binomial distribution. The ## elements of @var{p} must be probabilities ## @end itemize ## @var{n} and @var{p} must be of common size or one of them must be scalar ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the negative binomial distribution ## ## @item ## @var{v} is the variance of the negative binomial distribution ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## n = 1:4; ## p = 0.2:0.2:0.8; ## [m, v] = nbinstat (n, p) ## @end group ## ## @group ## [m, v] = nbinstat (n, 0.5) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the negative binomial distribution function [m, v] = nbinstat (n, p) # Check arguments if (nargin != 2) print_usage (); endif if (! isempty (n) && ! ismatrix (n)) error ("nbinstat: n must be a numeric matrix"); endif if (! isempty (p) && ! ismatrix (p)) error ("nbinstat: p must be a numeric matrix"); endif if (! isscalar (n) || ! isscalar (p)) [retval, n, p] = common_size (n, p); if (retval > 0) error ("nbinstat: n and p must be of common size or scalar"); endif endif # Calculate moments q = 1 - p; m = n .* q ./ p; v = n .* q ./ (p .^ 2); # Continue argument check k = find (! (n > 0) | ! (n < Inf) | ! (p > 0) | ! (p < 1)); if (any (k)) m(k) = NaN; v(k) = NaN; endif endfunction %!test %! n = 1:4; %! p = 0.2:0.2:0.8; %! [m, v] = nbinstat (n, p); %! expected_m = [ 4.0000, 3.0000, 2.0000, 1.0000]; %! expected_v = [20.0000, 7.5000, 3.3333, 1.2500]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); %!test %! n = 1:4; %! [m, v] = nbinstat (n, 0.5); %! expected_m = [1, 2, 3, 4]; %! expected_v = [2, 4, 6, 8]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); statistics-1.4.3/inst/ncx2pdf.m0000644000000000000000000000323214153320774014604 0ustar0000000000000000## Copyright (C) 2018 gold holk ## ## This program is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} ncx2pdf (@var{X}, @var{N}, @var{LAMBDA}) ## @deftypefnx {Function File} ncx2pdf (@dots{}, @var{TERM}) ## compute the non-central chi square probalitity density function ## at @var{X} , degree of freedom @var{N} , ## and non-centrality parameter @var{LAMBDA} . ## ## @var{TERM} is the term number of series, default is 32. ## ## @end deftypefn ## Author: gold holk ## Created: 2018-10-25 function f = ncx2pdf(x, n, lambda, term = 32) f = exp(-lambda/2) * arrayfun(@(x) sum_expression([0:term],x,n,lambda), x); end function t = sum_expression(j,v,n,l) # j is vector, v is scalar. numerator = (l/2).^j .* v.^(n/2+j-1) * exp(-v/2); denominator = factorial(j) .* 2.^(n/2+j) .* gamma(n/2+j); t = sum(numerator ./ denominator); end %!assert (ncx2pdf (3, 4, 0), chi2pdf(3, 4), eps) %!assert (ncx2pdf (5, 3, 1), 0.091858459565020, 1E-15) #compared with Matlab's values %!assert (ncx2pdf (4, 5, 2), 0.109411958414115, 1E-15) statistics-1.4.3/inst/normalise_distribution.m0000644000000000000000000002142614153320774020035 0ustar0000000000000000## Copyright (C) 2011 Alexander Klein ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn{Function File} {@var{NORMALISED} =} normalise_distribution (@var{DATA}) ## @deftypefnx{Function File} {@var{NORMALISED} =} normalise_distribution (@var{DATA}, @var{DISTRIBUTION}) ## @deftypefnx{Function File} {@var{NORMALISED} =} normalise_distribution (@var{DATA}, @var{DISTRIBUTION}, @var{DIMENSION}) ## ## Transform a set of data so as to be N(0,1) distributed according to an idea ## by van Albada and Robinson. ## This is achieved by first passing it through its own cumulative distribution ## function (CDF) in order to get a uniform distribution, and then mapping ## the uniform to a normal distribution. ## The data must be passed as a vector or matrix in @var{DATA}. ## If the CDF is unknown, then [] can be passed in @var{DISTRIBUTION}, and in ## this case the empirical CDF will be used. ## Otherwise, if the CDFs for all data are known, they can be passed in ## @var{DISTRIBUTION}, ## either in the form of a single function name as a string, ## or a single function handle, ## or a cell array consisting of either all function names as strings, ## or all function handles. ## In the latter case, the number of CDFs passed must match the number ## of rows, or columns respectively, to normalise. ## If the data are passed as a matrix, then the transformation will ## operate either along the first non-singleton dimension, ## or along @var{DIMENSION} if present. ## ## Notes: ## The empirical CDF will map any two sets of data ## having the same size and their ties in the same places after sorting ## to some permutation of the same normalised data: ## @example ## @code{normalise_distribution([1 2 2 3 4])} ## @result{} -1.28 0.00 0.00 0.52 1.28 ## ## @code{normalise_distribution([1 10 100 10 1000])} ## @result{} -1.28 0.00 0.52 0.00 1.28 ## @end example ## ## Original source: ## S.J. van Albada, P.A. Robinson ## "Transformation of arbitrary distributions to the ## normal distribution with application to EEG ## test-retest reliability" ## Journal of Neuroscience Methods, Volume 161, Issue 2, ## 15 April 2007, Pages 205-211 ## ISSN 0165-0270, 10.1016/j.jneumeth.2006.11.004. ## (http://www.sciencedirect.com/science/article/pii/S0165027006005668) ## @end deftypefn function [ normalised ] = normalise_distribution ( data, distribution, dimension ) if ( nargin < 1 || nargin > 3 ) print_usage; elseif ( !ismatrix ( data ) || length ( size ( data ) ) > 2 ) error ( "First argument must be a vector or matrix" ); end if ( nargin >= 2 ) if ( !isempty ( distribution ) ) #Wrap a single handle in a cell array. if ( strcmp ( typeinfo ( distribution ), typeinfo ( @(x)(x) ) ) ) distribution = { distribution }; #Do we have a string argument instead? elseif ( ischar ( distribution ) ) ##Is it a single string? if ( rows ( distribution ) == 1 ) distribution = { str2func( distribution ) }; else error ( ["Second argument cannot contain more than one string" ... " unless in a cell array"] ); end ##Do we have a cell array of distributions instead? elseif ( iscell ( distribution ) ) ##Does it consist of strings only? if ( all ( cellfun ( @ischar, distribution ) ) ) distribution = cellfun ( @str2func, distribution, "UniformOutput", false ); end ##Does it eventually consist of function handles only if ( !all ( cellfun ( @ ( h ) ( strcmp ( typeinfo ( h ), typeinfo ( @(x)(x) ) ) ), distribution ) ) ) error ( ["Second argument must contain either" ... " a single function name or handle or " ... " a cell array of either all function names or handles!"] ); end else error ( "Illegal second argument: ", typeinfo ( distribution ) ); end end else distribution = []; end if ( nargin == 3 ) if ( !isscalar ( dimension ) || ( dimension != 1 && dimension != 2 ) ) error ( "Third argument must be either 1 or 2" ); end else if ( isvector ( data ) && rows ( data ) == 1 ) dimension = 2; else dimension = 1; end end trp = ( dimension == 2 ); if ( trp ) data = data'; end r = rows ( data ); c = columns ( data ); normalised = NA ( r, c ); ##Do we know the distribution of the sample? if ( isempty ( distribution ) ) precomputed_normalisation = []; for k = 1 : columns ( data ) ##Note that this line is in accordance with equation (16) in the ##original text. The author's original program, however, produces ##different values in the presence of ties, namely those you'd ##get replacing "last" by "first". [ uniq, indices ] = unique ( sort ( data ( :, k ) ), "last" ); ##Does the sample have ties? if ( rows ( uniq ) != r ) ##Transform to uniform, then normal distribution. uniform = ( indices - 1/2 ) / r; normal = norminv ( uniform ); else ## Without ties everything is pretty much straightforward as ## stated in the text. if ( isempty ( precomputed_normalisation ) ) precomputed_normalisation = norminv ( 1 / (2*r) : 1/r : 1 - 1 / (2*r) ); end normal = precomputed_normalisation; end #Find the original indices in the unsorted sample. #This somewhat quirky way of doing it is still faster than #using a for-loop. [ ignore, ignore, target_indices ] = unique ( data (:, k ) ); #Put normalised values in the places where they belong. f_remap = @( k ) ( normal ( k ) ); normalised ( :, k ) = arrayfun ( f_remap, target_indices ); end else ##With known distributions, everything boils down to a few lines of code ##The same distribution for all data? if ( all ( size ( distribution ) == 1 ) ) normalised = norminv ( distribution {1,1} ( data ) ); elseif ( length ( vec ( distribution ) ) == c ) for k = 1 : c normalised ( :, k ) = norminv ( distribution { k } ( data ) ( :, k ) ); end else error ( "Number of distributions does not match data size! ") end end if ( trp ) normalised = normalised'; end endfunction %!test %! v = normalise_distribution ( [ 1 2 3 ], [], 1 ); %! assert ( v, [ 0 0 0 ] ) %!test %! v = normalise_distribution ( [ 1 2 3 ], [], 2 ); %! assert ( v, norminv ( [ 1 3 5 ] / 6 ), 3 * eps ) %!test %! v = normalise_distribution ( [ 1 2 3 ]', [], 2 ); %! assert ( v, [ 0 0 0 ]' ) %!test %! v = normalise_distribution ( [ 1 2 3 ]' , [], 1 ); %! assert ( v, norminv ( [ 1 3 5 ]' / 6 ), 3 * eps ) %!test %! v = normalise_distribution ( [ 1 1 2 2 3 3 ], [], 2 ); %! assert ( v, norminv ( [ 3 3 7 7 11 11 ] / 12 ), 3 * eps ) %!test %! v = normalise_distribution ( [ 1 1 2 2 3 3 ]', [], 1 ); %! assert ( v, norminv ( [ 3 3 7 7 11 11 ]' / 12 ), 3 * eps ) %!test %! A = randn ( 10 ); %! N = normalise_distribution ( A, @normcdf ); %! assert ( A, N, 1000 * eps ) %!xtest %! A = exprnd ( 1, 100 ); %! N = normalise_distribution ( A, @ ( x ) ( expcdf ( x, 1 ) ) ); %! assert ( mean ( vec ( N ) ), 0, 0.1 ) %! assert ( std ( vec ( N ) ), 1, 0.1 ) %!xtest %! A = rand (1000,1); %! N = normalise_distribution ( A, "unifcdf" ); %! assert ( mean ( vec ( N ) ), 0, 0.1 ) %! assert ( std ( vec ( N ) ), 1, 0.1 ) %!xtest %! A = [rand(1000,1), randn( 1000, 1)]; %! N = normalise_distribution ( A, { "unifcdf", "normcdf" } ); %! assert ( mean ( N ), [ 0, 0 ], 0.1 ) %! assert ( std ( N ), [ 1, 1 ], 0.1 ) %!xtest %! A = [rand(1000,1), randn( 1000, 1), exprnd( 1, 1000, 1 )]'; %! N = normalise_distribution ( A, { @unifcdf; @normcdf; @( x )( expcdf ( x, 1 ) ) }, 2 ); %! assert ( mean ( N, 2 ), [ 0, 0, 0 ]', 0.1 ) %! assert ( std ( N, [], 2 ), [ 1, 1, 1 ]', 0.1 ) %!xtest %! A = exprnd ( 1, 1000, 9 ); A ( 300 : 500, 4:6 ) = 17; %! N = normalise_distribution ( A ); %! assert ( mean ( N ), [ 0 0 0 0.38 0.38 0.38 0 0 0 ], 0.1 ); %! assert ( var ( N ), [ 1 1 1 2.59 2.59 2.59 1 1 1 ], 0.1 ); %!test %! fail ("normalise_distribution( zeros ( 3, 4 ), { @unifcdf; @normcdf; @( x )( expcdf ( x, 1 ) ) } )", ... %! "Number of distributions does not match data size!"); statistics-1.4.3/inst/normplot.m0000644000000000000000000000435114153320774015115 0ustar0000000000000000## Author: Paul Kienzle ## This program is granted to the public domain. ## -*- texinfo -*- ## @deftypefn {Function File} normplot (@var{X}) ## Produce normal probability plot for each column of @var{X}. ## ## The line joing the 1st and 3rd quantile is drawn on the ## graph. If the underlying distribution is normal, the ## points will cluster around this line. ## ## Note that this function sets the title, xlabel, ylabel, ## axis, grid, tics and hold properties of the graph. These ## need to be cleared before subsequent graphs using 'clf'. ## @end deftypefn function normplot(X) if nargin!=1, print_usage; end if (rows(X) == 1), X=X(:); end # Transform data n = rows(X); if n<2, error("normplot requires a vector"); end q = norminv([1:n]'/(n+1)); Y = sort(X); # Find the line joining the first to the third quartile for each column q1 = ceil(n/4); q3 = n-q1+1; m = (q(q3)-q(q1))./(Y(q3,:)-Y(q1,:)); p = [ m; q(q1)-m.*Y(q1,:) ]; # Plot the lines one at a time. Plot the lines before overlaying the # normals so that the default label is 'line n'. if columns(Y)==1, leg = "+;;"; else leg = "%d+;Column %d;"; endif for i=1:columns(Y) plot(Y(:,i),q,sprintf(leg,i,i)); hold on; # estimate the mean and standard deviation by linear regression # [v,dv] = wpolyfit(q,Y(:,i),1) end # Overlay the estimated normal lines. for i=1:columns(Y) # Use the end points and one point guaranteed to be in the view since # gnuplot skips any lines whose points are all outside the view. pts = [Y(1,i);Y(q1,i);Y(end,i)]; plot(pts, polyval(p(:,i),pts), [num2str(i),";;"]); end hold off; # plot labels title "Normal Probability Plot" ylabel "% Probability" xlabel "Data" # plot grid t = [0.00001;0.0001;0.001;0.01;0.1;0.3;1;2;5;10;25;50; 75;90;95;98;99;99.7;99.9;99.99;99.999;99.9999;99.99999]; set(gca, "ytick", norminv(t/100), "yticklabel", num2str(t)); grid on # Set view range with a bit of space around data miny = min(Y(:)); minq = min(q(1),norminv(0.05)); maxy = max(Y(:)); maxq = max(q(end),norminv(0.95)); yspace = (maxy-miny)*0.05; qspace = (q(end)-q(1))*0.05; axis ([miny-yspace, maxy+yspace, minq-qspace, maxq+qspace]); end statistics-1.4.3/inst/normstat.m0000644000000000000000000000611114153320774015106 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mn}, @var{v}] =} normstat (@var{m}, @var{s}) ## Compute mean and variance of the normal distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{m} is the mean of the normal distribution ## ## @item ## @var{s} is the standard deviation of the normal distribution. ## @var{s} must be positive ## @end itemize ## @var{m} and @var{s} must be of common size or one of them must be ## scalar ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{mn} is the mean of the normal distribution ## ## @item ## @var{v} is the variance of the normal distribution ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## m = 1:6; ## s = 0:0.2:1; ## [mn, v] = normstat (m, s) ## @end group ## ## @group ## [mn, v] = normstat (0, s) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the normal distribution function [mn, v] = normstat (m, s) # Check arguments if (nargin != 2) print_usage (); endif if (! isempty (m) && ! ismatrix (m)) error ("normstat: m must be a numeric matrix"); endif if (! isempty (s) && ! ismatrix (s)) error ("normstat: s must be a numeric matrix"); endif if (! isscalar (m) || ! isscalar (s)) [retval, m, s] = common_size (m, s); if (retval > 0) error ("normstat: m and s must be of common size or scalar"); endif endif # Set moments mn = m; v = s .* s; # Continue argument check k = find (! (s > 0) | ! (s < Inf)); if (any (k)) mn(k) = NaN; v(k) = NaN; endif endfunction %!test %! m = 1:6; %! s = 0.2:0.2:1.2; %! [mn, v] = normstat (m, s); %! expected_v = [0.0400, 0.1600, 0.3600, 0.6400, 1.0000, 1.4400]; %! assert (mn, m); %! assert (v, expected_v, 0.001); %!test %! s = 0.2:0.2:1.2; %! [mn, v] = normstat (0, s); %! expected_mn = [0, 0, 0, 0, 0, 0]; %! expected_v = [0.0400, 0.1600, 0.3600, 0.6400, 1.0000, 1.4400]; %! assert (mn, expected_mn, 0.001); %! assert (v, expected_v, 0.001); statistics-1.4.3/inst/optimalleaforder.m0000644000000000000000000002325714153320774016602 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {@var{leafOrder} =} optimalleaforder (@var{tree}, @var{D}) ## @deftypefnx {Function File} @ ## {@var{leafOrder} =} optimalleaforder (..., @var{Name}, @var{Value}) ## ## Compute the optimal leaf ordering of a hierarchical binary cluster tree. ## ## The optimal leaf ordering of a tree is the ordering which minimizes the sum ## of the distances between each leaf and its adjacent leaves, without altering ## the structure of the tree, that is without redefining the clusters of the ## tree. ## ## Required inputs: ## @itemize ## @item ## @var{tree}: a hierarchical cluster tree @var{tree} generated by the ## @code{linkage} function. ## ## @item ## @var{D}: a matrix of distances as computed by @code{pdist}. ## @end itemize ## ## Optional inputs can be the following property/value pairs: ## @itemize ## @item ## property 'Criteria' at the moment can only have the value 'adjacent', ## for minimizing the distances between leaves. ## ## @item ## property 'Transformation' can have one of the values 'linear', 'inverse' ## or a handle to a custom function which computes @var{S} the similarity ## matrix. ## @end itemize ## ## optimalleaforder's output @var{leafOrder} is the optimal leaf ordering. ## ## @strong{Reference} ## Bar-Joseph, Z., Gifford, D.K., and Jaakkola, T.S. Fast optimal leaf ordering ## for hierarchical clustering. Bioinformatics vol. 17 suppl. 1, 2001. ## @end deftypefn ## ## @seealso{dendrogram,linkage,pdist} function leafOrder = optimalleaforder ( varargin ) ## check the input if ( nargin < 2 ) print_usage (); endif tree = varargin{1}; D = varargin{2}; criterion = "adjacent"; # default and only value at the moment transformation = "linear"; if ((columns (tree) != 3) || (! isnumeric (tree)) || ... (! (max (tree(end, 1:2)) == rows (tree) * 2))) error (["optimalleaforder: tree must be a matrix as generated by the " ... "linkage function"]); endif ## read the paired arguments if (! all (cellfun ("ischar", varargin(3:end)))) error ("optimalleaforder: character inputs expected for arguments 3 and up"); else varargin(3:end) = lower (varargin(3:end)); endif pair_index = 3; while (pair_index <= (nargin - 1)) switch (varargin{pair_index}) case "criteria" criterion = varargin{pair_index + 1}; if (strcmp (criterion, "group")) ## MATLAB compatibility: ## the 'group' criterion is not implemented error ("optimalleaforder: unavailable criterion 'group'"); elseif (! strcmp (criterion, "adjacent")) error ("optimalleaforder: invalid criterion %s", criterion); endif case "transformation" transformation = varargin{pair_index + 1}; otherwise error ("optimalleaforder: unknown property %s", varargin{pair_index}); endswitch pair_index += 2; endwhile ## D can be either a vector or a matrix, ## but it is easier to work with a matrix if (isvector (D)) D = squareform (D); endif n = rows (D); m = rows (tree); if (n != (m + 1)) error (["optimalleaforder: D must be a matrix or vector generated by " ... "the pdist function"]); endif ## the similarity matrix, basically an inverted distance matrix S = zeros (n); if (strcmpi (transformation, "linear")) ## linear similarity maxD = max (max (D)); S = maxD - D; elseif (strcmpi (transformation, "inverse")) ## similarity as inverted distance S = 1 ./ D; elseif (is_function_handle (transformation)) ## custom similarity S = feval (transformation, D); else error ("optimalleaforder: invalid transformation %s", transformation); endif ## main body ## for each node v we compute the maximum similarity of the subtree M(w,u,v), ## where the leftmost leaf is w and the rightmost is u; remember that ## M(w,u,v) = M(u,w,v) M = zeros (n, n, n + m); ## O is a utility matrix: for each node of the tree we store the left and ## right leaves of the optimal subtree O = [1:( n + m ); 1:( n + m ); (zeros (1, (n + m)))]'; ## compute M for every node v for iter = 1 : m v = iter + n; # current node l = optimalleaforder_getLeafList (tree(iter, 1)); # the left subtree r = optimalleaforder_getLeafList (tree(iter, 2)); # the right subtree if (tree(iter,1) > n) l_l = optimalleaforder_getLeafList (tree(tree(iter, 1) - n, 1)); l_r = optimalleaforder_getLeafList (tree(tree(iter, 1) - n, 2)); else l_l = l_r = l; endif if (tree(iter,2) > n) r_l = optimalleaforder_getLeafList (tree(tree(iter, 2) - n, 1)); r_r = optimalleaforder_getLeafList (tree(tree(iter, 2) - n, 2)); else r_l = r_r = r; endif ## let's find the maximum value of M(w,u,v) when: w is a leaf of the left ## subtree of v and u is a leaf of the right subtree of v for i = 1 : length (l) if (isempty (find (l(i) == l_l))) x = l_l; else x = l_r; endif for j = 1 : length (r) if (isempty (find (r(j) == r_l))) y = r_l; else y = r_r; endif ## max(M(w,u,v)) = max(M(w,k,v_l)) + max(M(h,u,v_r)) + S(k,h) ## where: v_l is the left child of v and v_r the right child of v M_tmp = repmat (M(l(i), x(:), tree(iter, 1)), length (y), 1) + ... repmat (M(y(:), r(j), tree(iter, 2)), 1, length (x)) + ... S(y(:), x(:)); M_max = max (max (M_tmp)); # this is M(l(i), r(j), v) [h, k] = find (M_tmp == M_max); M(l(i), r(j), v) = M_max; M(r(j), l(i), v) = M(l(i), r(j), v); if (M_max > O(v,3)) O(v, 1) = l(i); # this is w O(v, 2) = r(j); # this is u O(v, 3) = M_max; # this is M(w, u, v) endif endfor endfor endfor ## reordering: ## we found the M(w,u,v) corresponding to the optimal leaf order, now we can ## compute the optimal leaf order given our M(w,u,v) ## the return value leafOrder = zeros ( 1, n ); leafOrder(1) = O(end, 1); leafOrder(n) = O(end, 2); ## the inverse operation, only easier, to get the leaf order: now we know the ## leftmost and rightmost leaves of the best subtree, we may have to flip it ## though for iter = m : -1 : 1 v = iter + n; extremes = O(v, [1, 2]); l_node = tree(iter, 1); r_node = tree(iter, 2); l = optimalleaforder_getLeafList (l_node); r = optimalleaforder_getLeafList (r_node); if (l_node > n) l_l = optimalleaforder_getLeafList (tree(l_node - n, 1)); l_r = optimalleaforder_getLeafList (tree(l_node - n, 2)); else l_l = l_r = l; endif if (r_node > n) r_l = optimalleaforder_getLeafList (tree(r_node - n, 1)); r_r = optimalleaforder_getLeafList (tree(r_node - n, 2)); else r_l = r_r = r; endif ## this means that we need to flip the subtree if (isempty (find (extremes(1) == l))) l_tmp = l; l_l_tmp = l_l; l_r_tmp = l_r; l = r; l_l = r_l; l_r = r_r; r = l_tmp; r_l = l_l_tmp; r_r = l_r_tmp; node_tmp = l_node; l_node = r_node; r_node = node_tmp; endif if (isempty (find (extremes(1) == l_l))) x = l_l; else x = l_r; endif if (isempty (find (extremes(2) == r_l))) y = r_l; else y = r_r; endif M_tmp = repmat (M(extremes(1), x(:), l_node), length (y), 1) + ... repmat (M(y(:), extremes(2), r_node), 1, length (x)) + ... S(y(:), x(:)); M_max = max (max (M_tmp)); [h, k] = find (M_tmp == M_max); O(l_node, 1) = extremes(1); O(l_node, 2) = x(k); O(r_node, 1) = y(h); O(r_node, 2) = extremes(2); p_1 = find (leafOrder == extremes(1)); p_2 = find (leafOrder == extremes(2)); leafOrder (p_1 + (length (l)) - 1) = x(k); leafOrder (p_1 + (length (l))) = y(h); endfor ## function: optimalleaforder_getLeafList ## get the list of leaves under a given node function vector = optimalleaforder_getLeafList (nodes_to_visit) vector = []; while (! isempty (nodes_to_visit)) currentnode = nodes_to_visit(1); nodes_to_visit(1) = []; if (currentnode > n) node = currentnode - n; nodes_to_visit = [tree(node, [2 1]) nodes_to_visit]; endif if (currentnode <= n) vector = [vector currentnode]; endif endwhile endfunction endfunction ## Test input validation %!error optimalleaforder () %!error optimalleaforder (1) %!error optimalleaforder (ones (2, 2), 1) %!error optimalleaforder ([1 2 3], [1 2; 3 4], "criteria", 5) %!error optimalleaforder ([1 2 1], [1 2 3]) %!error optimalleaforder ([1 2 1], 1, "xxx", "xxx") %!error optimalleaforder ([1 2 1], 1, "Transformation", "xxx") ## Demonstration %!demo %! X = randn (10, 2); %! D = pdist (X); %! tree = linkage(D, 'average'); %! optimalleaforder (tree, D, 'Transformation', 'linear') statistics-1.4.3/inst/pca.m0000644000000000000000000004564114153320774014015 0ustar0000000000000000## Copyright (C) 2013-2019 Fernando Damian Nieuwveldt ## Copyright (C) 2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or ## modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 ## of the License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{coeff}]} = pca(@var{X}) ## @deftypefnx {Function File} {[@var{coeff}]} = pca(@var{X}, Name, Value) ## @deftypefnx {Function File} {[@var{coeff},@var{score},@var{latent}]} = pca(@dots{}) ## @deftypefnx {Function File} {[@var{coeff},@var{score},@var{latent},@var{tsquared}]} = pca(@dots{}) ## @deftypefnx {Function File} {[@var{coeff},@var{score},@var{latent},@var{tsquared},@var{explained},@var{mu}]} = pca(@dots{}) ## Performs a principal component analysis on a data matrix X ## ## A principal component analysis of a data matrix of @code{n} observations in a ## @code{p}-dimensional space returns a @code{p}-by-@code{p} transformation ## matrix, to perform a change of basis on the data. The first component of the ## new basis is the direction that maximizes the variance of the projected data. ## ## Input argument: ## @itemize @bullet ## @item ## @var{x} : a @code{n}-by-@code{p} data matrix ## @end itemize ## ## Pair arguments: ## @itemize @bullet ## @item ## @code{Algorithm} : the algorithm to use, it can be either @code{eig}, ## for eigenvalue decomposition, or @code{svd} (default), for singular value ## decomposition ## @item ## @code{Centered} : boolean indicator for centering the observation data, it is ## @code{true} by default ## @item ## @code{Economy} : boolean indicator for the economy size output, it is ## @code{true} by default; @code{pca} returns only the elements of @var{latent} ## that are not necessarily zero, and the corresponding columns of @var{coeff} ## and @var{score}, that is, when @code{n <= p}, only the first @code{n - 1} ## @item ## @code{NumComponents} : the number of components @code{k} to return, if ## @code{k < p}, then only the first @code{k} columns of @var{coeff} ## and @var{score} are returned ## @item ## @code{Rows} : action to take with missing values, it can be either ## @code{complete} (default), missing values are removed before computation, ## @code{pairwise} (only with algorithm @code{eig}), the covariance of rows with ## missing data is computed using the available data, but the covariance matrix ## could be not positive definite, which triggers the termination of @code{pca}, ## @code{complete}, missing values are not allowed, @code{pca} terminates with ## an error if there are any ## @item ## @code{Weights} : observation weights, it is a vector of positive values of ## length @code{n} ## @item ## @code{VariableWeights} : variable weights, it can be either a vector of ## positive values of length @code{p} or the string @code{variance} to use the ## sample variance as weights ## @end itemize ## ## Return values: ## @itemize @bullet ## @item ## @var{coeff} : the principal component coefficients, a @code{p}-by-@code{p} ## transformation matrix ## @item ## @var{score} : the principal component scores, the representation of @var{x} ## in the principal component space ## @item ## @var{latent} : the principal component variances, i.e., the eigenvalues of ## the covariance matrix of @var{x} ## @item ## @var{tsquared} : Hotelling's T-squared Statistic for each observation in ## @var{x} ## @item ## @var{explained} : the percentage of the variance explained by each principal ## component ## @item ## @var{mu} : the estimated mean of each variable of @var{x}, it is zero if the ## data are not centered ## @end itemize ## ## Matlab compatibility note: the alternating least square method 'als' and ## associated options 'Coeff0', 'Score0', and 'Options' are not yet implemented ## ## @subheading References ## ## @enumerate ## @item ## Jolliffe, I. T., Principal Component Analysis, 2nd Edition, Springer, 2002 ## ## @end enumerate ## @end deftypefn ## BUGS: ## - tsquared with weights (xtest below) ##FIXME ## -- can change isnan to ismissing once the latter is implemented in Octave ## -- change mystd to std and remove the helper function mystd once weighting is available in the Octave function function [coeff, score, latent, tsquared, explained, mu] = pca (X, varargin) if (nargin < 1) print_usage (); endif [nobs, nvars] = size (X); ## default options optAlgorithmS = "svd"; optCenteredB = true; optEconomyB = true; optNumComponentsI = nvars; optWeights = []; optVariableWeights = []; optRowsB = false; TF = []; ## parse parameters pair_index = 1; while (pair_index <= (nargin - 1)) switch (lower (varargin{pair_index})) ## decomposition algorithm: singular value decomposition, eigenvalue ## decomposition or (currently unavailable) alternating least square case "algorithm" optAlgorithmS = varargin{pair_index + 1}; switch (optAlgorithmS) case {"svd", "eig"} ; case "als" error ("pca: alternating least square algorithm not implemented"); otherwise error ("pca: invalid algorithm %s", optAlgorithmS); endswitch ## centering of the columns, around the mean case "centered" if (isbool (varargin{pair_index + 1})) optCenteredB = varargin{pair_index + 1}; else error ("pca: 'centered' requires a boolean value"); endif ## limit the size of the output to the degrees of freedom, when a smaller ## number than the number of variables case "economy" if (isbool (varargin{pair_index + 1})) optEconomyB = varargin{pair_index + 1}; else error ("pca: 'economy' requires a boolean value"); endif ## choose the number of components to show case "numcomponents" optNumComponentsI = varargin{pair_index + 1}; if ((! isscalar (optNumComponentsI)) || (! isnumeric (optNumComponentsI)) || optNumComponentsI != floor (optNumComponentsI) || optNumComponentsI <= 0 || optNumComponentsI > nvars) error (["pca: the number of components must be a positive integer"... "number smaller or equal to the number of variables"]); endif ## observation weights: some observations can be more accurate than others case "weights" optWeights = varargin{pair_index + 1}; if ((! isvector (optWeights)) || length (optWeights) != nobs || length (find (optWeights < 0)) > 0) error ("pca: weights must be a numerical array of positive numbers"); endif if (rows (optWeights) == 1 ) optWeights = transpose (optWeights); endif ## variable weights: weights used for the variables case "variableweights" optVariableWeights = varargin{pair_index + 1}; if (ischar (optVariableWeights) && strcmpi (optVariableWeights, "variance")) optVariableWeights = "variance"; # take care of this later elseif ((! isvector (optVariableWeights)) || length (optVariableWeights) != nvars || (! isnumeric (optVariableWeights)) || length (find (optVariableWeights < 0)) > 0) error (["pca: variable weights must be a numerical array of "... "positive numbers or the string 'variance'"]); else optVariableWeights = 1 ./ sqrt (optVariableWeights); ## it is used as a row vector if (columns (optVariableWeights) == 1 ) optVariableWeights = transpose (optVariableWeights); endif endif ## rows: policy for missing values case "rows" switch (varargin{pair_index + 1}) case "complete" optRowsB = false; case "pairwise" optRowsB = true; case "all" if (any (isnan (X))) error (["pca: when all rows are requested the dataset cannot"... " include NaN values"]); endif otherwise error ("pca: %s is an invalid value for rows", ... varargin{pair_index + 1}); endswitch case {"coeff0", "score0", "options"} error ("pca: parameter %s is only valid with the 'als' method, which is not yet implemented", varargin{pair_index}); otherwise error ("pca: unknown property %s", varargin{pair_index}); endswitch pair_index += 2; endwhile ## Preparing the dataset according to the chosen policy for missing values if (optRowsB) if (! strcmp (optAlgorithmS, "eig")) optAlgorithmS = "eig"; warning (["pca: setting algorithm to 'eig' because 'rows' option is "... "set to 'pairwise'"]); endif TF = isnan (X); missingRows = zeros (nobs, 1); nmissing = 0; else ## "complete": remove all the rows with missing values TF = isnan (X); missingRows = any (TF, 2); nmissing = sum (missingRows); endif ## indices of the available rows ridcs = find (missingRows == 0); ## Center the columns to mean zero if requested if (optCenteredB) if (isempty (optWeights) && nmissing == 0 && ! optRowsB) ## no weights and no missing values mu = mean (X); elseif (nmissing == 0 && ! optRowsB) ## weighted observations: some observations are more valuable, i.e. they ## can be trusted more mu = sum (optWeights .* X) ./ sum (optWeights); else ## missing values: the mean is computed column by column mu = zeros (1, nvars); if (isempty (optWeights)) for iter = 1 : nvars mu(iter) = mean (X(find (TF(:, iter) == 0), iter)); endfor else ## weighted mean with missing data for iter = 1 : nvars mu(iter) = sum (X(find (TF(:, iter) == 0), iter) .* ... optWeights(find (TF(:, iter) == 0))) ./ ... sum (optWeights(find (TF(:, iter) == 0))); endfor endif endif Xc = X - mu; else Xc = X; ## The mean of the variables of the original dataset: ## return zero if the dataset is not centered mu = zeros (1, nvars); endif ## Change the columns according to the variable weights if (! isempty (optVariableWeights)) if (ischar (optVariableWeights)) if (isempty (optWeights)) sqrtBias = 1; # see below optVariableWeights = std (X); else ## unbiased variance estimation: the bias when using reliability weights ## is 1 - var(weights) / std(weigths)^2 sqrtBias = sqrt (1 - (sumsq (optWeights) / sum (optWeights) ^ 2)); optVariableWeights = mystd (X, optWeights) / sqrtBias; endif endif Xc = Xc ./ optVariableWeights; endif ## Compute the observation weight matrix if (isempty (optWeights)) Wd = eye (nobs - nmissing); else Wd = diag (optWeights) ./ sum (optWeights); endif ## Compute the coefficients switch (optAlgorithmS) case "svd" ## Check if there are more variables than observations if (nvars <= nobs) [U, S, coeff] = svd (sqrt (Wd) * Xc(ridcs,:), "econ"); else ## Calculate the svd on the transpose matrix, much faster if (optEconomyB) [coeff, S, V] = svd (Xc(ridcs,:)' * sqrt (Wd), "econ"); else [coeff, S, V] = svd (Xc(ridcs,:)' * sqrt (Wd)); endif endif case "eig" ## this method requires the computation of the sample covariance matrix if (optRowsB) ## pairwise: ## in this case the degrees of freedom for each element of the matrix ## are equal to the number of valid rows for the couple of columns ## used to compute the element Xpairwise = Xc; Xpairwise(find (isnan (Xc))) = 0; Ndegrees = (nobs - 1) * ones (nvars, nvars); for i_iter = 1 : nvars for j_iter = i_iter : nvars Ndegrees(i_iter, j_iter) = Ndegrees(i_iter, j_iter) - ... sum (any (TF(:,[i_iter j_iter]), 2)); Ndegrees(j_iter, i_iter) = Ndegrees(i_iter, j_iter); endfor endfor Mcov = Xpairwise' * Wd * Xpairwise ./ Ndegrees; else ## the degrees of freedom are not really important here ndegrees = nobs - nmissing - 1; Mcov = Xc(ridcs, :)' * Wd * Xc(ridcs, :) / ndegrees; endif [coeff, S] = eigs (Mcov, nvars); endswitch ## Change the coefficients according to the variable weights if (! isempty (optVariableWeights)) coeff = coeff .* transpose (optVariableWeights); endif ## MATLAB compatibility: the sign convention is that the ## greatest absolute value for each column is positive switchSignV = find (max (coeff) < abs (min (coeff))); if (! isempty (switchSignV)) coeff(:, switchSignV) = -1 * coeff(:, switchSignV); endif ## Compute the scores if (nargout > 1) ## This is for the score when using variable weights, it is not really ## a new definition of Xc if (! isempty (optVariableWeights)) Xc = Xc ./ optVariableWeights; endif ## Get the Scores score = Xc(ridcs,:) * coeff; ## Get the rank of the score matrix r = rank (score); ## If there is missing data, put it back ## FIXME: this needs tests if (nmissing) scoretmp = zeros (nobs, nvars); scoretmp(find (missingRows == 0), :) = score; scoretmp(find (missingRows), :) = NaN; score = scoretmp; endif ## Only use the first r columns, pad rest with zeros if economy != true score = score(:, 1:r) ; if (! optEconomyB) score = [score, (zeros (nobs , nvars-r))]; else coeff = coeff(: , 1:r); endif endif ## Compute the variances if (nargout > 2) ## degrees of freedom: n - 1 for centered data if (optCenteredB) dof = size (Xc(ridcs,:), 1) - 1; else dof = size (Xc(ridcs,:), 1); endif ## This is the same as the eigenvalues of the covariance matrix of X if (strcmp (optAlgorithmS, "eig")) latent = diag (S, 0); else latent = (diag (S'*S) / dof)(1:r); endif ## If observation weights were used, we need to scale back these values if (! isempty (optWeights)) latent = latent .* sum (optWeights(ridcs)); endif if (! optEconomyB) latent= [latent; (zeros (nvars - r, 1))]; endif endif ## Compute the Hotelling T-square statistics ## MATLAB compatibility: when using weighted observations the T-square ## statistics differ by some rounding error if (nargout > 3) ## Calculate the Hotelling T-Square statistic for the observations ## formally: tsquared = sumsq (zscore (score(:, 1:r)),2); if (! isempty (optWeights)) ## probably splitting the weights, using the square roots, is not the ## best solution, numerically weightedScore = score .* sqrt (optWeights); tsquared = mahal (weightedScore(ridcs, 1:r), weightedScore(ridcs, 1:r))... ./ optWeights; else tsquared = mahal (score(ridcs, 1:r), score(ridcs, 1:r)); endif endif ## Compute the variance explained by each principal component if (nargout > 4) explained = 100 * latent / sum (latent); endif ## When a number of components is chosen, the coefficients and score matrix ## only show that number of columns if (optNumComponentsI != nvars) coeff = coeff(:, 1:optNumComponentsI); score = score(:, 1:optNumComponentsI); endif endfunction #return the weighted standard deviation function retval = mystd (x, w) (dim = find (size(x) != 1, 1)) || (dim = 1); den = sum (w); mu = sum (w .* x, dim) ./ sum (w); retval = sum (w .* ((x - mu) .^ 2), dim) / den; retval = sqrt (retval); endfunction %!shared COEFF,SCORE,latent,tsquare,m,x,R,V,lambda,i,S,F #NIST Engineering Statistics Handbook example (6.5.5.2) %!test %! x=[7 4 3 %! 4 1 8 %! 6 3 5 %! 8 6 1 %! 8 5 7 %! 7 2 9 %! 5 3 3 %! 9 5 8 %! 7 4 5 %! 8 2 2]; %! R = corrcoef (x); %! [V, lambda] = eig (R); %! [~, i] = sort(diag(lambda), "descend"); #arrange largest PC first %! S = V(:, i) * diag(sqrt(diag(lambda)(i))); %!assert(diag(S(:, 1:2)*S(:, 1:2)'), [0.8662; 0.8420; 0.9876], 1E-4); #contribution of first 2 PCs to each original variable %! B = V(:, i) * diag( 1./ sqrt(diag(lambda)(i))); %! F = zscore(x)*B; %! [COEFF,SCORE,latent,tsquare] = pca(zscore(x, 1)); %!assert(tsquare,sumsq(F, 2),1E4*eps); %!test %! x=[1,2,3;2,1,3]'; %! [COEFF,SCORE,latent,tsquare] = pca(x, "Economy", false); %! m=[sqrt(2),sqrt(2);sqrt(2),-sqrt(2);-2*sqrt(2),0]/2; %! m(:,1) = m(:,1)*sign(COEFF(1,1)); %! m(:,2) = m(:,2)*sign(COEFF(1,2)); %!assert(COEFF,m(1:2,:),10*eps); %!assert(SCORE,-m,10*eps); %!assert(latent,[1.5;.5],10*eps); %!assert(tsquare,[4;4;4]/3,10*eps); #test with observation weights (using Matlab's results for this case as a reference) %! [COEFF,SCORE,latent,tsquare] = pca(x, "Economy", false, "weights", [1 2 1], "variableweights", "variance"); %!assert(COEFF, [0.632455532033676 -0.632455532033676; 0.741619848709566 0.741619848709566], 10*eps); %!assert(SCORE, [-0.622019449426284 0.959119380657905; -0.505649896847432 -0.505649896847431; 1.633319243121148 0.052180413036957], 10*eps); %!assert(latent, [1.783001790889027; 0.716998209110974], 10*eps); %!xtest assert(tsquare, [1.5; 0.5; 1.5], 10*eps); #currently, [4; 2; 4]/3 is actually returned; see comments above %!test %! x=x'; %! [COEFF,SCORE,latent,tsquare] = pca(x, "Economy", false); %! m=[sqrt(2),sqrt(2),0;-sqrt(2),sqrt(2),0;0,0,2]/2; %! m(:,1) = m(:,1)*sign(COEFF(1,1)); %! m(:,2) = m(:,2)*sign(COEFF(1,2)); %! m(:,3) = m(:,3)*sign(COEFF(3,3)); %!assert(COEFF,m,10*eps); %!assert(SCORE(:,1),-m(1:2,1),10*eps); %!assert(SCORE(:,2:3),zeros(2),10*eps); %!assert(latent,[1;0;0],10*eps); %!assert(tsquare,[0.5;0.5],10*eps) %!test %! [COEFF,SCORE,latent,tsquare] = pca(x); %!assert(COEFF,m(:, 1),10*eps); %!assert(SCORE,-m(1:2,1),10*eps); %!assert(latent,[1],10*eps); %!assert(tsquare,[0.5;0.5],10*eps) %!error pca([1 2; 3 4], "Algorithm", "xxx") %!error <'centered' requires a boolean value> pca([1 2; 3 4], "Centered", "xxx") %!error pca([1 2; 3 4], "NumComponents", -4) %!error pca([1 2; 3 4], "Rows", 1) %!error pca([1 2; 3 4], "Weights", [1 2 3]) %!error pca([1 2; 3 4], "Weights", [-1 2]) %!error pca([1 2; 3 4], "VariableWeights", [-1 2]) %!error pca([1 2; 3 4], "VariableWeights", "xxx") %!error pca([1 2; 3 4], "XXX", 1) statistics-1.4.3/inst/pcacov.m0000644000000000000000000000453514153320774014522 0ustar0000000000000000## Copyright (C) 2013-2019 Fernando Damian Nieuwveldt ## ## This program is free software; you can redistribute it and/or ## modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 ## of the License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{COEFF}]} = pcacov(@var{X}) ## @deftypefnx {Function File} {[@var{COEFF},@var{latent}]} = pcacov(@var{X}) ## @deftypefnx {Function File} {[@var{COEFF},@var{latent},@var{explained}]} = pcacov(@var{X}) ## Perform principal component analysis on the nxn covariance matrix X ## ## @itemize @bullet ## @item ## @var{COEFF} : a nxn matrix with columns containing the principal component coefficients ## @item ## @var{latent} : a vector containing the principal component variances ## @item ## @var{explained} : a vector containing the percentage of the total variance explained by each principal component ## ## @end itemize ## ## @subheading References ## ## @enumerate ## @item ## Jolliffe, I. T., Principal Component Analysis, 2nd Edition, Springer, 2002 ## ## @end enumerate ## @end deftypefn ## Author: Fernando Damian Nieuwveldt ## Description: Principal Components Analysis using a covariance matrix function [COEFF, latent, explained] = pcacov(X) [U,S,V] = svd(X); if nargout == 1 COEFF = U; elseif nargout == 2 COEFF = U; latent = diag(S); else COEFF = U; latent = diag(S); explained = 100*latent./sum(latent); end endfunction %!demo %! X = [ 7 26 6 60; %! 1 29 15 52; %! 11 56 8 20; %! 11 31 8 47; %! 7 52 6 33; %! 11 55 9 22; %! 3 71 17 6; %! 1 31 22 44; %! 2 54 18 22; %! 21 47 4 26; %! 1 40 23 34; %! 11 66 9 12; %! 10 68 8 12 %! ]; %! covx = cov(X); %! [COEFF,latent,explained] = pcacov(covx) statistics-1.4.3/inst/pcares.m0000644000000000000000000000530714153320774014522 0ustar0000000000000000## Copyright (C) 2013-2019 Fernando Damian Nieuwveldt ## ## This program is free software; you can redistribute it and/or ## modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 ## of the License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{residuals},@var{reconstructed}]}=pcares(@var{X}, @var{NDIM}) ## Calulate residuals from principal component analysis ## ## @itemize @bullet ## @item ## @var{X} : N x P Matrix with N observations and P variables, the variables will be mean centered ## @item ## @var{ndim} : Is a scalar indicating the number of principal components to use and should be <= P ## @end itemize ## ## @subheading References ## ## @enumerate ## @item ## Jolliffe, I. T., Principal Component Analysis, 2nd Edition, Springer, 2002 ## ## @end enumerate ## @end deftypefn ## Author: Fernando Damian Nieuwveldt ## Description: Residuals from Principal Components Analysis function [residuals,reconstructed] = pcares(X,NDIM) if (nargin ~= 2) error('pcares takes two inputs: The data Matrix X and number of principal components NDIM') endif # Mean center data Xcentered = bsxfun(@minus,X,mean(X)); # Apply svd to get the principal component coefficients [U,S,V] = svd(Xcentered); # Use only the first ndim PCA components v = V(:,1:NDIM); if (nargout == 2) # Calculate the residuals residuals = Xcentered - Xcentered * (v*v'); # Reconstructed data using ndim PCA components reconstructed = X - residuals; else # Calculate the residuals residuals = Xcentered - Xcentered * (v*v'); endif endfunction %!demo %! X = [ 7 26 6 60; %! 1 29 15 52; %! 11 56 8 20; %! 11 31 8 47; %! 7 52 6 33; %! 11 55 9 22; %! 3 71 17 6; %! 1 31 22 44; %! 2 54 18 22; %! 21 47 4 26; %! 1 40 23 34; %! 11 66 9 12; %! 10 68 8 12 %! ]; %! # As we increase the number of principal components, the norm %! # of the residuals matrix will decrease %! r1 = pcares(X,1); %! n1 = norm(r1) %! r2 = pcares(X,2); %! n2 = norm(r2) %! r3 = pcares(X,3); %! n3 = norm(r3) %! r4 = pcares(X,4); %! n4 = norm(r4) statistics-1.4.3/inst/pdf.m0000644000000000000000000001005414153320774014011 0ustar0000000000000000## Copyright (C) 2016 Andreas Stahel ## strongly based on cdf.m by 2013 Pantxo Diribarne ## ## This program is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} pdf (@var{name}, @var{X}, @dots{}) ## Return probability density function of @var{name} function for value ## @var{x}. ## This is a wrapper around various @var{name}pdf and @var{name}_pdf ## functions. See the individual functions help to learn the signification of ## the arguments after @var{x}. Supported functions and corresponding number of ## additional arguments are: ## ## @multitable @columnfractions 0.02 0.3 0.45 0.2 ## @headitem @tab function @tab alternative @tab args ## @item @tab "beta" @tab "beta" @tab 2 ## @item @tab "bino" @tab "binomial" @tab 2 ## @item @tab "cauchy" @tab @tab 2 ## @item @tab "chi2" @tab "chisquare" @tab 1 ## @item @tab "discrete" @tab @tab 2 ## @item @tab "exp" @tab "exponential" @tab 1 ## @item @tab "f" @tab @tab 2 ## @item @tab "gam" @tab "gamma" @tab 2 ## @item @tab "geo" @tab "geometric" @tab 1 ## @item @tab "gev" @tab "generalized extreme value" @tab 3 ## @item @tab "hyge" @tab "hypergeometric" @tab 3 ## @item @tab "kolmogorov_smirnov" @tab @tab 1 ## @item @tab "laplace" @tab @tab 2 ## @item @tab "logistic" @tab @tab 0 ## @item @tab "logn" @tab "lognormal" @tab 2 ## @item @tab "norm" @tab "normal" @tab 2 ## @item @tab "poiss" @tab "poisson" @tab 1 ## @item @tab "rayl" @tab "rayleigh" @tab 1 ## @item @tab "t" @tab @tab 1 ## @item @tab "unif" @tab "uniform" @tab 2 ## @item @tab "wbl" @tab "weibull" @tab 2 ## @end multitable ## ## @seealso{betapdf, binopdf, cauchy_pdf, chi2pdf, discrete_pdf, ## exppdf, fpdf, gampdf, geopdf, gevpdf, hygepdf, laplace_pdf, ## logistic_pdf, lognpdf, normpdf, poisspdf, raylpdf, tpdf, ## unifpdf, wblpdf} ## @end deftypefn function [retval] = pdf (varargin) ## implemented functions persistent allpdf = {{"beta", "beta"}, @betapdf, 2, ... {"bino", "binomial"}, @binopdf, 2, ... {"cauchy"}, @cauchy_pdf, 2, ... {"chi2", "chisquare"}, @chi2pdf, 1, ... {"discrete"}, @discrete_pdf, 2, ... {"exp", "exponential"}, @exppdf, 1, ... {"f"}, @fpdf, 2, ... {"gam", "gamma"}, @gampdf, 2, ... {"geo", "geometric"}, @geopdf, 1, ... {"gev", "generalized extreme value"}, @gevpdf, 3, ... {"hyge", "hypergeometric"}, @hygepdf, 3, ... {"laplace"}, @laplace_pdf, 1, ... {"logistic"}, @logistic_pdf, 0, ... # ML has 2 args here {"logn", "lognormal"}, @lognpdf, 2, ... {"norm", "normal"}, @normpdf, 2, ... {"poiss", "poisson"}, @poisspdf, 1, ... {"rayl", "rayleigh"}, @raylpdf, 1, ... {"t"}, @tpdf, 1, ... {"unif", "uniform"}, @unifpdf, 2, ... {"wbl", "weibull"}, @wblpdf, 2}; if (numel (varargin) < 2 || ! ischar (varargin{1})) print_usage (); endif name = varargin{1}; x = varargin{2}; varargin(1:2) = []; nargs = numel (varargin); pdfnames = allpdf(1:3:end); pdfhdl = allpdf(2:3:end); pdfargs = allpdf(3:3:end); idx = cellfun (@(x) any (strcmpi (name, x)), pdfnames); if (any (idx)) if (nargs == pdfargs{idx}) retval = feval (pdfhdl{idx}, x, varargin{:}); else error ("pdf: %s requires %d arguments", name, pdfargs{idx}) endif else error ("pdf: %s not implemented", name); endif endfunction %!test %! assert(pdf ('norm', 1, 0, 1), normpdf (1, 0, 1))statistics-1.4.3/inst/pdist.m0000644000000000000000000001706614153320774014375 0ustar0000000000000000## Copyright (C) 2008 Francesco Potortì ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} pdist (@var{x}) ## @deftypefnx {Function File} {@var{y} =} pdist (@var{x}, @var{metric}) ## @deftypefnx {Function File} {@var{y} =} pdist (@var{x}, @var{metric}, @var{metricarg}, @dots{}) ## ## Return the distance between any two rows in @var{x}. ## ## @var{x} is the @var{n}x@var{d} matrix representing @var{q} row ## vectors of size @var{d}. ## ## The output is a dissimilarity matrix formatted as a row vector ## @var{y}, @math{(n-1)*n/2} long, where the distances are in ## the order [(1, 2) (1, 3) @dots{} (2, 3) @dots{} (n-1, n)]. You can ## use the @code{squareform} function to display the distances between ## the vectors arranged into an @var{n}x@var{n} matrix. ## ## @code{metric} is an optional argument specifying how the distance is ## computed. It can be any of the following ones, defaulting to ## "euclidean", or a user defined function that takes two arguments ## @var{x} and @var{y} plus any number of optional arguments, ## where @var{x} is a row vector and and @var{y} is a matrix having the ## same number of columns as @var{x}. @code{metric} returns a column ## vector where row @var{i} is the distance between @var{x} and row ## @var{i} of @var{y}. Any additional arguments after the @code{metric} ## are passed as metric (@var{x}, @var{y}, @var{metricarg1}, ## @var{metricarg2} @dots{}). ## ## Predefined distance functions are: ## ## @table @samp ## @item "euclidean" ## Euclidean distance (default). ## ## @item "squaredeuclidean" ## Squared Euclidean distance. It omits the square root from the calculation ## of the Euclidean distance. It does not satisfy the triangle inequality. ## ## @item "seuclidean" ## Standardized Euclidean distance. Each coordinate in the sum of ## squares is inverse weighted by the sample variance of that ## coordinate. ## ## @item "mahalanobis" ## Mahalanobis distance: see the function mahalanobis. ## ## @item "cityblock" ## City Block metric, aka Manhattan distance. ## ## @item "minkowski" ## Minkowski metric. Accepts a numeric parameter @var{p}: for @var{p}=1 ## this is the same as the cityblock metric, with @var{p}=2 (default) it ## is equal to the euclidean metric. ## ## @item "cosine" ## One minus the cosine of the included angle between rows, seen as ## vectors. ## ## @item "correlation" ## One minus the sample correlation between points (treated as ## sequences of values). ## ## @item "spearman" ## One minus the sample Spearman's rank correlation between ## observations, treated as sequences of values. ## ## @item "hamming" ## Hamming distance: the quote of the number of coordinates that differ. ## ## @item "jaccard" ## One minus the Jaccard coefficient, the quote of nonzero ## coordinates that differ. ## ## @item "chebychev" ## Chebychev distance: the maximum coordinate difference. ## @end table ## @seealso{linkage, mahalanobis, squareform, pdist2} ## @end deftypefn ## Author: Francesco Potortì function y = pdist (x, metric, varargin) if (nargin < 1) print_usage (); elseif ((nargin > 1) && ! ischar (metric) && ! isa (metric, "function_handle")) error (["pdist: the distance function must be either a string or a " "function handle."]); endif if (nargin < 2) metric = "euclidean"; endif if (! ismatrix (x) || isempty (x)) error ("pdist: x must be a nonempty matrix"); elseif (length (size (x)) > 2) error ("pdist: x must be 1 or 2 dimensional"); endif y = []; if (rows(x) == 1) return; endif if (ischar (metric)) order = nchoosek(1:rows(x),2); Xi = order(:,1); Yi = order(:,2); X = x'; metric = lower (metric); switch (metric) case "euclidean" d = X(:,Xi) - X(:,Yi); y = norm (d, "cols"); case "squaredeuclidean" d = X(:,Xi) - X(:,Yi); y = sumsq (d); case "seuclidean" d = X(:,Xi) - X(:,Yi); weights = inv (diag (var (x, 0, 1))); y = sqrt (sum ((weights * d) .* d, 1)); case "mahalanobis" d = X(:,Xi) - X(:,Yi); weights = inv (cov (x)); y = sqrt (sum ((weights * d) .* d, 1)); case "cityblock" d = X(:,Xi) - X(:,Yi); if (str2num(version()(1:3)) > 3.1) y = norm (d, 1, "cols"); else y = sum (abs (d), 1); endif case "minkowski" d = X(:,Xi) - X(:,Yi); p = 2; # default if (nargin > 2) p = varargin{1}; # explicitly assigned endif; y = norm (d, p, "cols"); case "cosine" prod = X(:,Xi) .* X(:,Yi); weights = sumsq (X(:,Xi), 1) .* sumsq (X(:,Yi), 1); y = 1 - sum (prod, 1) ./ sqrt (weights); case "correlation" if (rows(X) == 1) error ("pdist: correlation distance between scalars not defined") endif cor = corr (X); y = 1 - cor (sub2ind (size (cor), Xi, Yi))'; case "spearman" if (rows(X) == 1) error ("pdist: spearman distance between scalars not defined") endif cor = spearman (X); y = 1 - cor (sub2ind (size (cor), Xi, Yi))'; case "hamming" d = logical (X(:,Xi) - X(:,Yi)); y = sum (d, 1) / rows (X); case "jaccard" d = logical (X(:,Xi) - X(:,Yi)); weights = X(:,Xi) | X(:,Yi); y = sum (d & weights, 1) ./ sum (weights, 1); case "chebychev" d = X(:,Xi) - X(:,Yi); y = norm (d, Inf, "cols"); endswitch endif if (isempty (y)) ## Metric is a function handle or the name of an external function l = rows (x); y = zeros (1, nchoosek (l, 2)); idx = 1; for ii = 1:l-1 for jj = ii+1:l y(idx++) = feval (metric, x(ii,:), x, varargin{:})(jj); endfor endfor endif endfunction %!shared xy, t, eucl %! xy = [0 1; 0 2; 7 6; 5 6]; %! t = 1e-3; %! eucl = @(v,m) sqrt(sumsq(repmat(v,rows(m),1)-m,2)); %!assert(pdist(xy), [1.000 8.602 7.071 8.062 6.403 2.000],t); %!assert(pdist(xy,eucl), [1.000 8.602 7.071 8.062 6.403 2.000],t); %!assert(pdist(xy,"euclidean"), [1.000 8.602 7.071 8.062 6.403 2.000],t); %!assert(pdist(xy,"seuclidean"), [0.380 2.735 2.363 2.486 2.070 0.561],t); %!assert(pdist(xy,"mahalanobis"),[1.384 1.967 2.446 2.384 1.535 2.045],t); %!assert(pdist(xy,"cityblock"), [1.000 12.00 10.00 11.00 9.000 2.000],t); %!assert(pdist(xy,"minkowski"), [1.000 8.602 7.071 8.062 6.403 2.000],t); %!assert(pdist(xy,"minkowski",3),[1.000 7.763 6.299 7.410 5.738 2.000],t); %!assert(pdist(xy,"cosine"), [0.000 0.349 0.231 0.349 0.231 0.013],t); %!assert(pdist(xy,"correlation"),[0.000 2.000 0.000 2.000 0.000 2.000],t); %!assert(pdist(xy,"spearman"), [0.000 2.000 0.000 2.000 0.000 2.000],t); %!assert(pdist(xy,"hamming"), [0.500 1.000 1.000 1.000 1.000 0.500],t); %!assert(pdist(xy,"jaccard"), [1.000 1.000 1.000 1.000 1.000 0.500],t); %!assert(pdist(xy,"chebychev"), [1.000 7.000 5.000 7.000 5.000 2.000],t); statistics-1.4.3/inst/pdist2.m0000644000000000000000000001264114153320774014451 0ustar0000000000000000## Copyright (C) 2014-2019 Piotr Dollar ## ## This program is free software; you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation; either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; if not, see ## . ## -*- texinfo -*- ## @deftypefn {Function File} {} pdist2 (@var{x}, @var{y}) ## @deftypefnx {Function File} {} pdist2 (@var{x}, @var{y}, @var{metric}) ## Compute pairwise distance between two sets of vectors. ## ## Let @var{X} be an MxP matrix representing m points in P-dimensional space ## and @var{Y} be an NxP matrix representing another set of points in the same ## space. This function computes the M-by-N distance matrix @var{D} where ## @code{@var{D}(i,j)} is the distance between @code{@var{X}(i,:)} and ## @code{@var{Y}(j,:)}. ## ## The optional argument @var{metric} can be used to select different ## distances: ## ## @table @asis ## @item @qcode{"euclidean"} (default) ## ## @item @qcode{"sqeuclidean"} ## Compute the squared euclidean distance, i.e., the euclidean distance ## before computing square root. This is ideal when the interest is on the ## order of the euclidean distances rather than the actual distance value ## because it performs significantly faster while preserving the order. ## ## @item @qcode{"chisq'"} ## The chi-squared distance between two vectors is defined as: ## @code{d(x, y) = sum ((xi-yi)^2 / (xi+yi)) / 2}. ## The chi-squared distance is useful when comparing histograms. ## ## @item @qcode{"cosine"} ## Distance is defined as the cosine of the angle between two vectors. ## ## @item @qcode{"emd"} ## Earth Mover's Distance (EMD) between positive vectors (histograms). ## Note for 1D, with all histograms having equal weight, there is a simple ## closed form for the calculation of the EMD. The EMD between histograms ## @var{x} and @var{y} is given by @code{sum (abs (cdf (x) - cdf (y)))}, ## where @code{cdf} is the cumulative distribution function (computed ## simply by @code{cumsum}). ## ## @item @qcode{"L1"} ## The L1 distance between two vectors is defined as: @code{sum (abs (x-y))} ## ## @end table ## ## @seealso{pdist} ## @end deftypefn ## Taken from Piotr's Computer Vision Matlab Toolbox Version 2.52, with ## author permission to distribute under GPLv3 function D = pdist2 (X, Y, metric = "euclidean") if (nargin < 2 || nargin > 3) print_usage (); elseif (columns (X) != columns (Y)) error ("pdist2: X and Y must have equal number of columns"); elseif (ndims (X) != 2 || ndims (Y) != 2) error ("pdist2: X and Y must be 2 dimensional matrices"); endif switch (tolower (metric)) case "sqeuclidean", D = distEucSq (X, Y); case "euclidean", D = sqrt (distEucSq (X, Y)); case "l1", D = distL1 (X, Y); case "cosine", D = distCosine (X, Y); case "emd", D = distEmd (X, Y); case "chisq", D = distChiSq (X, Y); otherwise error ("pdist2: unknown distance METRIC %s", metric); endswitch D = max (0, D); endfunction ## TODO we could check the value of p and n first, and choose one ## or the other loop accordingly. ## L1 COMPUTATION WITH LOOP OVER p, FAST FOR SMALL p. ## function D = distL1( X, Y ) ## m = size(X,1); n = size(Y,1); p = size(X,2); ## mOnes = ones(1,m); nOnes = ones(1,n); D = zeros(m,n); ## for i=1:p ## yi = Y(:,i); yi = yi( :, mOnes ); ## xi = X(:,i); xi = xi( :, nOnes ); ## D = D + abs( xi-yi' ); ## end function D = distL1 (X, Y) m = rows (X); n = rows (Y); mOnes = ones (1, m); D = zeros (m, n); for i = 1:n yi = Y(i,:); yi = yi(mOnes,:); D(:,i) = sum (abs (X-yi), 2); endfor endfunction function D = distCosine (X, Y) p = columns (X); X = X ./ repmat (sqrt (sumsq (X, 2)), [1 p]); Y = Y ./ repmat (sqrt (sumsq (Y, 2)), [1 p]); D = 1 - X*Y'; endfunction function D = distEmd (X, Y) Xcdf = cumsum (X,2); Ycdf = cumsum (Y,2); m = rows (X); n = rows (Y); mOnes = ones (1, m); D = zeros (m, n); for i=1:n ycdf = Ycdf(i,:); ycdfRep = ycdf(mOnes,:); D(:,i) = sum (abs (Xcdf - ycdfRep), 2); endfor endfunction function D = distChiSq (X, Y) ## note: supposedly it's possible to implement this without a loop! m = rows (X); n = rows (Y); mOnes = ones (1, m); D = zeros (m, n); for i = 1:n yi = Y(i, :); yiRep = yi(mOnes, :); s = yiRep + X; d = yiRep - X; D(:,i) = sum (d.^2 ./ (s+eps), 2); endfor D = D/2; endfunction function dists = distEucSq (x, y) xx = sumsq (x, 2); yy = sumsq (y, 2)'; dists = max (0, bsxfun (@plus, xx, yy) - 2 * x * (y')); endfunction ## euclidean distance as loop for testing purposes %!function dist = euclidean_distance (x, y) %! [m, p] = size (X); %! [n, p] = size (Y); %! D = zeros (m, n); %! for i = 1:n %! d = X - repmat (Y(i,:), [m 1]); %! D(:,i) = sumsq (d, 2); %! endfor %!endfunction %!test %! x = [1 1 1; 2 2 2; 3 3 3]; %! y = [0 0 0; 1 2 3; 0 2 4; 4 7 1]; %! d = sqrt([ 3 5 11 45 %! 12 2 8 30 %! 27 5 11 21]); %! assert (pdist2 (x, y), d) statistics-1.4.3/inst/plsregress.m0000644000000000000000000000706714153320774015443 0ustar0000000000000000## Copyright (C) 2012-2019 Fernando Damian Nieuwveldt ## ## This program is free software; you can redistribute it and/or ## modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 ## of the License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{XLOADINGS},@var{YLOADINGS},@var{XSCORES},@var{YSCORES},@var{coefficients},@var{fitted}] =} plsregress(@var{X}, @var{Y}, @var{NCOMP}) ## Calculate partial least squares regression ## ## @itemize @bullet ## @item ## @var{X}: Matrix of observations ## @item ## @var{Y}: Is a vector or matrix of responses ## @item ## @var{NCOMP}: number of components used for modelling ## @item ## @var{X} and @var{Y} will be mean centered to improve accuracy ## @end itemize ## ## @subheading References ## ## @enumerate ## @item ## SIMPLS: An alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory ## Systems (1993) ## ## @end enumerate ## @end deftypefn ## Author: Fernando Damian Nieuwveldt ## Description: Partial least squares regression using SIMPLS algorithm function [XLOADINGS, YLOADINGS, XSCORES, YSCORES, coefficients, fitted] = plsregress (X, Y, NCOMP) if nargout != 6 print_usage(); end nobs = rows (X); # Number of observations npred = columns (X); # Number of predictor variables nresp = columns (Y); # Number of responses if (! isnumeric (X) || ! isnumeric (Y)) error ("plsregress:Data matrix X and reponse matrix Y must be real matrices"); elseif (nobs != rows (Y)) error ("plsregress:Number of observations for Data matrix X and Response Matrix Y must be equal"); elseif(! isscalar (NCOMP)) error ("plsregress: Third argument must be a scalar"); end ## Mean centering Data matrix Xmeans = mean (X); X = bsxfun (@minus, X, Xmeans); ## Mean centering responses Ymeans = mean (Y); Y = bsxfun (@minus, Y, Ymeans); S = X'*Y; R = P = V = zeros (npred, NCOMP); T = U = zeros (nobs, NCOMP); Q = zeros (nresp, NCOMP); for a = 1:NCOMP [eigvec eigval] = eig (S'*S); # Y factor weights domindex = find (diag (eigval) == max (diag (eigval))); # get dominant eigenvector q = eigvec(:,domindex); r = S*q; # X block factor weights t = X*r; # X block factor scores t = t - mean (t); nt = sqrt (t'*t); # compute norm t = t/nt; r = r/nt; # normalize p = X'*t; # X block factor loadings q = Y'*t; # Y block factor loadings u = Y*q; # Y block factor scores v = p; ## Ensure orthogonality if a > 1 v = v - V*(V'*p); u = u - T*(T'*u); endif v = v/sqrt(v'*v); # normalize orthogonal loadings S = S - v*(v'*S); # deflate S wrt loadings ## Store data R(:,a) = r; T(:,a) = t; P(:,a) = p; Q(:,a) = q; U(:,a) = u; V(:,a) = v; endfor ## Regression coefficients B = R*Q'; fitted = bsxfun (@plus, T*Q', Ymeans); # Add mean ## Return coefficients = B; XSCORES = T; XLOADINGS = P; YSCORES = U; YLOADINGS = Q; projection = R; endfunction statistics-1.4.3/inst/poisstat.m0000644000000000000000000000452714153320774015116 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} poisstat (@var{lambda}) ## Compute mean and variance of the Poisson distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{lambda} is the parameter of the Poisson distribution. The ## elements of @var{lambda} must be positive ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the Poisson distribution ## ## @item ## @var{v} is the variance of the Poisson distribution ## @end itemize ## ## @subheading Example ## ## @example ## @group ## lambda = 1 ./ (1:6); ## [m, v] = poisstat (lambda) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the Poisson distribution function [m, v] = poisstat (lambda) # Check arguments if (nargin != 1) print_usage (); endif if (! isempty (lambda) && ! ismatrix (lambda)) error ("poisstat: lambda must be a numeric matrix"); endif # Set moments m = lambda; v = lambda; # Continue argument check k = find (! (lambda > 0) | ! (lambda < Inf)); if (any (k)) m(k) = NaN; v(k) = NaN; endif endfunction %!test %! lambda = 1 ./ (1:6); %! [m, v] = poisstat (lambda); %! assert (m, lambda); %! assert (v, lambda); statistics-1.4.3/inst/princomp.m0000644000000000000000000001242314153320774015071 0ustar0000000000000000## Copyright (C) 2013-2019 Fernando Damian Nieuwveldt ## ## This program is free software; you can redistribute it and/or ## modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 ## of the License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{COEFF}]} = princomp(@var{X}) ## @deftypefnx {Function File} {[@var{COEFF},@var{SCORE}]} = princomp(@var{X}) ## @deftypefnx {Function File} {[@var{COEFF},@var{SCORE},@var{latent}]} = princomp(@var{X}) ## @deftypefnx {Function File} {[@var{COEFF},@var{SCORE},@var{latent},@var{tsquare}]} = princomp(@var{X}) ## @deftypefnx {Function File} {[...]} = princomp(@var{X},'econ') ## Performs a principal component analysis on a NxP data matrix X ## ## @itemize @bullet ## @item ## @var{COEFF} : returns the principal component coefficients ## @item ## @var{SCORE} : returns the principal component scores, the representation of X ## in the principal component space ## @item ## @var{LATENT} : returns the principal component variances, i.e., the ## eigenvalues of the covariance matrix X. ## @item ## @var{TSQUARE} : returns Hotelling's T-squared Statistic for each observation in X ## @item ## [...] = princomp(X,'econ') returns only the elements of latent that are not ## necessarily zero, and the corresponding columns of COEFF and SCORE, that is, ## when n <= p, only the first n-1. This can be significantly faster when p is ## much larger than n. In this case the svd will be applied on the transpose of ## the data matrix X ## ## @end itemize ## ## @subheading References ## ## @enumerate ## @item ## Jolliffe, I. T., Principal Component Analysis, 2nd Edition, Springer, 2002 ## ## @end enumerate ## @end deftypefn function [COEFF,SCORE,latent,tsquare] = princomp(X,varargin) if (nargin < 1 || nargin > 2) print_usage (); endif if (nargin == 2 && ! strcmpi (varargin{:}, "econ")) error ("princomp: if a second input argument is present, it must be the string 'econ'"); endif [nobs nvars] = size(X); # Center the columns to mean zero Xcentered = bsxfun(@minus,X,mean(X)); # Check if there are more variables then observations if nvars <= nobs [U,S,COEFF] = svd(Xcentered, "econ"); else # Calculate the svd on the transpose matrix, much faster if (nargin == 2 && strcmpi ( varargin{:} , "econ")) [COEFF,S,V] = svd(Xcentered' , 'econ'); else [COEFF,S,V] = svd(Xcentered'); endif endif if nargout > 1 # Get the Scores SCORE = Xcentered*COEFF; # Get the rank of the SCORE matrix r = rank(SCORE); # Only use the first r columns, pad rest with zeros if economy != 'econ' SCORE = SCORE(:,1:r) ; if !(nargin == 2 && strcmpi ( varargin{:} , "econ")) SCORE = [SCORE, zeros(nobs , nvars-r)]; else COEFF = COEFF(: , 1:r); endif endif if nargout > 2 # This is the same as the eigenvalues of the covariance matrix of X latent = (diag(S'*S)/(size(Xcentered,1)-1))(1:r); if !(nargin == 2 && strcmpi ( varargin{:} , "econ")) latent= [latent;zeros(nvars-r,1)]; endif endif if nargout > 3 # Calculate the Hotelling T-Square statistic for the observations tsquare = sumsq(zscore(SCORE(:,1:r)),2); endif endfunction %!shared COEFF,SCORE,latent,tsquare,m,x,R,V,lambda,i,S,F #NIST Engineering Statistics Handbook example (6.5.5.2) %!test %! x=[7 4 3 %! 4 1 8 %! 6 3 5 %! 8 6 1 %! 8 5 7 %! 7 2 9 %! 5 3 3 %! 9 5 8 %! 7 4 5 %! 8 2 2]; %! R = corrcoef (x); %! [V, lambda] = eig (R); %! [~, i] = sort(diag(lambda), "descend"); #arrange largest PC first %! S = V(:, i) * diag(sqrt(diag(lambda)(i))); %!assert(diag(S(:, 1:2)*S(:, 1:2)'), [0.8662; 0.8420; 0.9876], 1E-4); #contribution of first 2 PCs to each original variable %! B = V(:, i) * diag( 1./ sqrt(diag(lambda)(i))); %! F = zscore(x)*B; %! [COEFF,SCORE,latent,tsquare] = princomp(zscore(x, 1)); %!assert(tsquare,sumsq(F, 2),1E4*eps); %!test %! x=[1,2,3;2,1,3]'; %! [COEFF,SCORE,latent,tsquare] = princomp(x); %! m=[sqrt(2),sqrt(2);sqrt(2),-sqrt(2);-2*sqrt(2),0]/2; %! m(:,1) = m(:,1)*sign(COEFF(1,1)); %! m(:,2) = m(:,2)*sign(COEFF(1,2)); %!assert(COEFF,m(1:2,:),10*eps); %!assert(SCORE,-m,10*eps); %!assert(latent,[1.5;.5],10*eps); %!assert(tsquare,[4;4;4]/3,10*eps); %!test %! x=x'; %! [COEFF,SCORE,latent,tsquare] = princomp(x); %! m=[sqrt(2),sqrt(2),0;-sqrt(2),sqrt(2),0;0,0,2]/2; %! m(:,1) = m(:,1)*sign(COEFF(1,1)); %! m(:,2) = m(:,2)*sign(COEFF(1,2)); %! m(:,3) = m(:,3)*sign(COEFF(3,3)); %!assert(COEFF,m,10*eps); %!assert(SCORE(:,1),-m(1:2,1),10*eps); %!assert(SCORE(:,2:3),zeros(2),10*eps); %!assert(latent,[1;0;0],10*eps); %!assert(tsquare,[0.5;0.5],10*eps) %!test %! [COEFF,SCORE,latent,tsquare] = princomp(x, "econ"); %!assert(COEFF,m(:, 1),10*eps); %!assert(SCORE,-m(1:2,1),10*eps); %!assert(latent,[1],10*eps); %!assert(tsquare,[0.5;0.5],10*eps) statistics-1.4.3/inst/private/0000755000000000000000000000000014153320774014534 5ustar0000000000000000statistics-1.4.3/inst/private/CalinskiHarabaszEvaluation.m0000644000000000000000000002031514153320774022154 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . classdef CalinskiHarabaszEvaluation < ClusterCriterion ## -*- texinfo -*- ## @deftypefn {Function File} {@var{eva} =} evalclusters (@var{x}, @var{clust}, @qcode{CalinskiHarabasz}) ## @deftypefnx {Function File} {@var{eva} =} evalclusters (@dots{}, @qcode{Name}, @qcode{Value}) ## ## A Calinski-Harabasz object to evaluate clustering solutions. ## ## A @code{CalinskiHarabaszEvaluation} object is a @code{ClusterCriterion} ## object used to evaluate clustering solutions using the Calinski-Harabasz ## criterion. ## ## The Calinski-Harabasz index is based on the ratio between SSb and SSw. ## SSb is the overall variance between clusters, that is the variance of the ## distances between the centroids. ## SSw is the overall variance within clusters, that is the sum of the ## variances of the distances between each datapoint and its centroid. ## ## The best solution according to the Calinski-Harabasz criterion is the one ## that scores the highest value. ## @end deftypefn ## ## @seealso{ClusterCriterion, evalclusters} properties (GetAccess = public, SetAccess = private) endproperties properties (Access = protected) Centroids = {}; # a list of the centroids for every solution endproperties methods (Access = public) ## constructor function this = CalinskiHarabaszEvaluation (x, clust, KList) this@ClusterCriterion(x, clust, KList); this.CriterionName = "CalinskiHarabasz"; this.evaluate(this.InspectedK); # evaluate the list of cluster numbers endfunction ## set functions ## addK ## add new cluster sizes to evaluate function this = addK (this, K) addK@ClusterCriterion(this, K); ## if we have new data, we need a new evaluation if (this.OptimalK == 0) Centroids_tmp = {}; pS = 0; # position shift of the elements of Centroids for iter = 1 : length (this.InspectedK) ## reorganize Centroids according to the new list of cluster numbers if (any (this.InspectedK(iter) == K)) pS += 1; else Centroids_tmp{iter} = this.Centroids{iter - pS}; endif endfor this.Centroids = Centroids_tmp; this.evaluate(K); # evaluate just the new cluster numbers endif endfunction ## compact ## ... function this = compact (this) # FIXME: stub! warning ("CalinskiHarabaszEvaluation: compact is unavailable"); endfunction endmethods methods (Access = protected) ## evaluate ## do the evaluation function this = evaluate (this, K) ## use complete observations only UsableX = this.X(find (this.Missing == false), :); if (! isempty (this.ClusteringFunction)) ## build the clusters for iter = 1 : length (this.InspectedK) ## do it only for the specified K values if (any (this.InspectedK(iter) == K)) if (isa (this.ClusteringFunction, "function_handle")) ## custom function ClusteringSolution = ... this.ClusteringFunction(UsableX, this.InspectedK(iter)); if (ismatrix (ClusteringSolution) && ... rows (ClusteringSolution) == this.NumObservations && ... columns (ClusteringSolution) == this.P) ## the custom function returned a matrix: ## we take the index of the maximum value for every row [~, this.ClusteringSolutions(:, iter)] = ... max (ClusteringSolution, [], 2); elseif (iscolumn (ClusteringSolution) && length (ClusteringSolution) == this.NumObservations) this.ClusteringSolutions(:, iter) = ClusteringSolution; elseif (isrow (ClusteringSolution) && length (ClusteringSolution) == this.NumObservations) this.ClusteringSolutions(:, iter) = ClusteringSolution'; else error (["CalinskiHarabaszEvaluation: invalid return value "... "from custom clustering function"]); endif this.ClusteringSolutions(:, iter) = ... this.ClusteringFunction(UsableX, this.InspectedK(iter)); else switch (this.ClusteringFunction) case "kmeans" [this.ClusteringSolutions(:, iter), this.Centroids{iter}] =... kmeans (UsableX, this.InspectedK(iter), ... "Distance", "sqeuclidean", "EmptyAction", "singleton", ... "Replicates", 5); case "linkage" ## use clusterdata this.ClusteringSolutions(:, iter) = clusterdata (UsableX, ... "MaxClust", this.InspectedK(iter), ... "Distance", "euclidean", "Linkage", "ward"); this.Centroids{iter} = this.computeCentroids (UsableX, iter); case "gmdistribution" gmm = fitgmdist (UsableX, this.InspectedK(iter), ... "SharedCov", true, "Replicates", 5); this.ClusteringSolutions(:, iter) = cluster (gmm, UsableX); this.Centroids{iter} = gmm.mu; otherwise error (["CalinskiHarabaszEvaluation: unexpected error, " ... "report this bug"]); endswitch endif endif endfor endif ## get the criterion values for every clustering solution for iter = 1 : length (this.InspectedK) ## do it only for the specified K values if (any (this.InspectedK(iter) == K)) ## not defined for one cluster if (this.InspectedK(iter) == 1) this.CriterionValues(iter) = NaN; continue; endif ## CaliÅ„ski-Harabasz index ## reference: calinhara function from the fpc package of R, ## by Christian Hennig ## https://CRAN.R-project.org/package=fpc W = zeros (columns (UsableX)); # between clusters covariance for i = 1 : this.InspectedK(iter) vIndicesI = find (this.ClusteringSolutions(:, iter) == i); ni = length (vIndicesI); # size of cluster i if (ni == 1) ## if the cluster has just one member the covariance is zero continue; endif ## weighted update of the covariance matrix W += cov (UsableX(vIndicesI, :)) * (ni - 1); endfor S = (this.NumObservations - 1) * cov (UsableX); # within clusters cov. B = S - W; # between clusters means ## tr(B) / tr(W) * (N-k) / (k-1) this.CriterionValues(iter) = (this.NumObservations - ... this.InspectedK(iter)) * trace (B) / ... ((this.InspectedK(iter) - 1) * trace (W)); endif endfor [~, this.OptimalIndex] = max (this.CriterionValues); this.OptimalK = this.InspectedK(this.OptimalIndex(1)); this.OptimalY = this.ClusteringSolutions(:, this.OptimalIndex(1)); endfunction endmethods methods (Access = private) ## computeCentroids ## compute the centroids if they are not available by other means function C = computeCentroids (this, X, index) C = zeros (this.InspectedK(index), columns (X)); for iter = 1 : this.InspectedK(index) vIndicesI = find (this.ClusteringSolutions(:, index) == iter); C(iter, :) = mean (X(vIndicesI, :)); endfor endfunction endmethods endclassdef statistics-1.4.3/inst/private/ClusterCriterion.m0000644000000000000000000001742714153320774020225 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . classdef ClusterCriterion < handle ## -*- texinfo -*- ## @deftypefn {} {} ClusterCriterion () ## ## A clustering evaluation object as created by @code{evalclusters}. ## ## @code{ClusterCriterion} is a superclass for clustering evaluation objects ## as created by @code{evalclusters}. ## ## List of public properties: ## @table @code ## @item @qcode{ClusteringFunction} ## a valid clustering funtion name or function handle. It can be empty if ## the clustering solutions are passed as an input matric. ## ## @item @qcode{CriterionName} ## a valid criterion name to evaluate the clustering solutions. ## ## @item @qcode{CriterionValues} ## a vector of values as generated by the evaluation criterion for each ## clustering solution. ## ## @item @qcode{InspectedK} ## the list of proposed cluster numbers. ## ## @item @qcode{Missing} ## a logical vector of missing observations. When there are @code{NaN} ## values in the data matrix, the corresponding observation is excluded. ## ## @item @qcode{NumObservations} ## the number of non-missing observations in the data matrix. ## ## @item @qcode{OptimalK} ## the optimal number of clusters. ## ## @item @qcode{OptimalY} ## the clustering solution corresponding to @code{OptimalK}. ## ## @item @qcode{X} ## the data matrix. ## ## @end table ## ## List of public methods: ## @table @code ## @item @qcode{addK} ## add a list of numbers of clusters to evaluate. ## ## @item @qcode{compact} ## return a compact clustering evaluation object. Not implemented ## ## @item @qcode{plot} ## plot the clustering evaluation values against the corresponding number of ## clusters. ## ## @end table ## @end deftypefn ## ## @seealso{CalinskiHarabaszEvaluation, DaviesBouldinEvaluation, evalclusters, ## GapEvaluation, SilhouetteEvaluation} properties (Access = public) ## public properties endproperties properties (GetAccess = public, SetAccess = protected) ClusteringFunction = ""; CriterionName = ""; CriterionValues = []; InspectedK = []; Missing = []; NumObservations = 0; OptimalK = 0; OptimalY = []; X = []; endproperties properties (Access = protected) N = 0; # number of observations P = 0; # number of variables ClusteringSolutions = []; # OptimalIndex = 0; # index of the optimal K endproperties methods (Access = public) ## constructor function this = ClusterCriterion (x, clust, KList) ## parsing input data if ((! ismatrix (x)) || (! isnumeric (x))) error ("ClusterCriterion: 'x' must be a numeric matrix"); endif this.X = x; this.N = rows (this.X); this.P = columns (this.X); ## look for missing values for iter = 1 : this.N if (any (find (x(iter, :) == NaN))) this.Missing(iter) = true; else this.Missing(iter) = false; endif endfor ## number of usable observations this.NumObservations = sum (this.Missing == false); ## parsing the clustering algorithm if (ischar (clust)) if (any (strcmpi (clust, {"kmeans", "linkage", "gmdistribution"}))) this.ClusteringFunction = lower (clust); else error ("ClusterCriterion: unknown clustering algorithm '%s'", clust); endif elseif (isa (clust, "function_handle")) this.ClusteringFunction = clust; elseif (ismatrix (clust)) if (isnumeric (clust) && (length (size (clust)) == 2) && ... (rows (clust) == this.N)) this.ClusteringFunction = ""; this.ClusteringSolutions = clust(find (this.Missing == false), :); else error ("ClusterCriterion: invalid matrix of clustering solutions"); endif else error ("ClusterCriterion: invalid argument"); endif ## parsing the list of cluster sizes to inspect this.InspectedK = parseKList (this, KList); endfunction ## addK ## add one or more new cluster sizes to evaluate function this = addK (this, k) ## -*- texinfo -*- ## @deftypefn {} {} ClusterCriterion.addK (@var{K}) ## ## Add an array of cluster numbers to inspect to the evaluation object. ## @end deftypefn ## if there is not a clustering function, then we are using a predefined ## set of clustering solutions, hence we cannot redefine the number of ## solutions if (isempty (this.ClusteringFunction)) warning (["ClusterCriterion: cannot redefine the list of cluster"... "numbers to evaluate when there is not a clustering function"]); return; endif ## otherwise go on newList = this.parseKList ([this.InspectedK k]); ## check if the list has changed if (length (newList) == length (this.InspectedK)) warning ("ClusterCriterion: the list has not changed"); else ## update ClusteringSolutions and CriterionValues ClusteringSolutions_tmp = zeros (this.NumObservations, ... length (newList)); CriterionValues_tmp = zeros (length (newList), 1); for iter = 1 : length (this.InspectedK) idx = find (newList == this.InspectedK(iter)); if (! isempty (idx)) ClusteringSolutions_tmp(:, idx) = this.ClusteringSolutions(:, iter); CriterionValues_tmp(idx) = this.CriterionValues(iter); endif endfor this.ClusteringSolutions = ClusteringSolutions_tmp; this.CriterionValues = CriterionValues_tmp; ## reset the old results this.OptimalK = 0; this.OptimalY = []; this.OptimalIndex = 0; ## update the list of cluster numbers to evaluate this.InspectedK = newList; endif endfunction ## plot ## plot the CriterionValues against InspectedK and return a handle to the ## plot function h = plot (this) ## -*- texinfo -*- ## @deftypefn {} {} ClusterCriterion.plot () ## ## Plot the evaluation results. ## @end deftypefn yLabel = sprintf ("%s value", this.CriterionName); h = gca (); hold on; plot (this.InspectedK, this.CriterionValues, "bo-"); plot (this.OptimalK, this.CriterionValues(this.OptimalIndex), "b*"); xlabel ("number of clusters"); ylabel (yLabel); hold off; endfunction endmethods methods (Abstract = true) function compact () ## -*- texinfo -*- ## @deftypefn {} {@var{eva} =} ClusterCriterion.compact () ## ## Return a compact evaluation object. ## @end deftypefn endfunction endmethods methods (Access = private) ## check if a list of cluster sizes is correct function retList = parseKList (this, KList) if (isnumeric (KList) && isvector (KList) && all (find (KList > 0)) && ... all (floor (KList) == KList)) retList = unique (KList); else error (["ClusterCriterion: the list of cluster sizes must be an " ... "array of positive integer numbers"]); endif endfunction endmethods endclassdef statistics-1.4.3/inst/private/DaviesBouldinEvaluation.m0000644000000000000000000002036114153320774021474 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . classdef DaviesBouldinEvaluation < ClusterCriterion ## -*- texinfo -*- ## @deftypefn {Function File} {@var{eva} =} evalclusters (@var{x}, @var{clust}, @qcode{DaviesBouldin}) ## @deftypefnx {Function File} {@var{eva} =} evalclusters (@dots{}, @qcode{Name}, @qcode{Value}) ## ## A Davies-Bouldin object to evaluate clustering solutions. ## ## A @code{DaviesBouldinEvaluation} object is a @code{ClusterCriterion} ## object used to evaluate clustering solutions using the Davies-Bouldin ## criterion. ## ## The Davies-Bouldin criterion is based on the ratio between the distances ## between clusters and within clusters, that is the distances between the ## centroids and the distances between each datapoint and its centroid. ## ## The best solution according to the Davies-Bouldin criterion is the one ## that scores the lowest value. ## @end deftypefn ## ## @seealso{ClusterCriterion, evalclusters} properties (GetAccess = public, SetAccess = private) endproperties properties (Access = protected) Centroids = {}; # a list of the centroids for every solution endproperties methods (Access = public) ## constructor function this = DaviesBouldinEvaluation (x, clust, KList) this@ClusterCriterion(x, clust, KList); this.CriterionName = "DaviesBouldin"; this.evaluate(this.InspectedK); # evaluate the list of cluster numbers endfunction ## set functions ## addK ## add new cluster sizes to evaluate function this = addK (this, K) addK@ClusterCriterion(this, K); ## if we have new data, we need a new evaluation if (this.OptimalK == 0) Centroids_tmp = {}; pS = 0; # position shift of the elements of Centroids for iter = 1 : length (this.InspectedK) ## reorganize Centroids according to the new list of cluster numbers if (any (this.InspectedK(iter) == K)) pS += 1; else Centroids_tmp{iter} = this.Centroids{iter - pS}; endif endfor this.Centroids = Centroids_tmp; this.evaluate(K); # evaluate just the new cluster numbers endif endfunction ## compact ## ... function this = compact (this) # FIXME: stub! warning ("DaviesBouldinEvaluation: compact is unavailable"); endfunction endmethods methods (Access = protected) ## evaluate ## do the evaluation function this = evaluate (this, K) ## use complete observations only UsableX = this.X(find (this.Missing == false), :); if (! isempty (this.ClusteringFunction)) ## build the clusters for iter = 1 : length (this.InspectedK) ## do it only for the specified K values if (any (this.InspectedK(iter) == K)) if (isa (this.ClusteringFunction, "function_handle")) ## custom function ClusteringSolution = ... this.ClusteringFunction(UsableX, this.InspectedK(iter)); if (ismatrix (ClusteringSolution) && ... rows (ClusteringSolution) == this.NumObservations && ... columns (ClusteringSolution) == this.P) ## the custom function returned a matrix: ## we take the index of the maximum value for every row [~, this.ClusteringSolutions(:, iter)] = ... max (ClusteringSolution, [], 2); elseif (iscolumn (ClusteringSolution) && length (ClusteringSolution) == this.NumObservations) this.ClusteringSolutions(:, iter) = ClusteringSolution; elseif (isrow (ClusteringSolution) && length (ClusteringSolution) == this.NumObservations) this.ClusteringSolutions(:, iter) = ClusteringSolution'; else error (["DaviesBouldinEvaluation: invalid return value "... "from custom clustering function"]); endif this.ClusteringSolutions(:, iter) = ... this.ClusteringFunction(UsableX, this.InspectedK(iter)); else switch (this.ClusteringFunction) case "kmeans" [this.ClusteringSolutions(:, iter), this.Centroids{iter}] =... kmeans (UsableX, this.InspectedK(iter), ... "Distance", "sqeuclidean", "EmptyAction", "singleton", ... "Replicates", 5); case "linkage" ## use clusterdata this.ClusteringSolutions(:, iter) = clusterdata (UsableX, ... "MaxClust", this.InspectedK(iter), ... "Distance", "euclidean", "Linkage", "ward"); this.Centroids{iter} = this.computeCentroids (UsableX, iter); case "gmdistribution" gmm = fitgmdist (UsableX, this.InspectedK(iter), ... "SharedCov", true, "Replicates", 5); this.ClusteringSolutions(:, iter) = cluster (gmm, UsableX); this.Centroids{iter} = gmm.mu; otherwise error (["DaviesBouldinEvaluation: unexpected error, " ... "report this bug"]); endswitch endif endif endfor endif ## get the criterion values for every clustering solution for iter = 1 : length (this.InspectedK) ## do it only for the specified K values if (any (this.InspectedK(iter) == K)) ## not defined for one cluster if (this.InspectedK(iter) == 1) this.CriterionValues(iter) = NaN; continue; endif ## Davies-Bouldin value ## an evaluation of the ratio between within-cluster and ## between-cluster distances ## mean distances between cluster members and their centroid vD = zeros (this.InspectedK(iter), 1); for i = 1 : this.InspectedK(iter) vIndicesI = find (this.ClusteringSolutions(:, iter) == i); vD(i) = mean (vecnorm (UsableX(vIndicesI, :) - ... this.Centroids{iter}(i, :), 2, 2)); endfor ## within-to-between cluster distance ratio Dij = zeros (this.InspectedK(iter)); for i = 1 : (this.InspectedK(iter) - 1) for j = (i + 1) : this.InspectedK(iter) ## centroid to centroid distance dij = vecnorm (this.Centroids{iter}(i, :) - ... this.Centroids{iter}(j, :)); ## within-to-between cluster distance ratio for clusters i and j Dij(i, j) = (vD(i) + vD(j)) / dij; endfor endfor ## ( max_j D1j + max_j D2j + ... + max_j Dkj) / k this.CriterionValues(iter) = sum (max (Dij(i, :), [], 2)) / ... this.InspectedK(iter); endif endfor [~, this.OptimalIndex] = min (this.CriterionValues); this.OptimalK = this.InspectedK(this.OptimalIndex(1)); this.OptimalY = this.ClusteringSolutions(:, this.OptimalIndex(1)); endfunction endmethods methods (Access = private) ## computeCentroids ## compute the centroids if they are not available by other means function C = computeCentroids (this, X, index) C = zeros (this.InspectedK(index), columns (X)); for iter = 1 : this.InspectedK(index) vIndicesI = find (this.ClusteringSolutions(:, index) == iter); C(iter, :) = mean (X(vIndicesI, :)); endfor endfunction endmethods endclassdef statistics-1.4.3/inst/private/GapEvaluation.m0000644000000000000000000003501714153320774017457 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . classdef GapEvaluation < ClusterCriterion ## -*- texinfo -*- ## @deftypefn {Function File} {@var{eva} =} evalclusters (@var{x}, @var{clust}, @qcode{gap}) ## @deftypefnx {Function File} {@var{eva} =} evalclusters (@dots{}, @qcode{Name}, @qcode{Value}) ## ## A gap object to evaluate clustering solutions. ## ## A @code{GapEvaluation} object is a @code{ClusterCriterion} ## object used to evaluate clustering solutions using the gap criterion, ## which is a mathematical formalization of the elbow method. ## ## List of public properties specific to @code{SilhouetteEvaluation}: ## @table @code ## @item @qcode{B} ## the number of reference datasets to generate. ## ## @item @qcode{Distance} ## a valid distance metric name, or a function handle as accepted by the ## @code{pdist} function. ## ## @item @qcode{ExpectedLogW} ## a vector of the expected values for the logarithm of the within clusters ## dispersion. ## ## @item @qcode{LogW} ## a vector of the values of the logarithm of the within clusters dispersion. ## ## @item @qcode{ReferenceDistribution} ## a valid name for the reference distribution, namely: @code{PCA} (default) ## or @code{uniform}. ## ## @item @qcode{SE} ## a vector of the standard error of the expected values for the logarithm ## of the within clusters dispersion. ## ## @item @qcode{SearchMethod} ## a valid name for the search method to use: @code{globalMaxSE} (default) or ## @code{firstMaxSE}. ## ## @item @qcode{StdLogW} ## a vector of the standard deviation of the expected values for the logarithm ## of the within clusters dispersion. ## @end table ## ## The best solution according to the gap criterion depends on the chosen ## search method. When the search method is @code{globalMaxSE}, the chosen ## gap value is the smaller one which is inside a standard error from the ## max gap value; when the search method is @code{firstMaxSE}, the chosen ## gap value is the first one which is inside a standard error from the next ## gap value. ## @end deftypefn ## ## @seealso{ClusterCriterion, evalclusters} properties (GetAccess = public, SetAccess = private) B = 0; # number of reference datasets Distance = ""; # pdist parameter ReferenceDistribution = ""; # distribution to use as reference SearchMethod = ""; # the method do identify the optimal number of clusters ExpectedLogW = []; # expected value for the natural logarithm of W LogW = []; # natural logarithm of W SE = []; # standard error for the natural logarithm of W StdLogW = []; # standard deviation of the natural logarithm of W endproperties properties (Access = protected) DistanceVector = []; # vector of pdist distances mExpectedLogW = []; # the result of the Monte-Carlo simulations endproperties methods (Access = public) ## constructor function this = GapEvaluation (x, clust, KList, b = 100, ... distanceMetric = "sqeuclidean", ... referenceDistribution = "pca", searchMethod = "globalmaxse") this@ClusterCriterion(x, clust, KList); ## parsing the distance criterion if (ischar (distanceMetric)) if (any (strcmpi (distanceMetric, {"sqeuclidean", "euclidean", ... "cityblock", "cosine", "correlation", "hamming", "jaccard"}))) this.Distance = lower (distanceMetric); ## kmeans can use only a subset if (strcmpi (clust, "kmeans") && any (strcmpi (this.Distance, ... {"euclidean", "jaccard"}))) error (["GapEvaluation: invalid distance criterion '%s' "... "for 'kmeans'"], distanceMetric); endif else error ("GapEvaluation: unknown distance criterion '%s'", ... distanceMetric); endif elseif (isa (distanceMetric, "function_handle")) this.Distance = distanceMetric; ## kmeans cannot use a function handle if (strcmpi (clust, "kmeans")) error ("GapEvaluation: invalid distance criterion for 'kmeans'"); endif elseif (isvector (distanceMetric) && isnumeric (distanceMetric)) this.Distance = ""; this.DistanceVector = distanceMetric; # the validity check is delegated ## kmeans cannot use a distance vector if (strcmpi (clust, "kmeans")) error (["GapEvaluation: invalid distance criterion for "... "'kmeans'"]); endif else error ("GapEvaluation: invalid distance metric"); endif ## B: number of Monte-Carlo iterations if (! isnumeric (b) || ! isscalar (b) || b != floor (b) || b < 1) error ("GapEvaluation: b must a be positive integer number"); endif this.B = b; ## reference distribution if (! ischar (referenceDistribution) || ! any (strcmpi ... (referenceDistribution, {"pca", "uniform"}))) error (["GapEvaluation: the reference distribution must be either" ... "'PCA' or 'uniform'"]); elseif (strcmpi (referenceDistribution, "pca")) warning (["GapEvaluation: 'PCA' distribution not implemented, " ... "using 'uniform'"]); endif this.ReferenceDistribution = lower (referenceDistribution); if (! ischar (searchMethod) || ! any (strcmpi (searchMethod, ... {"globalmaxse", "firstmaxse"}))) error (["evalclusters: the search method must be either" ... "'globalMaxSE' or 'firstMaxSE'"]); endif this.SearchMethod = lower (searchMethod); ## a matrix to store the results from the Monte-Carlo runs this.mExpectedLogW = zeros (this.B, length (this.InspectedK)); this.CriterionName = "gap"; this.evaluate(this.InspectedK); # evaluate the list of cluster numbers endfunction ## set functions ## addK ## add new cluster sizes to evaluate function this = addK (this, K) addK@ClusterCriterion(this, K); ## if we have new data, we need a new evaluation if (this.OptimalK == 0) mExpectedLogW_tmp = zeros (this.B, length (this.InspectedK)); pS = 0; # position shift for iter = 1 : length (this.InspectedK) ## reorganize all the arrays according to the new list ## of cluster numbers if (any (this.InspectedK(iter) == K)) pS += 1; else mExpectedLogW_tmp(:, iter) = this.mExpectedLogW(:, iter - pS); endif endfor this.mExpectedLogW = mExpectedLogW_tmp; this.evaluate(K); # evaluate just the new cluster numbers endif endfunction ## compact ## ... function this = compact (this) # FIXME: stub! warning ("GapEvaluation: compact is unavailable"); endfunction ## plot ## plot the CriterionValues against InspectedK, show the standard deviation ## and return a handle to the plot function h = plot (this) yLabel = sprintf ("%s value", this.CriterionName); h = gca (); hold on; errorbar (this.InspectedK, this.CriterionValues, this.StdLogW); plot (this.InspectedK, this.CriterionValues, "bo"); plot (this.OptimalK, this.CriterionValues(this.OptimalIndex), "b*"); xlabel ("number of clusters"); ylabel (yLabel); hold off; endfunction endmethods methods (Access = protected) ## evaluate ## do the evaluation function this = evaluate (this, K) ## Monte-Carlo runs for mcrun = 1 : (this.B + 1) ## use complete observations only UsableX = this.X(find (this.Missing == false), :); ## the last run use tha actual data, ## the others are Monte-Carlo runs with reconstructed data if (mcrun <= this.B) ## uniform distribution colMins = min (UsableX); colMaxs = max (UsableX); for col = 1 : columns (UsableX) UsableX(:, col) = colMins(col) + rand (this.NumObservations, 1) *... (colMaxs(col) - colMins(col)); endfor endif if (! isempty (this.ClusteringFunction)) ## build the clusters for iter = 1 : length (this.InspectedK) ## do it only for the specified K values if (any (this.InspectedK(iter) == K)) if (isa (this.ClusteringFunction, "function_handle")) ## custom function ClusteringSolution = ... this.ClusteringFunction(UsableX, this.InspectedK(iter)); if (ismatrix (ClusteringSolution) && ... rows (ClusteringSolution) == this.NumObservations && ... columns (ClusteringSolution) == this.P) ## the custom function returned a matrix: ## we take the index of the maximum value for every row [~, this.ClusteringSolutions(:, iter)] = ... max (ClusteringSolution, [], 2); elseif (iscolumn (ClusteringSolution) && length (ClusteringSolution) == this.NumObservations) this.ClusteringSolutions(:, iter) = ClusteringSolution; elseif (isrow (ClusteringSolution) && length (ClusteringSolution) == this.NumObservations) this.ClusteringSolutions(:, iter) = ClusteringSolution'; else error (["GapEvaluation: invalid return value from " ... "custom clustering function"]); endif this.ClusteringSolutions(:, iter) = ... this.ClusteringFunction(UsableX, this.InspectedK(iter)); else switch (this.ClusteringFunction) case "kmeans" this.ClusteringSolutions(:, iter) = kmeans (UsableX, ... this.InspectedK(iter), "Distance", this.Distance, ... "EmptyAction", "singleton", "Replicates", 5); case "linkage" if (! isempty (this.Distance)) ## use clusterdata Distance_tmp = this.Distance; LinkageMethod = "average"; # for non euclidean methods if (strcmpi (this.Distance, "sqeuclidean")) ## pdist uses different names for its algorithms Distance_tmp = "squaredeuclidean"; LinkageMethod = "ward"; elseif (strcmpi (this.Distance, "euclidean")) LinkageMethod = "ward"; endif this.ClusteringSolutions(:, iter) = clusterdata ... (UsableX, "MaxClust", this.InspectedK(iter), ... "Distance", Distance_tmp, "Linkage", LinkageMethod); else ## use linkage Z = linkage (this.DistanceVector, "average"); this.ClusteringSolutions(:, iter) = ... cluster (Z, "MaxClust", this.InspectedK(iter)); endif case "gmdistribution" gmm = fitgmdist (UsableX, this.InspectedK(iter), ... "SharedCov", true, "Replicates", 5); this.ClusteringSolutions(:, iter) = cluster (gmm, UsableX); otherwise ## this should not happen error (["GapEvaluation: unexpected error, " ... "report this bug"]); endswitch endif endif endfor endif ## get the gap values for every clustering distance_pdist = this.Distance; if (strcmpi (distance_pdist, "sqeuclidean")) distance_pdist = "squaredeuclidean"; endif ## compute LogW for iter = 1 : length (this.InspectedK) ## do it only for the specified K values if (any (this.InspectedK(iter) == K)) wk = 0; for r = 1 : this.InspectedK(iter) vIndicesR = find (this.ClusteringSolutions(:, iter) == r); nr = length (vIndicesR); Dr = pdist (UsableX(vIndicesR, :), distance_pdist); wk += sum (Dr) / (2 * nr); endfor if (mcrun <= this.B) this.mExpectedLogW(mcrun, iter) = log (wk); else this.LogW(iter) = log (wk); endif endif endfor endfor this.ExpectedLogW = mean (this.mExpectedLogW); this.SE = sqrt ((1 + 1 / this.B) * sumsq (this.mExpectedLogW - ... this.ExpectedLogW) / this.B); this.StdLogW = std (this.mExpectedLogW); this.CriterionValues = this.ExpectedLogW - this.LogW; this.OptimalIndex = this.gapSearch (); this.OptimalK = this.InspectedK(this.OptimalIndex(1)); this.OptimalY = this.ClusteringSolutions(:, this.OptimalIndex(1)); endfunction ## gapSearch ## find the best solution according to the gap method function ind = gapSearch (this) if (strcmpi (this.SearchMethod, "globalmaxse")) [gapmax, indgp] = max (this.CriterionValues); for iter = 1 : length (this.InspectedK) ind = iter; if (this.CriterionValues(iter) > (gapmax - this.SE(indgp))) return endif endfor elseif (strcmpi (this.SearchMethod, "firstmaxse")) for iter = 1 : (length (this.InspectedK) - 1) ind = iter; if (this.CriterionValues(iter) > (this.CriterionValues(iter + 1) - ... this.SE(iter + 1))) return endif endfor else ## this should not happen error (["GapEvaluation: unexpected error, please report this bug"]); endif endfunction endmethods endclassdef statistics-1.4.3/inst/private/SilhouetteEvaluation.m0000644000000000000000000002474014153320774021076 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . classdef SilhouetteEvaluation < ClusterCriterion ## -*- texinfo -*- ## @deftypefn {Function File} {@var{eva} =} evalclusters (@var{x}, @var{clust}, @qcode{silhouette}) ## @deftypefnx {Function File} {@var{eva} =} evalclusters (@dots{}, @qcode{Name}, @qcode{Value}) ## ## A silhouette object to evaluate clustering solutions. ## ## A @code{SilhouetteEvaluation} object is a @code{ClusterCriterion} ## object used to evaluate clustering solutions using the silhouette ## criterion. ## ## List of public properties specific to @code{SilhouetteEvaluation}: ## @table @code ## @item @qcode{Distance} ## a valid distance metric name, or a function handle or a numeric array as ## generated by the @code{pdist} function. ## ## @item @qcode{ClusterPriors} ## a valid name for the evaluation of silhouette values: @code{empirical} ## (default) or @code{equal}. ## ## @item @qcode{ClusterSilhouettes} ## a cell array with the silhouette values of each data point for each cluster ## number. ## ## @end table ## ## The best solution according to the silhouette criterion is the one ## that scores the highest average silhouette value. ## @end deftypefn ## ## @seealso{ClusterCriterion, evalclusters, silhouette} properties (GetAccess = public, SetAccess = private) Distance = ""; # pdist parameter ClusterPriors = ""; # evaluation of silhouette values: equal or empirical ClusterSilhouettes = {}; # results of the silhoutte function for each K endproperties properties (Access = protected) DistanceVector = []; # vector of pdist distances endproperties methods (Access = public) ## constructor function this = SilhouetteEvaluation (x, clust, KList, ... distanceMetric = "sqeuclidean", clusterPriors = "empirical") this@ClusterCriterion(x, clust, KList); ## parsing the distance criterion if (ischar (distanceMetric)) if (any (strcmpi (distanceMetric, {"sqeuclidean", ... "euclidean", "cityblock", "cosine", "correlation", ... "hamming", "jaccard"}))) this.Distance = lower (distanceMetric); ## kmeans can use only a subset if (strcmpi (clust, "kmeans") && any (strcmpi (this.Distance, ... {"euclidean", "jaccard"}))) error (["SilhouetteEvaluation: invalid distance criterion '%s' "... "for 'kmeans'"], distanceMetric); endif else error ("SilhouetteEvaluation: unknown distance criterion '%s'", ... distanceMetric); endif elseif (isa (distanceMetric, "function_handle")) this.Distance = distanceMetric; ## kmeans cannot use a function handle if (strcmpi (clust, "kmeans")) error (["SilhouetteEvaluation: invalid distance criterion for "... "'kmeans'"]); endif elseif (isvector (distanceMetric) && isnumeric (distanceMetric)) this.Distance = ""; this.DistanceVector = distanceMetric; # the validity check is delegated ## kmeans cannot use a distance vector if (strcmpi (clust, "kmeans")) error (["SilhouetteEvaluation: invalid distance criterion for "... "'kmeans'"]); endif else error ("SilhouetteEvaluation: invalid distance metric"); endif ## parsing the prior probabilities of each cluster if (ischar (distanceMetric)) if (any (strcmpi (clusterPriors, {"empirical", "equal"}))) this.ClusterPriors = lower (clusterPriors); else error (["SilhouetteEvaluation: unknown prior probability criterion"... " '%s'"], clusterPriors); endif else error ("SilhouetteEvaluation: invalid prior probabilities"); endif this.CriterionName = "silhouette"; this.evaluate(this.InspectedK); # evaluate the list of cluster numbers endfunction ## set functions ## addK ## add new cluster sizes to evaluate function this = addK (this, K) addK@ClusterCriterion(this, K); ## if we have new data, we need a new evaluation if (this.OptimalK == 0) ClusterSilhouettes_tmp = {}; pS = 0; # position shift of the elements of ClusterSilhouettes for iter = 1 : length (this.InspectedK) ## reorganize ClusterSilhouettes according to the new list ## of cluster numbers if (any (this.InspectedK(iter) == K)) pS += 1; else ClusterSilhouettes_tmp{iter} = this.ClusterSilhouettes{iter - pS}; endif endfor this.ClusterSilhouettes = ClusterSilhouettes_tmp; this.evaluate(K); # evaluate just the new cluster numbers endif endfunction ## compact ## ... function this = compact (this) # FIXME: stub! warning ("SilhouetteEvaluation: compact is unavailable"); endfunction endmethods methods (Access = protected) ## evaluate ## do the evaluation function this = evaluate (this, K) ## use complete observations only UsableX = this.X(find (this.Missing == false), :); if (! isempty (this.ClusteringFunction)) ## build the clusters for iter = 1 : length (this.InspectedK) ## do it only for the specified K values if (any (this.InspectedK(iter) == K)) if (isa (this.ClusteringFunction, "function_handle")) ## custom function ClusteringSolution = ... this.ClusteringFunction(UsableX, this.InspectedK(iter)); if (ismatrix (ClusteringSolution) && ... rows (ClusteringSolution) == this.NumObservations && ... columns (ClusteringSolution) == this.P) ## the custom function returned a matrix: ## we take the index of the maximum value for every row [~, this.ClusteringSolutions(:, iter)] = ... max (ClusteringSolution, [], 2); elseif (iscolumn (ClusteringSolution) && length (ClusteringSolution) == this.NumObservations) this.ClusteringSolutions(:, iter) = ClusteringSolution; elseif (isrow (ClusteringSolution) && length (ClusteringSolution) == this.NumObservations) this.ClusteringSolutions(:, iter) = ClusteringSolution'; else error (["SilhouetteEvaluation: invalid return value from " ... "custom clustering function"]); endif this.ClusteringSolutions(:, iter) = ... this.ClusteringFunction(UsableX, this.InspectedK(iter)); else switch (this.ClusteringFunction) case "kmeans" this.ClusteringSolutions(:, iter) = kmeans (UsableX, ... this.InspectedK(iter), "Distance", this.Distance, ... "EmptyAction", "singleton", "Replicates", 5); case "linkage" if (! isempty (this.Distance)) ## use clusterdata Distance_tmp = this.Distance; LinkageMethod = "average"; # for non euclidean methods if (strcmpi (this.Distance, "sqeuclidean")) ## pdist uses different names for its algorithms Distance_tmp = "squaredeuclidean"; LinkageMethod = "ward"; elseif (strcmpi (this.Distance, "euclidean")) LinkageMethod = "ward"; endif this.ClusteringSolutions(:, iter) = clusterdata (UsableX,... "MaxClust", this.InspectedK(iter), ... "Distance", Distance_tmp, "Linkage", LinkageMethod); else ## use linkage Z = linkage (this.DistanceVector, "average"); this.ClusteringSolutions(:, iter) = ... cluster (Z, "MaxClust", this.InspectedK(iter)); endif case "gmdistribution" gmm = fitgmdist (UsableX, this.InspectedK(iter), ... "SharedCov", true, "Replicates", 5); this.ClusteringSolutions(:, iter) = cluster (gmm, UsableX); otherwise error (["SilhouetteEvaluation: unexpected error, " ... "report this bug"]); endswitch endif endif endfor endif ## get the silhouette values for every clustering set (0, 'DefaultFigureVisible', 'off'); # temporarily disable figures for iter = 1 : length (this.InspectedK) ## do it only for the specified K values if (any (this.InspectedK(iter) == K)) this.ClusterSilhouettes{iter} = silhouette (UsableX, ... this.ClusteringSolutions(:, iter)); if (strcmpi (this.ClusterPriors, "empirical")) this.CriterionValues(iter) = mean (this.ClusterSilhouettes{iter}); else ## equal this.CriterionValues(iter) = 0; si = this.ClusterSilhouettes{iter}; for k = 1 : this.InspectedK(iter) this.CriterionValues(iter) += mean (si(find ... (this.ClusteringSolutions(:, iter) == k))); endfor this.CriterionValues(iter) /= this.InspectedK(iter); endif endif endfor set (0, 'DefaultFigureVisible', 'on'); # enable figures again [~, this.OptimalIndex] = max (this.CriterionValues); this.OptimalK = this.InspectedK(this.OptimalIndex(1)); this.OptimalY = this.ClusteringSolutions(:, this.OptimalIndex(1)); endfunction endmethods endclassdef statistics-1.4.3/inst/private/tbl_delim.m0000644000000000000000000000401614153320774016646 0ustar0000000000000000## Copyright (C) 2008 Bill Denney ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{d}, @var{err}] = } tbl_delim (@var{d}) ## Return the delimiter for tblread or tblwrite. ## ## The delimeter, @var{d} may be any single character or ## @itemize ## @item "space" " " (default) ## @item "tab" "\t" ## @item "comma" "," ## @item "semi" ";" ## @item "bar" "|" ## @end itemize ## ## @var{err} will be empty if there is no error, and @var{d} will be NaN ## if there is an error. You MUST check the value of @var{err}. ## @seealso{tblread, tblwrite} ## @end deftypefn function [d, err] = tbl_delim (d) ## Check arguments if nargin != 1 print_usage (); endif err = ""; ## Format the delimiter if ischar (d) ## allow for escape characters d = sprintf (d); if numel (d) > 1 ## allow the word forms s.space = " "; s.tab = "\t"; s.comma = ","; s.semi = ";"; s.bar = "|"; if ! ismember (d, fieldnames (s)) err = ["tblread: delimiter must be either a single " ... "character or one of\n" ... sprintf("%s, ", fieldnames (s){:})(1:end-2)]; d = NaN; else d = s.(d); endif endif else err = "delimiter must be a character"; d = NaN; endif if isempty (d) err = "the delimiter may not be empty"; d = NaN; endif endfunction #tested in tblwrite statistics-1.4.3/inst/qrandn.m0000644000000000000000000000533714153320774014533 0ustar0000000000000000## Copyright (C) 2014 - Juan Pablo Carbajal ## ## This progrm is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## Author: Juan Pablo Carbajal ## -*- texinfo -*- ## @deftypefn {Function File} {@var{z} =} qrandn (@var{q}, @var{r},@var{c}) ## @deftypefnx {Function File} {@var{z} =} qrandn (@var{q}, [@var{r},@var{c}]) ## Returns random deviates drawn from a q-Gaussian distribution. ## ## Parameter @var{q} charcterizes the q-Gaussian distribution. ## The result has the size indicated by @var{s}. ## ## Reference: ## W. Thistleton, J. A. Marsh, K. Nelson, C. Tsallis (2006) ## "Generalized Box-Muller method for generating q-Gaussian random deviates" ## arXiv:cond-mat/0605570 http://arxiv.org/abs/cond-mat/0605570 ## ## @seealso{rand, randn} ## @end deftypefn function z = qrandn(q,R,C=[]) if !isscalar (q) error ('Octave:invalid-input-arg', 'The parameter q must be a scalar.') endif # Check that q < 3 if q > 3 error ('Octave:invalid-input-arg', 'The parameter q must be lower than 3.'); endif if numel (R) > 1 S = R; elseif numel (R) ==1 && isempty (C) S = [R,1]; elseif numel (R) ==1 && !isempty (C) S = [R,C]; endif # Calaulate the q to be used on the q-log qGen = (1 + q) / (3 - q); # Initialize the output vector z = sqrt (-2 * log_q (rand (S),qGen)) .* sin (2*pi*rand (S)); endfunction function a = log_q (x,q) # # Returns the q-log of x, using q # dq = 1 - q; # Check to see if q = 1 (to double precision) if abs (dq) < 10*eps # If q is 1, use the usual natural logarithm a = log (x); else # If q differs from 1, use the definition of the q-log a = ( x .^ dq - 1 ) ./ dq; endif endfunction %!demo %! z = qrandn (-5, 5e6); %! [c x] = hist (z,linspace(-1.5,1.5,200),1); %! figure(1) %! plot(x,c,"r."); axis tight; axis([-1.5,1.5]); %! %! z = qrandn (-0.14286, 5e6); %! [c x] = hist (z,linspace(-2,2,200),1); %! figure(2) %! plot(x,c,"r."); axis tight; axis([-2,2]); %! %! z = qrandn (2.75, 5e6); %! [c x] = hist (z,linspace(-1e3,1e3,1e3),1); %! figure(3) %! semilogy(x,c,"r."); axis tight; axis([-100,100]); %! %! # --------- %! # Figures from the reference paper. statistics-1.4.3/inst/random.m0000644000000000000000000001546214153320774014530 0ustar0000000000000000## Copyright (C) 2007 Soren Hauberg ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{r} = random(@var{name}, @var{arg1}) ## @deftypefnx{Function File} @var{r} = random(@var{name}, @var{arg1}, @var{arg2}) ## @deftypefnx{Function File} @var{r} = random(@var{name}, @var{arg1}, @var{arg2}, @var{arg3}) ## @deftypefnx{Function File} @var{r} = random(@var{name}, ..., @var{s1}, ...) ## Generates pseudo-random numbers from a given one-, two-, or three-parameter ## distribution. ## ## The variable @var{name} must be a string that names the distribution from ## which to sample. If this distribution is a one-parameter distribution @var{arg1} ## should be supplied, if it is a two-paramter distribution @var{arg2} must also ## be supplied, and if it is a three-parameter distribution @var{arg3} must also ## be present. Any arguments following the distribution paramters will determine ## the size of the result. ## ## As an example, the following code generates a 10 by 20 matrix containing ## random numbers from a normal distribution with mean 5 and standard deviation ## 2. ## @example ## R = random("normal", 5, 2, [10, 20]); ## @end example ## ## The variable @var{name} can be one of the following strings ## ## @table @asis ## @item "beta" ## @itemx "beta distribution" ## Samples are drawn from the Beta distribution. ## @item "bino" ## @itemx "binomial" ## @itemx "binomial distribution" ## Samples are drawn from the Binomial distribution. ## @item "chi2" ## @itemx "chi-square" ## @itemx "chi-square distribution" ## Samples are drawn from the Chi-Square distribution. ## @item "exp" ## @itemx "exponential" ## @itemx "exponential distribution" ## Samples are drawn from the Exponential distribution. ## @item "f" ## @itemx "f distribution" ## Samples are drawn from the F distribution. ## @item "gam" ## @itemx "gamma" ## @itemx "gamma distribution" ## Samples are drawn from the Gamma distribution. ## @item "geo" ## @itemx "geometric" ## @itemx "geometric distribution" ## Samples are drawn from the Geometric distribution. ## @item "hyge" ## @itemx "hypergeometric" ## @itemx "hypergeometric distribution" ## Samples are drawn from the Hypergeometric distribution. ## @item "logn" ## @itemx "lognormal" ## @itemx "lognormal distribution" ## Samples are drawn from the Log-Normal distribution. ## @item "nbin" ## @itemx "negative binomial" ## @itemx "negative binomial distribution" ## Samples are drawn from the Negative Binomial distribution. ## @item "norm" ## @itemx "normal" ## @itemx "normal distribution" ## Samples are drawn from the Normal distribution. ## @item "poiss" ## @itemx "poisson" ## @itemx "poisson distribution" ## Samples are drawn from the Poisson distribution. ## @item "rayl" ## @itemx "rayleigh" ## @itemx "rayleigh distribution" ## Samples are drawn from the Rayleigh distribution. ## @item "t" ## @itemx "t distribution" ## Samples are drawn from the T distribution. ## @item "unif" ## @itemx "uniform" ## @itemx "uniform distribution" ## Samples are drawn from the Uniform distribution. ## @item "unid" ## @itemx "discrete uniform" ## @itemx "discrete uniform distribution" ## Samples are drawn from the Uniform Discrete distribution. ## @item "wbl" ## @itemx "weibull" ## @itemx "weibull distribution" ## Samples are drawn from the Weibull distribution. ## @end table ## @seealso{rand, betarnd, binornd, chi2rnd, exprnd, frnd, gamrnd, geornd, hygernd, ## lognrnd, nbinrnd, normrnd, poissrnd, raylrnd, trnd, unifrnd, unidrnd, wblrnd} ## @end deftypefn function retval = random(name, varargin) ## General input checking if (nargin < 2) print_usage(); endif if (!ischar(name)) error("random: first input argument must be a string"); endif ## Select distribution switch (lower(name)) case {"beta", "beta distribution"} retval = betarnd(varargin{:}); case {"bino", "binomial", "binomial distribution"} retval = binornd(varargin{:}); case {"chi2", "chi-square", "chi-square distribution"} retval = chi2rnd(varargin{:}); case {"exp", "exponential", "exponential distribution"} retval = exprnd(varargin{:}); case {"ev", "extreme value", "extreme value distribution"} error("random: distribution type '%s' is not yet implemented", name); case {"f", "f distribution"} retval = frnd(varargin{:}); case {"gam", "gamma", "gamma distribution"} retval = gamrnd(varargin{:}); case {"gev", "generalized extreme value", "generalized extreme value distribution"} error("random: distribution type '%s' is not yet implemented", name); case {"gp", "generalized pareto", "generalized pareto distribution"} error("random: distribution type '%s' is not yet implemented", name); case {"geo", "geometric", "geometric distribution"} retval = geornd(varargin{:}); case {"hyge", "hypergeometric", "hypergeometric distribution"} retval = hygernd(varargin{:}); case {"logn", "lognormal", "lognormal distribution"} retval = lognrnd(varargin{:}); case {"nbin", "negative binomial", "negative binomial distribution"} retval = nbinrnd(varargin{:}); case {"ncf", "noncentral f", "noncentral f distribution"} error("random: distribution type '%s' is not yet implemented", name); case {"nct", "noncentral t", "noncentral t distribution"} error("random: distribution type '%s' is not yet implemented", name); case {"ncx2", "noncentral chi-square", "noncentral chi-square distribution"} error("random: distribution type '%s' is not yet implemented", name); case {"norm", "normal", "normal distribution"} retval = normrnd(varargin{:}); case {"poiss", "poisson", "poisson distribution"} retval = poissrnd(varargin{:}); case {"rayl", "rayleigh", "rayleigh distribution"} retval = raylrnd(varargin{:}); case {"t", "t distribution"} retval = trnd(varargin{:}); case {"unif", "uniform", "uniform distribution"} retval = unifrnd(varargin{:}); case {"unid", "discrete uniform", "discrete uniform distribution"} retval = unidrnd(varargin{:}); case {"wbl", "weibull", "weibull distribution"} retval = wblrnd(varargin{:}); otherwise error("random: unsupported distribution type '%s'", name); endswitch endfunction statistics-1.4.3/inst/randsample.m0000644000000000000000000001047414153320774015374 0ustar0000000000000000## Copyright (C) 2014 - Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## Author: Nir Krakauer ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} randsample (@var{v}, @var{k}, @var{replacement}=false [, @var{w}]) ## Elements sampled from a vector. ## ## Returns @var{k} random elements from a vector @var{v} with @var{n} elements, sampled without or with @var{replacement}. ## ## If @var{v} is a scalar, samples from 1:@var{v}. ## ## If a weight vector @var{w} of the same size as @var{v} is specified, the probablility of each element being sampled is proportional to @var{w}. Unlike Matlab's function of the same name, this can be done for sampling with or without replacement. ## ## Randomization is performed using rand(). ## ## @seealso{datasample, randperm} ## @end deftypefn function y = randsample(v,k,replacement=false,w=[]) if (isscalar (v) && isreal (v)) n = v; vector_v = false; elseif (isvector (v)) n = numel (v); vector_v = true; else error ('Octave:invalid-input-arg', 'randsample: The input v must be a vector or positive integer.'); endif if k < 0 || ( k > n && !replacement ) error ('Octave:invalid-input-arg', 'randsample: The input k must be a non-negative integer. Sampling without replacement needs k <= n.'); endif if (all (length (w) != [0, n])) error ('Octave:invalid-input-arg', 'randsample: the size w (%d) must match the first argument (%d)', length(w), n); endif if (replacement) # sample with replacement if (isempty (w)) # all elements are equally likely to be sampled y = round (n * rand(1, k) + 0.5); else y = weighted_replacement (k, w); endif else # sample without replacement if (isempty (w)) # all elements are equally likely to be sampled y = randperm (n, k); else # use "accept-reject"-like sampling y = weighted_replacement (k, w); while (1) [yy, idx] = sort (y); # Note: sort keeps order of equal elements. Idup = [false, (diff (yy)==0)]; if !any (Idup) break else Idup(idx) = Idup; # find duplicates in original vector w(y) = 0; # don't permit resampling # remove duplicates, then sample again y = [y(~Idup), (weighted_replacement (sum (Idup), w))]; endif endwhile endif endif if vector_v y = v(y); endif endfunction function y = weighted_replacement (k, w) w = w / sum(w); w = [0 cumsum(w(:))']; # distribute k uniform random deviates based on the given weighting y = arrayfun (@(x) find (w <= x, 1, "last"), rand (1, k)); endfunction %!test %! n = 20; %! k = 5; %! x = randsample(n, k); %! assert (size(x), [1 k]); %! x = randsample(n, k, true); %! assert (size(x), [1 k]); %! x = randsample(n, k, false); %! assert (size(x), [1 k]); %! x = randsample(n, k, true, ones(n, 1)); %! assert (size(x), [1 k]); %! x = randsample(1:n, k); %! assert (size(x), [1 k]); %! x = randsample(1:n, k, true); %! assert (size(x), [1 k]); %! x = randsample(1:n, k, false); %! assert (size(x), [1 k]); %! x = randsample(1:n, k, true, ones(n, 1)); %! assert (size(x), [1 k]); %! x = randsample((1:n)', k); %! assert (size(x), [k 1]); %! x = randsample((1:n)', k, true); %! assert (size(x), [k 1]); %! x = randsample((1:n)', k, false); %! assert (size(x), [k 1]); %! x = randsample((1:n)', k, true, ones(n, 1)); %! assert (size(x), [k 1]); %! n = 10; %! k = 100; %! x = randsample(n, k, true, 1:n); %! assert (size(x), [1 k]); %! x = randsample((1:n)', k, true); %! assert (size(x), [k 1]); %! x = randsample(k, k, false, 1:k); %! assert (size(x), [1 k]); statistics-1.4.3/inst/raylcdf.m0000644000000000000000000000617414153320774014674 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} =} raylcdf (@var{x}, @var{sigma}) ## Compute the cumulative distribution function of the Rayleigh ## distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{x} is the support. The elements of @var{x} must be non-negative. ## ## @item ## @var{sigma} is the parameter of the Rayleigh distribution. The elements ## of @var{sigma} must be positive. ## @end itemize ## @var{x} and @var{sigma} must be of common size or one of them must be ## scalar. ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{p} is the cumulative distribution of the Rayleigh distribution at ## each element of @var{x} and corresponding parameter @var{sigma}. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## x = 0:0.5:2.5; ## sigma = 1:6; ## p = raylcdf (x, sigma) ## @end group ## ## @group ## p = raylcdf (x, 0.5) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. pages 104 and 148, McGraw-Hill, New York, second edition, ## 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: CDF of the Rayleigh distribution function p = raylcdf (x, sigma) # Check arguments if (nargin != 2) print_usage (); endif if (! isempty (x) && ! ismatrix (x)) error ("raylcdf: x must be a numeric matrix"); endif if (! isempty (sigma) && ! ismatrix (sigma)) error ("raylcdf: sigma must be a numeric matrix"); endif if (! isscalar (x) || ! isscalar (sigma)) [retval, x, sigma] = common_size (x, sigma); if (retval > 0) error ("raylcdf: x and sigma must be of common size or scalar"); endif endif # Calculate cdf p = 1 - exp ((-x .^ 2) ./ (2 * sigma .^ 2)); # Continue argument check k = find (! (x >= 0) | ! (x < Inf) | ! (sigma > 0)); if (any (k)) p(k) = NaN; endif endfunction %!test %! x = 0:0.5:2.5; %! sigma = 1:6; %! p = raylcdf (x, sigma); %! expected_p = [0.0000, 0.0308, 0.0540, 0.0679, 0.0769, 0.0831]; %! assert (p, expected_p, 0.001); %!test %! x = 0:0.5:2.5; %! p = raylcdf (x, 0.5); %! expected_p = [0.0000, 0.3935, 0.8647, 0.9889, 0.9997, 1.0000]; %! assert (p, expected_p, 0.001); statistics-1.4.3/inst/raylinv.m0000644000000000000000000000636314153320774014734 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{x} =} raylinv (@var{p}, @var{sigma}) ## Compute the quantile of the Rayleigh distribution. The quantile is the ## inverse of the cumulative distribution function. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{p} is the cumulative distribution. The elements of @var{p} must be ## probabilities. ## ## @item ## @var{sigma} is the parameter of the Rayleigh distribution. The elements ## of @var{sigma} must be positive. ## @end itemize ## @var{p} and @var{sigma} must be of common size or one of them must be ## scalar. ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{x} is the quantile of the Rayleigh distribution at each element of ## @var{p} and corresponding parameter @var{sigma}. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## p = 0:0.1:0.5; ## sigma = 1:6; ## x = raylinv (p, sigma) ## @end group ## ## @group ## x = raylinv (p, 0.5) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. pages 104 and 148, McGraw-Hill, New York, second edition, ## 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Quantile of the Rayleigh distribution function x = raylinv (p, sigma) # Check arguments if (nargin != 2) print_usage (); endif if (! isempty (p) && ! ismatrix (p)) error ("raylinv: p must be a numeric matrix"); endif if (! isempty (sigma) && ! ismatrix (sigma)) error ("raylinv: sigma must be a numeric matrix"); endif if (! isscalar (p) || ! isscalar (sigma)) [retval, p, sigma] = common_size (p, sigma); if (retval > 0) error ("raylinv: p and sigma must be of common size or scalar"); endif endif # Calculate quantile x = sqrt (-2 .* log (1 - p) .* sigma .^ 2); k = find (p == 1); if (any (k)) x(k) = Inf; endif # Continue argument check k = find (! (p >= 0) | ! (p <= 1) | ! (sigma > 0)); if (any (k)) x(k) = NaN; endif endfunction %!test %! p = 0:0.1:0.5; %! sigma = 1:6; %! x = raylinv (p, sigma); %! expected_x = [0.0000, 0.9181, 2.0041, 3.3784, 5.0538, 7.0645]; %! assert (x, expected_x, 0.001); %!test %! p = 0:0.1:0.5; %! x = raylinv (p, 0.5); %! expected_x = [0.0000, 0.2295, 0.3340, 0.4223, 0.5054, 0.5887]; %! assert (x, expected_x, 0.001); statistics-1.4.3/inst/raylpdf.m0000644000000000000000000000620314153320774014702 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} raylpdf (@var{x}, @var{sigma}) ## Compute the probability density function of the Rayleigh distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{x} is the support. The elements of @var{x} must be non-negative. ## ## @item ## @var{sigma} is the parameter of the Rayleigh distribution. The elements ## of @var{sigma} must be positive. ## @end itemize ## @var{x} and @var{sigma} must be of common size or one of them must be ## scalar. ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{y} is the probability density of the Rayleigh distribution at each ## element of @var{x} and corresponding parameter @var{sigma}. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## x = 0:0.5:2.5; ## sigma = 1:6; ## y = raylpdf (x, sigma) ## @end group ## ## @group ## y = raylpdf (x, 0.5) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. pages 104 and 148, McGraw-Hill, New York, second edition, ## 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: PDF of the Rayleigh distribution function y = raylpdf (x, sigma) # Check arguments if (nargin != 2) print_usage (); endif if (! isempty (x) && ! ismatrix (x)) error ("raylpdf: x must be a numeric matrix"); endif if (! isempty (sigma) && ! ismatrix (sigma)) error ("raylpdf: sigma must be a numeric matrix"); endif if (! isscalar (x) || ! isscalar (sigma)) [retval, x, sigma] = common_size (x, sigma); if (retval > 0) error ("raylpdf: x and sigma must be of common size or scalar"); endif endif # Calculate pdf y = x .* exp ((-x .^ 2) ./ (2 .* sigma .^ 2)) ./ (sigma .^ 2); # Continue argument check k = find (! (x >= 0) | ! (x < Inf) | ! (sigma > 0)); if (any (k)) y(k) = NaN; endif endfunction %!test %! x = 0:0.5:2.5; %! sigma = 1:6; %! y = raylpdf (x, sigma); %! expected_y = [0.0000, 0.1212, 0.1051, 0.0874, 0.0738, 0.0637]; %! assert (y, expected_y, 0.001); %!test %! x = 0:0.5:2.5; %! y = raylpdf (x, 0.5); %! expected_y = [0.0000, 1.2131, 0.5413, 0.0667, 0.0027, 0.0000]; %! assert (y, expected_y, 0.001); statistics-1.4.3/inst/raylrnd.m0000644000000000000000000001053514153320774014717 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{x} =} raylrnd (@var{sigma}) ## @deftypefnx {Function File} {@var{x} =} raylrnd (@var{sigma}, @var{sz}) ## @deftypefnx {Function File} {@var{x} =} raylrnd (@var{sigma}, @var{r}, @var{c}) ## Generate a matrix of random samples from the Rayleigh distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{sigma} is the parameter of the Rayleigh distribution. The elements ## of @var{sigma} must be positive. ## ## @item ## @var{sz} is the size of the matrix to be generated. @var{sz} must be a ## vector of non-negative integers. ## ## @item ## @var{r} is the number of rows of the matrix to be generated. @var{r} must ## be a non-negative integer. ## ## @item ## @var{c} is the number of columns of the matrix to be generated. @var{c} ## must be a non-negative integer. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{x} is a matrix of random samples from the Rayleigh distribution with ## corresponding parameter @var{sigma}. If neither @var{sz} nor @var{r} and ## @var{c} are specified, then @var{x} is of the same size as @var{sigma}. ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## sigma = 1:6; ## x = raylrnd (sigma) ## @end group ## ## @group ## sz = [2, 3]; ## x = raylrnd (0.5, sz) ## @end group ## ## @group ## r = 2; ## c = 3; ## x = raylrnd (0.5, r, c) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. pages 104 and 148, McGraw-Hill, New York, second edition, ## 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Random samples from the Rayleigh distribution function x = raylrnd (sigma, r, c) # Check arguments if (nargin == 1) sz = size (sigma); elseif (nargin == 2) if (! isvector (r) || any ((r < 0) | round (r) != r)) error ("raylrnd: sz must be a vector of non-negative integers") endif sz = r(:)'; if (! isscalar (sigma) && ! isempty (sigma) && (length (size (sigma)) != length (sz) || any (size (sigma) != sz))) error ("raylrnd: sigma must be scalar or of size sz"); endif elseif (nargin == 3) if (! isscalar (r) || any ((r < 0) | round (r) != r)) error ("raylrnd: r must be a non-negative integer") endif if (! isscalar (c) || any ((c < 0) | round (c) != c)) error ("raylrnd: c must be a non-negative integer") endif sz = [r, c]; if (! isscalar (sigma) && ! isempty (sigma) && (length (size (sigma)) != length (sz) || any (size (sigma) != sz))) error ("raylrnd: sigma must be scalar or of size [r, c]"); endif else print_usage (); endif if (! isempty (sigma) && ! ismatrix (sigma)) error ("raylrnd: sigma must be a numeric matrix"); endif if (isempty (sigma)) x = []; elseif (isscalar (sigma) && ! (sigma > 0)) x = NaN .* ones (sz); else # Draw random samples x = sqrt (-2 .* log (1 - rand (sz)) .* sigma .^ 2); # Continue argument check k = find (! (sigma > 0)); if (any (k)) x(k) = NaN; endif endif endfunction %!test %! sigma = 1:6; %! x = raylrnd (sigma); %! assert (size (x), size (sigma)); %! assert (all (x >= 0)); %!test %! sigma = 0.5; %! sz = [2, 3]; %! x = raylrnd (sigma, sz); %! assert (size (x), sz); %! assert (all (x >= 0)); %!test %! sigma = 0.5; %! r = 2; %! c = 3; %! x = raylrnd (sigma, r, c); %! assert (size (x), [r, c]); %! assert (all (x >= 0)); statistics-1.4.3/inst/raylstat.m0000644000000000000000000000477214153320774015115 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} raylstat (@var{sigma}) ## Compute mean and variance of the Rayleigh distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{sigma} is the parameter of the Rayleigh distribution. The elements ## of @var{sigma} must be positive. ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the Rayleigh distribution. ## ## @item ## @var{v} is the variance of the Rayleigh distribution. ## @end itemize ## ## @subheading Example ## ## @example ## @group ## sigma = 1:6; ## [m, v] = raylstat (sigma) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the Rayleigh distribution function [m, v] = raylstat (sigma) # Check arguments if (nargin != 1) print_usage (); endif if (! isempty (sigma) && ! ismatrix (sigma)) error ("raylstat: sigma must be a numeric matrix"); endif # Calculate moments m = sigma .* sqrt (pi ./ 2); v = (2 - pi ./ 2) .* sigma .^ 2; # Continue argument check k = find (! (sigma > 0)); if (any (k)) m(k) = NaN; v(k) = NaN; endif endfunction %!test %! sigma = 1:6; %! [m, v] = raylstat (sigma); %! expected_m = [1.2533, 2.5066, 3.7599, 5.0133, 6.2666, 7.5199]; %! expected_v = [0.4292, 1.7168, 3.8628, 6.8673, 10.7301, 15.4513]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); statistics-1.4.3/inst/regress.m0000644000000000000000000001521114153320774014712 0ustar0000000000000000## Copyright (C) 2005, 2006 William Poetra Yoga Hadisoeseno ## Copyright (C) 2011 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{b}, @var{bint}, @var{r}, @var{rint}, @var{stats}] =} regress (@var{y}, @var{X}, [@var{alpha}]) ## Multiple Linear Regression using Least Squares Fit of @var{y} on @var{X} ## with the model @code{y = X * beta + e}. ## ## Here, ## ## @itemize ## @item ## @code{y} is a column vector of observed values ## @item ## @code{X} is a matrix of regressors, with the first column filled with ## the constant value 1 ## @item ## @code{beta} is a column vector of regression parameters ## @item ## @code{e} is a column vector of random errors ## @end itemize ## ## Arguments are ## ## @itemize ## @item ## @var{y} is the @code{y} in the model ## @item ## @var{X} is the @code{X} in the model ## @item ## @var{alpha} is the significance level used to calculate the confidence ## intervals @var{bint} and @var{rint} (see `Return values' below). If not ## specified, ALPHA defaults to 0.05 ## @end itemize ## ## Return values are ## ## @itemize ## @item ## @var{b} is the @code{beta} in the model ## @item ## @var{bint} is the confidence interval for @var{b} ## @item ## @var{r} is a column vector of residuals ## @item ## @var{rint} is the confidence interval for @var{r} ## @item ## @var{stats} is a row vector containing: ## ## @itemize ## @item The R^2 statistic ## @item The F statistic ## @item The p value for the full model ## @item The estimated error variance ## @end itemize ## @end itemize ## ## @var{r} and @var{rint} can be passed to @code{rcoplot} to visualize ## the residual intervals and identify outliers. ## ## NaN values in @var{y} and @var{X} are removed before calculation begins. ## ## @end deftypefn ## References: ## - Matlab 7.0 documentation (pdf) ## - Â¡Â¶Â´Ă³Ă‘Â§ĂĂ½Ă‘Â§ĂÂµĂ‘Ă©Â¡Â· Â½ÂªĂ†Ă´Ă”Â´ ÂµĂˆ (textbook) ## - http://www.netnam.vn/unescocourse/statistics/12_5.htm ## - wsolve.m in octave-forge ## - http://www.stanford.edu/class/ee263/ls_ln_matlab.pdf function [b, bint, r, rint, stats] = regress (y, X, alpha) if (nargin < 2 || nargin > 3) print_usage; endif if (! ismatrix (y)) error ("regress: y must be a numeric matrix"); endif if (! ismatrix (X)) error ("regress: X must be a numeric matrix"); endif if (columns (y) != 1) error ("regress: y must be a column vector"); endif if (rows (y) != rows (X)) error ("regress: y and X must contain the same number of rows"); endif if (nargin < 3) alpha = 0.05; elseif (! isscalar (alpha)) error ("regress: alpha must be a scalar value") endif notnans = ! logical (sum (isnan ([y X]), 2)); y = y(notnans); X = X(notnans,:); [Xq Xr] = qr (X, 0); pinv_X = Xr \ Xq'; b = pinv_X * y; if (nargout > 1) n = rows (X); p = columns (X); dof = n - p; t_alpha_2 = tinv (alpha / 2, dof); r = y - X * b; # added -- Nir SSE = sum (r .^ 2); v = SSE / dof; # c = diag(inv (X' * X)) using (economy) QR decomposition # which means that we only have to use Xr c = diag (inv (Xr' * Xr)); db = t_alpha_2 * sqrt (v * c); bint = [b + db, b - db]; endif if (nargout > 3) dof1 = n - p - 1; h = sum(X.*pinv_X', 2); #added -- Nir (same as diag(X*pinv_X), without doing the matrix multiply) # From Matlab's documentation on Multiple Linear Regression, # sigmaihat2 = norm (r) ^ 2 / dof1 - r .^ 2 / (dof1 * (1 - h)); # dr = -tinv (1 - alpha / 2, dof) * sqrt (sigmaihat2 .* (1 - h)); # Substitute # norm (r) ^ 2 == sum (r .^ 2) == SSE # -tinv (1 - alpha / 2, dof) == tinv (alpha / 2, dof) == t_alpha_2 # We get # sigmaihat2 = (SSE - r .^ 2 / (1 - h)) / dof1; # dr = t_alpha_2 * sqrt (sigmaihat2 .* (1 - h)); # Combine, we get # dr = t_alpha_2 * sqrt ((SSE * (1 - h) - (r .^ 2)) / dof1); dr = t_alpha_2 * sqrt ((SSE * (1 - h) - (r .^ 2)) / dof1); rint = [r + dr, r - dr]; endif if (nargout > 4) R2 = 1 - SSE / sum ((y - mean (y)) .^ 2); # F = (R2 / (p - 1)) / ((1 - R2) / dof); F = dof / (p - 1) / (1 / R2 - 1); pval = 1 - fcdf (F, p - 1, dof); stats = [R2 F pval v]; endif endfunction %!test %! % Longley data from the NIST Statistical Reference Dataset %! Z = [ 60323 83.0 234289 2356 1590 107608 1947 %! 61122 88.5 259426 2325 1456 108632 1948 %! 60171 88.2 258054 3682 1616 109773 1949 %! 61187 89.5 284599 3351 1650 110929 1950 %! 63221 96.2 328975 2099 3099 112075 1951 %! 63639 98.1 346999 1932 3594 113270 1952 %! 64989 99.0 365385 1870 3547 115094 1953 %! 63761 100.0 363112 3578 3350 116219 1954 %! 66019 101.2 397469 2904 3048 117388 1955 %! 67857 104.6 419180 2822 2857 118734 1956 %! 68169 108.4 442769 2936 2798 120445 1957 %! 66513 110.8 444546 4681 2637 121950 1958 %! 68655 112.6 482704 3813 2552 123366 1959 %! 69564 114.2 502601 3931 2514 125368 1960 %! 69331 115.7 518173 4806 2572 127852 1961 %! 70551 116.9 554894 4007 2827 130081 1962 ]; %! % Results certified by NIST using 500 digit arithmetic %! % b and standard error in b %! V = [ -3482258.63459582 890420.383607373 %! 15.0618722713733 84.9149257747669 %! -0.358191792925910E-01 0.334910077722432E-01 %! -2.02022980381683 0.488399681651699 %! -1.03322686717359 0.214274163161675 %! -0.511041056535807E-01 0.226073200069370 %! 1829.15146461355 455.478499142212 ]; %! Rsq = 0.995479004577296; %! F = 330.285339234588; %! y = Z(:,1); X = [ones(rows(Z),1), Z(:,2:end)]; %! alpha = 0.05; %! [b, bint, r, rint, stats] = regress (y, X, alpha); %! assert(b,V(:,1),3e-6); %! assert(stats(1),Rsq,1e-12); %! assert(stats(2),F,3e-8); %! assert(((bint(:,1)-bint(:,2))/2)/tinv(alpha/2,9),V(:,2),-1.e-5); statistics-1.4.3/inst/regress_gp.m0000644000000000000000000001065014153320774015402 0ustar0000000000000000## Copyright (c) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{K}] =} regress_gp (@var{x}, @var{y}, @var{Sp}) ## @deftypefnx {Function File} {[@dots{} @var{yi} @var{dy}] =} regress_gp (@dots{}, @var{xi}) ## Linear scalar regression using gaussian processes. ## ## It estimates the model @var{y} = @var{x}'*m for @var{x} R^D and @var{y} in R. ## The information about errors of the predictions (interpolation/extrapolation) is given ## by the covarianve matrix @var{K}. If D==1 the inputs must be column vectors, ## if D>1 then @var{x} is n-by-D, with n the number of data points. @var{Sp} defines ## the prior covariance of @var{m}, it should be a (D+1)-by-(D+1) positive definite matrix, ## if it is empty, the default is @code{Sp = 100*eye(size(x,2)+1)}. ## ## If @var{xi} inputs are provided, the model is evaluated and returned in @var{yi}. ## The estimation of the variation of @var{yi} are given in @var{dy}. ## ## Run @code{demo regress_gp} to see an examples. ## ## The function is a direc implementation of the formulae in pages 11-12 of ## Gaussian Processes for Machine Learning. Carl Edward Rasmussen and @ ## Christopher K. I. Williams. The MIT Press, 2006. ISBN 0-262-18253-X. ## available online at @url{http://gaussianprocess.org/gpml/}. ## ## @seealso{regress} ## @end deftypefn function [wm K yi dy] = regress_gp (x,y,Sp=[],xi=[]) if isempty(Sp) Sp = 100*eye(size(x,2)+1); end x = [ones(1,size(x,1)); x']; ## Juan Pablo Carbajal ## Note that in the book the equation (below 2.11) for the A reads ## A = (1/sy^2)*x*x' + inv (Vp); ## where sy is the scalar variance of the of the residuals (i.e y = x' * w + epsilon) ## and epsilon is drawn from N(0,sy^2). Vp is the variance of the parameters w. ## Note that ## (sy^2 * A)^{-1} = (1/sy^2)*A^{-1} = (x*x' + sy^2 * inv(Vp))^{-1}; ## and that the formula for the w mean is ## (1/sy^2)*A^{-1}*x*y ## Then one obtains ## inv(x*x' + sy^2 * inv(Vp))*x*y ## Looking at the formula bloew we see that Sp = (1/sy^2)*Vp ## making the regression depend on only one parameter, Sp, and not two. A = x*x' + inv (Sp); K = inv (A); wm = K*x*y; yi =[]; dy =[]; if !isempty (xi); xi = [ones(size(xi,1),1) xi]; yi = xi*wm; dy = diag (xi*K*xi'); end endfunction %!demo %! % 1D Data %! x = 2*rand (5,1)-1; %! y = 2*x -1 + 0.3*randn (5,1); %! %! % Points for interpolation/extrapolation %! xi = linspace (-2,2,10)'; %! %! [m K yi dy] = regress_gp (x,y,[],xi); %! %! plot (x,y,'xk',xi,yi,'r-',xi,bsxfun(@plus, yi, [-dy +dy]),'b-'); %!demo %! % 2D Data %! x = 2*rand (4,2)-1; %! y = 2*x(:,1)-3*x(:,2) -1 + 1*randn (4,1); %! %! % Mesh for interpolation/extrapolation %! [xi yi] = meshgrid (linspace (-1,1,10)); %! %! [m K zi dz] = regress_gp (x,y,[],[xi(:) yi(:)]); %! zi = reshape (zi, 10,10); %! dz = reshape (dz,10,10); %! %! plot3 (x(:,1),x(:,2),y,'.g','markersize',8); %! hold on; %! h = mesh (xi,yi,zi,zeros(10,10)); %! set(h,'facecolor','none'); %! h = mesh (xi,yi,zi+dz,ones(10,10)); %! set(h,'facecolor','none'); %! h = mesh (xi,yi,zi-dz,ones(10,10)); %! set(h,'facecolor','none'); %! hold off %! axis tight %! view(80,25) %!demo %! % Projection over basis function %! pp = [2 2 0.3 1]; %! n = 10; %! x = 2*rand (n,1)-1; %! y = polyval(pp,x) + 0.3*randn (n,1); %! %! % Powers %! px = [sqrt(abs(x)) x x.^2 x.^3]; %! %! % Points for interpolation/extrapolation %! xi = linspace (-1,1,100)'; %! pxi = [sqrt(abs(xi)) xi xi.^2 xi.^3]; %! %! Sp = 100*eye(size(px,2)+1); %! Sp(2,2) = 1; # We don't believe the sqrt is present %! [m K yi dy] = regress_gp (px,y,Sp,pxi); %! disp(m) %! %! plot (x,y,'xk;Data;',xi,yi,'r-;Estimation;',xi,polyval(pp,xi),'g-;True;'); %! axis tight %! axis manual %! hold on %! plot (xi,bsxfun(@plus, yi, [-dy +dy]),'b-'); %! hold off statistics-1.4.3/inst/repanova.m0000644000000000000000000001002614153320774015052 0ustar0000000000000000## Copyright (C) 2011 Kyle Winfree ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{pval}, @var{table}, @var{st}] =} repanova (@var{X}, @var{cond}) ## @deftypefnx {Function File} {[@var{pval}, @var{table}, @var{st}] =} repanova (@var{X}, @var{cond}, ['string' | 'cell']) ## Perform a repeated measures analysis of variance (Repeated ANOVA). ## X is formated such that each row is a subject and each column is a condition. ## ## condition is typically a point in time, say t=1 then t=2, etc ## condition can also be thought of as groups. ## ## The optional flag can be either 'cell' or 'string' and reflects ## the format of the table returned. Cell is the default. ## ## NaNs are ignored using nanmean and nanstd. ## ## This fuction does not currently support multiple columns of the same ## condition! ## @end deftypefn function [p, table, st] = repanova(varargin) switch nargin case 0 error('Too few inputs.'); case 1 X = varargin{1}; for c = 1:size(X, 2) condition{c} = ['time', num2str(c)]; end option = 'cell'; case 2 X = varargin{1}; condition = varargin{2}; option = 'cell'; case 3 X = varargin{1}; condition = varargin{2}; option = varargin{3}; otherwise error('Too many inputs.'); end % Find the means of the subjects and measures, ignoring any NaNs u_subjects = nanmean(X,2); u_measures = nanmean(X,1); u_grand = nansum(nansum(X)) / (size(X,1) * size(X,2)); % Differences between rows will be reflected in SS subjects, differences % between columns will be reflected in SS_within subjects. N = size(X,1); % number of subjects J = size(X,2); % number of samples per subject SS_measures = N * nansum((u_measures - u_grand).^2); SS_subjects = J * nansum((u_subjects - u_grand).^2); SS_total = nansum(nansum((X - u_grand).^2)); SS_error = SS_total - SS_measures - SS_subjects; df_measures = J - 1; df_subjects = N - 1; df_grand = (N*J) - 1; df_error = df_grand - df_measures - df_subjects; MS_measures = SS_measures / df_measures; MS_subjects = SS_subjects / df_subjects; MS_error = SS_error / df_error; % variation expected as a result of sampling error alone F = MS_measures / MS_error; p = 1 - fcdf(F, df_measures, df_error); % Probability of F given equal means. if strcmp(option, 'string') table = [sprintf('\nSource\tSS\tdf\tMS\tF\tProb > F'), ... sprintf('\nSubject\t%g\t%i\t%g', SS_subjects, df_subjects, MS_subjects), ... sprintf('\nMeasure\t%g\t%i\t%g\t%g\t%g', SS_measures, df_measures, MS_measures, F, p), ... sprintf('\nError\t%g\t%i\t%g', SS_error, df_error, MS_error), ... sprintf('\n')]; else table = {'Source', 'Partial SS', 'df', 'MS', 'F', 'Prob > F'; ... 'Subject', SS_subjects, df_subjects, MS_subjects, '', ''; ... 'Measure', SS_measures, df_measures, MS_measures, F, p}; end st.gnames = condition'; % this is the same struct format used in anova1 st.n = repmat(N, 1, J); st.source = 'anova1'; % it cannot be assumed that 'repanova' is a supported source for multcompare st.means = u_measures; st.df = df_error; st.s = sqrt(MS_error); end % This function was created with guidance from the following websites: % http://courses.washington.edu/stat217/rmANOVA.html % http://grants.hhp.coe.uh.edu/doconnor/PEP6305/Topic%20010%20Repeated%20Measures.htm statistics-1.4.3/inst/runstest.m0000644000000000000000000001243114153320774015130 0ustar0000000000000000## Copyright (C) 2013 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h}, @var{p}, @var{stats} =} runstest (@var{x}, @var{v}) ## Runs test for detecting serial correlation in the vector @var{x}. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{x} is the vector of given values. ## @item ## @var{v} is the value to subtract from @var{x} to get runs (defaults to @code{median(x)}) ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{h} is true if serial correlation is detected at the 95% confidence level (two-tailed), false otherwise. ## @item ## @var{p} is the probablity of obtaining a test statistic of the magnitude found under the null hypothesis of no serial correlation. ## @item ## @var{stats} is the structure containing as fields the number of runs @var{nruns}; the numbers of positive and negative values of @code{x - v}, @var{n1} and @var{n0}; and the test statistic @var{z}. ## ## @end itemize ## ## Note: the large-sample normal approximation is used to find @var{h} and @var{p}. This is accurate if @var{n1}, @var{n0} are both greater than 10. ## ## Reference: ## NIST Engineering Statistics Handbook, 1.3.5.13. Runs Test for Detecting Non-randomness, http://www.itl.nist.gov/div898/handbook/eda/section3/eda35d.htm ## ## @seealso{} ## @end deftypefn ## Author: Nir Krakauer ## Description: Runs test for detecting serial correlation function [h, p, stats] = runstest (x, x2) # Check arguments if (nargin < 1) print_usage; endif if nargin > 1 && isnumeric(x2) v = x2; else v = median(x); endif x = x(~isnan(x)); #delete missing values x = sign(x - v); x = x(x ~= 0); #delete any zeros R = sum((x(1:(end-1)) .* x(2:end)) < 0) + 1; #number of runs #expected number of runs for an iid sequence n1 = sum(x > 0); n2 = sum(x < 0); R_bar = 1 + 2*n1*n2/(n1 + n2); #standard deviation of number of runs for an iid sequence s_R = sqrt(2*n1*n2*(2*n1*n2 - n1 - n2)/((n1 + n2)^2 * (n1 + n2 - 1))); #desired significance level alpha = 0.05; Z = (R - R_bar) / s_R; #test statistic p = 2 * normcdf(-abs(Z)); h = p < alpha; if nargout > 2 stats.nruns = R; stats.n1 = n1; stats.n0 = n2; stats.z = Z; endif endfunction %!test %! data = [-213 -564 -35 -15 141 115 -420 -360 203 -338 -431 194 -220 -513 154 -125 -559 92 -21 -579 -52 99 -543 -175 162 -457 -346 204 -300 -474 164 -107 -572 -8 83 -541 -224 180 -420 -374 201 -236 -531 83 27 -564 -112 131 -507 -254 199 -311 -495 143 -46 -579 -90 136 -472 -338 202 -287 -477 169 -124 -568 17 48 -568 -135 162 -430 -422 172 -74 -577 -13 92 -534 -243 194 -355 -465 156 -81 -578 -64 139 -449 -384 193 -198 -538 110 -44 -577 -6 66 -552 -164 161 -460 -344 205 -281 -504 134 -28 -576 -118 156 -437 -381 200 -220 -540 83 11 -568 -160 172 -414 -408 188 -125 -572 -32 139 -492 -321 205 -262 -504 142 -83 -574 0 48 -571 -106 137 -501 -266 190 -391 -406 194 -186 -553 83 -13 -577 -49 103 -515 -280 201 300 -506 131 -45 -578 -80 138 -462 -361 201 -211 -554 32 74 -533 -235 187 -372 -442 182 -147 -566 25 68 -535 -244 194 -351 -463 174 -125 -570 15 72 -550 -190 172 -424 -385 198 -218 -536 96]; #NIST beam deflection data, http://www.itl.nist.gov/div898/handbook/eda/section4/eda425.htm %! [h, p, stats] = runstest (data); %! expected_h = true; %! expected_p = 0.0070646; %! expected_z = 2.6938; %! assert (h, expected_h); %! assert (p, expected_p, 1E-6); %! assert (stats.z, expected_z, 1E-4); statistics-1.4.3/inst/sigma_pts.m0000644000000000000000000000764614153320774015243 0ustar0000000000000000## Copyright (C) 2017 - Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## Author: Juan Pablo Carbajal ## -*- texinfo -*- ## @deftypefn {} {@var{pts} =} sigma_pts (@var{n}) ## @deftypefnx {@var{pts} =} sigma_pts (@var{n}, @var{m}) ## @deftypefnx {@var{pts} =} sigma_pts (@var{n}, @var{m}, @var{K}) ## @deftypefnx {@var{pts} =} sigma_pts (@var{n}, @var{m}, @var{K}, @var{l}) ## Calculates 2*@var{n}+1 sigma points in @var{n} dimensions. ## ## Sigma points are used in the unscented transfrom to estimate ## the result of applying a given nonlinear transformation to a probability ## distribution that is characterized only in terms of a finite set of statistics. ## ## If only the dimension @var{n} is given the resulting points have zero mean ## and identity covariance matrix. ## If the mean @var{m} or the covaraince matrix @var{K} are given, then the resulting points ## will have those statistics. ## The factor @var{l} scaled the points away from the mean. It is useful to tune ## the accuracy of the unscented transfrom. ## ## There is no unique way of computing sigma points, this function implements the ## algorithm described in section 2.6 "The New Filter" pages 40-41 of ## ## Uhlmann, Jeffrey (1995). "Dynamic Map Building and Localization: New Theoretical Foundations". ## Ph.D. thesis. University of Oxford. ## ## @end deftypefn function pts = sigma_pts (n, m = [], K = [], l = 0) if isempty (K) K = eye (n); endif if isempty (m) m = zeros (1, n); endif if (n ~= length (m)) error ("Dimension and size of mean vector don't match.") endif if any(n ~= size (K)) error ("Dimension and size of covariance matrix don't match.") endif if isdefinite (K) <= 0 error ("Covariance matrix should be positive definite.") endif pts = zeros (2 * n + 1, n); pts(1,:) = m; K = sqrtm ((n + l) * K); pts(2:n+1,:) = bsxfun (@plus, m , K); pts(n+2:end,:) = bsxfun (@minus, m , K); endfunction %!demo %! K = [1 0.5; 0.5 1]; # covaraince matrix %! # calculate and build associated ellipse %! [R,S,~] = svd (K); %! theta = atan2 (R(2,1), R(1,1)); %! v = sqrt (diag (S)); %! v = v .* [cos(theta) sin(theta); -sin(theta) cos(theta)]; %! t = linspace (0, 2*pi, 100).'; %! xe = v(1,1) * cos (t) + v(2,1) * sin (t); %! ye = v(1,2) * cos (t) + v(2,2) * sin (t); %! %! figure(1); clf; hold on %! # Plot ellipse and axes %! line ([0 0; v(:,1).'],[0 0; v(:,2).']) %! plot (xe,ye,'-r'); %! %! col = 'rgb'; %! l = [-1.8 -1 1.5]; %! for li = 1:3 %! p = sigma_pts (2, [], K, l(li)); %! tmp = plot (p(2:end,1), p(2:end,2), ['x' col(li)], ... %! p(1,1), p(1,2), ['o' col(li)]); %! h(li) = tmp(1); %! endfor %! hold off %! axis image %! legend (h, arrayfun (@(x) sprintf ("l:%.2g", x), l, "unif", 0)); %!test %! p = sigma_pts (5); %! assert (mean (p), zeros(1,5), sqrt(eps)); %! assert (cov (p), eye(5), sqrt(eps)); %!test %! m = randn(1, 5); %! p = sigma_pts (5, m); %! assert (mean (p), m, sqrt(eps)); %! assert (cov (p), eye(5), sqrt(eps)); %!test %! x = linspace (0,1,5); %! K = exp (- (x.' - x).^2/ 0.5); %! p = sigma_pts (5, [], K); %! assert (mean (p), zeros(1,5), sqrt(eps)); %! assert (cov (p), K, sqrt(eps)); %!error sigma_pts(2,1); %!error sigma_pts(2,[],1); %!error sigma_pts(2,1,1); %!error sigma_pts(2,[0.5 0.5],[-1 0; 0 0]); statistics-1.4.3/inst/signtest.m0000644000000000000000000001236214153320774015104 0ustar0000000000000000## Copyright (C) 2014 Tony Richardson ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{pval}, @var{h}, @var{stats}] =} signtest (@var{x}) ## @deftypefnx {Function File} {[@var{pval}, @var{h}, @var{stats}] =} signtest (@var{x}, @var{m}) ## @deftypefnx {Function File} {[@var{pval}, @var{h}, @var{stats}] =} signtest (@var{x}, @var{y}) ## @deftypefnx {Function File} {[@var{pval}, @var{h}, @var{stats}] =} signtest (@var{x}, @var{y}, @var{Name}, @var{Value}) ## Test for median. ## ## Perform a signtest of the null hypothesis that @var{x} is from a distribution ## that has a zero median. ## ## If the second argument @var{m} is a scalar, the null hypothesis is that ## X has median m. ## ## If the second argument @var{y} is a vector, the null hypothesis is that ## the distribution of @code{@var{x} - @var{y}} has zero median. ## ## The argument @qcode{"alpha"} can be used to specify the significance level ## of the test (the default value is 0.05). The string ## argument @qcode{"tail"}, can be used to select the desired alternative ## hypotheses. If @qcode{"alt"} is @qcode{"both"} (default) the null is ## tested against the two-sided alternative @code{median (@var{x}) != @var{m}}. ## If @qcode{"alt"} is @qcode{"right"} the one-sided ## alternative @code{median (@var{x}) > @var{m}} is considered. ## Similarly for @qcode{"left"}, the one-sided alternative @code{median ## (@var{x}) < @var{m}} is considered. When @qcode{"method"} is @qcode{"exact"} ## the p-value is computed using an exact method (this is the default). When ## @qcode{"method"} is @qcode{"approximate"} a normal approximation is used for the ## test statistic. ## ## The p-value of the test is returned in @var{pval}. If @var{h} is 0 the ## null hypothesis is accepted, if it is 1 the null hypothesis is rejected. ## @var{stats} is a structure containing the value of the test statistic ## (@var{sign}) and the value of the z statistic (@var{zval}) (only computed ## when the 'method' is 'approximate'. ## ## @end deftypefn ## Author: Tony Richardson function [p, h, stats] = signtest(x, my, varargin) my_default = 0; alpha = 0.05; tail = 'both'; method = 'exact'; % Find the first non-singleton dimension of x dim = min(find(size(x)~=1)); if isempty(dim), dim = 1; end if (nargin == 1) my = my_default; end i = 1; while ( i <= length(varargin) ) switch lower(varargin{i}) case 'alpha' i = i + 1; alpha = varargin{i}; case 'tail' i = i + 1; tail = varargin{i}; case 'method' i = i + 1; method = varargin{i}; case 'dim' i = i + 1; dim = varargin{i}; otherwise error('Invalid Name argument.',[]); end i = i + 1; end if ~isa(tail, 'char') error('tail argument to signtest must be a string\n',[]); end if ~isa(method, 'char') error('method argument to signtest must be a string\n',[]); end % Set default values if arguments are present but empty if isempty(my) my = my_default; end % This adjustment allows everything else to remain the % same for both the one-sample t test and paired tests. % If second argument is a vector if ~isscalar(my) x = x - my; my = my_default; end n = size(x, dim); switch lower(method) case 'exact' stats.zval = nan; switch lower(tail) case 'both' w = min(sum(xmy)); pl = binocdf(w, n, 0.5); p = 2*min(pl,1-pl); case 'left' w = sum(xmy); p = 1 - binocdf(w, n, 0.5); otherwise error('Invalid tail argument to signtest\n',[]); end case 'approximate' switch lower(tail) case 'both' npos = sum(x>my); nneg = sum(xmy); nneg = sum(xmy); nneg = sum(xmy); stats.zval = (w - 0.5*n - 0.5*sign(npos-nneg))/sqrt(0.25*n); p = 1-normcdf(stats.zval); otherwise error('Invalid tail argument to signtest\n',[]); end otherwise error('Invalid method argument to signtest\n',[]); end stats.sign = w; h = double(p < alpha); end statistics-1.4.3/inst/silhouette.m0000644000000000000000000001502114153320774015424 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## Copyright (C) 2016 Nan Zhou ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @ ## {[@var{si}, @var{h}] =} silhouette (@var{X}, @var{clust}) ## @deftypefnx {Function File} @ ## {[@var{si}, @var{h}] =} silhouette (@dots{}, @var{Metric}, @var{MetricArg}) ## ## Compute the silhouette values of clustered data and show them on a plot. ## ## @var{X} is a n-by-p matrix of n data points in a p-dimensional space. Each ## datapoint is assigned to a cluster using @var{clust}, a vector of n elements, ## one cluster assignment for each data point. ## ## Each silhouette value of @var{si}, a vector of size n, is a measure of the ## likelihood that a data point is accurately classified to the right cluster. ## Defining "a" as the mean distance between a point and the other points from ## its cluster, and "b" as the mean distance between that point and the points ## from other clusters, the silhouette value of the i-th point is: ## ## @tex ## \def\frac#1#2{{\begingroup#1\endgroup\over#2}} ## $$ S_i = \frac{b_i - a_i}{max(a_1,b_i)} $$ ## @end tex ## @ifnottex ## @verbatim ## bi - ai ## Si = ------------ ## max(ai,bi) ## @end verbatim ## @end ifnottex ## ## Each element of @var{si} ranges from -1, minimum likelihood of a correct ## classification, to 1, maximum likelihood. ## ## Optional input value @var{Metric} is the metric used to compute the distances ## between data points. Since @code{silhouette} uses @code{pdist} to compute ## these distances, @var{Metric} is quite similar to the option @var{Metric} of ## pdist and it can be: ## @itemize @bullet ## @item A known distance metric defined as a string: @qcode{Euclidean}, ## @qcode{sqEuclidean} (default), @qcode{cityblock}, @qcode{cosine}, ## @qcode{correlation}, @qcode{Hamming}, @qcode{Jaccard}. ## ## @item A vector as those created by @code{pdist}. In this case @var{X} does ## nothing. ## ## @item A function handle that is passed to @code{pdist} with @var{MetricArg} ## as optional inputs. ## @end itemize ## ## Optional return value @var{h} is a handle to the silhouette plot. ## ## @strong{Reference} ## Peter J. Rousseeuw, Silhouettes: a Graphical Aid to the Interpretation and ## Validation of Cluster Analysis. 1987. doi:10.1016/0377-0427(87)90125-7 ## @end deftypefn ## ## @seealso{dendrogram, evalcluster, kmeans, linkage, pdist} function [si, h] = silhouette (X, clust, metric = "sqeuclidean", varargin) ## check the input parameters if (nargin < 2) print_usage (); endif n = size (clust, 1); ## check size if (! isempty (X)) if (size (X, 1) != n) error ("First dimension of X <%d> doesn't match that of clust <%d>",... size (X, 1), n); endif endif ## check metric if (ischar (metric)) metric = lower (metric); switch (metric) case "sqeuclidean" metric = "squaredeuclidean"; case { "euclidean", "cityblock", "cosine", ... "correlation", "hamming", "jaccard" } ; otherwise error ("silhouette: invalid metric '%s'", metric); endswitch elseif (isnumeric (metric) && isvector (metric)) ## X can be omitted when using this distMatrix = squareform (metric); if (size (distMatrix, 1) != n) error ("First dimension of X <%d> doesn't match that of clust <%d>",... size (distMatrix, 1), n); endif endif ## main si = zeros(n, 1); clusterIDs = unique (clust); # eg [1; 2; 3; 4] m = length (clusterIDs); ## if only one cluster is defined, the silhouette value is not defined if (m == 1) si = NaN * ones (n, 1); return; endif ## distance matrix showing the distance for any two rows of X if (! exist ('distMatrix', 'var')) distMatrix = squareform (pdist (X, metric, varargin{:})); endif ## calculate values of si one by one for iii = 1 : length (si) ## allocate values to clusters groupedValues = {}; for jjj = 1 : m groupedValues{clusterIDs(jjj)} = [distMatrix(iii, ... clust == clusterIDs(jjj))]; endfor ## end allocation ## calculate a(i) ## average distance of iii to all other objects in the same cluster if (length (groupedValues{clust(iii)}) == 1) si(iii) = 1; continue; else a_i = (sum (groupedValues{clust(iii)})) / ... (length (groupedValues{clust(iii)}) - 1); endif ## end a(i) ## calculate b(i) clusterIDs_new = clusterIDs; ## remove the cluster iii in clusterIDs_new(find (clusterIDs_new == clust(iii))) = []; ## average distance of iii to all objects of another cluster a_iii_2others = zeros (length (clusterIDs_new), 1); for jjj = 1 : length (clusterIDs_new) a_iii_2others(jjj) = mean (groupedValues{clusterIDs_new(jjj)}); endfor b_i = min (a_iii_2others); ## end b(i) ## calculate s(i) si(iii) = (b_i - a_i) / (max ([a_i; b_i])); ## end s(i) endfor ## plot ## a poor man silhouette graph vBarsc = zeros (m, 1); vPadding = [0; 0; 0; 0]; Bars = vPadding; for i = 1 : m vBar = si(find (clust == clusterIDs(i))); vBarsc(i) = length (Bars) + (length (vBar) / 2); Bars = [Bars; (sort (vBar, "descend")); vPadding]; endfor figure(); h = barh (Bars, "hist", "facecolor", [0 0.4471 0.7412]); xlabel ("Silhouette Value"); ylabel ("Cluster"); set (gca, "ytick", vBarsc, "yticklabel", clusterIDs); ylim ([0 (length (Bars))]); axis ("ij"); endfunction %!error silhouette (); %!error silhouette ([1 2; 1 1]); %!error silhouette ([1 2; 1 1], [1 2 3]'); %!error silhouette ([1 2; 1 1], [1 2]', "xxx"); %!demo %! load fisheriris; %! X = meas(:,3:4); %! cidcs = kmeans (X, 3, "Replicates", 5); %! silhouette (X, cidcs); %! y_labels(cidcs([1 51 101])) = unique (species); %! set (gca, "yticklabel", y_labels); %! title ("Fisher's iris data"); statistics-1.4.3/inst/slicesample.m0000644000000000000000000002171314153320774015545 0ustar0000000000000000######################################################################## ## ## Copyright (C) 1993-2021 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or . ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {[@var{smpl}, @var{neval}] =} slicesample (@var{start}, @var{nsamples}, @var{property}, @var{value}, @dots{}) ## Draws @var{nsamples} samples from a target stationary distribution @var{pdf} ## using slice sampling of Radford M. Neal. ## ## Input: ## @itemize ## @item ## @var{start} is a 1 by @var{dim} vector of the starting point of the ## Markov chain. Each column corresponds to a different dimension. ## ## @item ## @var{nsamples} is the number of samples, the length of the Markov chain. ## @end itemize ## ## Next, several property-value pairs can or must be specified, they are: ## ## (Required properties) One of: ## ## @itemize ## @item ## @var{"pdf"}: the value is a function handle of the target stationary ## distribution to be sampled. The function should accept different locations ## in each row and each column corresponds to a different dimension. ## ## or ## ## @item ## @var{logpdf}: the value is a function handle of the log of the target ## stationary distribution to be sampled. The function should accept different ## locations in each row and each column corresponds to a different dimension. ## @end itemize ## ## The following input property/pair values may be needed depending on the ## desired outut: ## ## @itemize ## @item ## "burnin" @var{burnin} the number of points to discard at the beginning, the default ## is 0. ## ## @item ## "thin" @var{thin} omitts @var{m}-1 of every @var{m} points in the generated ## Markov chain. The default is 1. ## ## @item ## "width" @var{width} the maximum Manhattan distance between two samples. ## The default is 10. ## @end itemize ## ## Outputs: ## @itemize ## ## @item ## @var{smpl} is a @var{nsamples} by @var{dim} matrix of random ## values drawn from @var{pdf} where the rows are different random values, the ## columns correspond to the dimensions of @var{pdf}. ## ## @item ## @var{neval} is the number of function evaluations per sample. ## @end itemize ## Example : Sampling from a normal distribution ## ## @example ## @group ## start = 1; ## nsamples = 1e3; ## pdf = @@(x) exp (-.5 * x .^ 2) / (pi ^ .5 * 2 ^ .5); ## [smpl, accept] = slicesample (start, nsamples, "pdf", pdf, "thin", 4); ## histfit (smpl); ## @end group ## @end example ## ## @seealso{rand, mhsample, randsample} ## @end deftypefn function [smpl, neval] = slicesample (start, nsamples, varargin) if (nargin < 4) print_usage (); endif sizestart = size (start); pdf = []; logpdf = []; width = 10; burnin = 0; thin = 1; for k = 1:2:length (varargin) if (ischar (varargin{k})) switch lower (varargin{k}) case "pdf" if (isa (varargin{k+1}, "function_handle")) pdf = varargin{k+1}; else error ("slicesample: pdf must be a function handle"); endif case "logpdf" if (isa (varargin{k+1}, "function_handle")) pdf = varargin{k+1}; else error ("slicesample: logpdf must be a function handle"); endif case "width" if (numel (varargin{k+1}) == 1 || numel (varargin{k+1}) == sizestart(2)) width = varargin{k+1}(:).'; else error ("slicesample: width must be a scalar or 1 by dim vector"); endif case "burnin" if (varargin{k+1}>=0) burnin = varargin{k+1}; else error ("slicesample: burnin must be greater than or equal to 0"); endif case "thin" if (varargin{k+1}>=1) thin = varargin{k+1}; else error ("slicesample: thin must be greater than or equal to 1"); endif otherwise warning (["slicesample: Ignoring unknown option " varargin{k}]); endswitch else error (["slicesample: " varargin{k} " is not a valid property."]); endif endfor if (! isempty (pdf) && isempty (logpdf)) logpdf = @(x) rloge (pdf (x)); elseif (isempty (pdf) && isempty (logpdf)) error ("slicesample: pdf or logpdf must be input."); endif dim = sizestart(2); smpl = zeros (nsamples, dim); if (all (sizestart == [1 dim])) smpl(1, :) = start; else error ("slicesample: start must be a 1 by dim vector."); endif maxit = 100; neval = 0; fgraterthan = @(x, fxc) logpdf (x) >= fxc; ti = burnin + nsamples * thin; rndexp = rande (ti, 1); crand = rand (ti, dim); prand = rand (ti, dim); xc = smpl(1, :); for i = 1:ti neval++; sliceheight = logpdf (xc) - rndexp(i); c = width .* crand(i, :); lb = xc - c; ub = xc + width - c; #Only for single variable as bounds can not be found with point when dim > 1 if (dim == 1) for k=1:maxit neval++; if (! fgraterthan (lb, sliceheight)) break endif lb -= width; end if (k == maxit) warning ("slicesample: Step out exceeded maximum iterations"); endif for k = 1:maxit neval++; if (! fgraterthan (ub, sliceheight)) break endif ub += width; end if (k == maxit) warning ("slicesample: Step out exceeded maximum iterations"); endif end xp = (ub - lb) .* prand(i, :) + lb; for k=1:maxit neval++; isgt = fgraterthan (xp,sliceheight); if (all (isgt)) break endif lc = ! isgt & xp < xc; uc = ! isgt & xp > xc; lb(lc) = xp(lc); ub(uc) = xp(uc); xp = (ub - lb) .* rand (1, dim) + lb; end if (k == maxit) warning ("slicesample: Step in exceeded maximum iterations"); endif xc = xp; if (i > burnin) indx = (i - burnin) / thin; if rem (indx, 1) == 0 smpl(indx, :) = xc; end end end neval = neval / (nsamples * thin + burnin); endfunction function y = rloge (x) y = -inf (size (x)); xg0 = x > 0; y(xg0) = log (x(xg0)); endfunction %!demo %! ## Define function to sample %! d = 2; %! mu = [-1; 2]; %! Sigma = rand (d); %! Sigma = (Sigma + Sigma'); %! Sigma += eye (d)*abs (eigs (Sigma, 1, "sa")) * 1.1; %! pdf = @(x)(2*pi)^(-d/2)*det(Sigma)^-.5*exp(-.5*sum((x.'-mu).*(Sigma\(x.'-mu)),1)); %! ##Inputs %! start = ones (1,2); %! nsamples = 500; %! K = 500; %! m = 10; %! [smpl, accept]=slicesample (start, nsamples, "pdf", pdf, "burnin", K, "thin", m, "width", [20, 30]); %! figure; %! hold on; %! plot (smpl(:,1), smpl(:,2), 'x'); %! [x, y] = meshgrid (linspace (-6,4), linspace(-3,7)); %! z = reshape (pdf ([x(:), y(:)]), size(x)); %! mesh (x, y, z, "facecolor", "None"); %! ## Using sample points to find the volume of half a sphere with radius of .5 %! f = @(x) ((.25-(x(:,1)+1).^2-(x(:,2)-2).^2).^.5.*(((x(:,1)+1).^2+(x(:,2)-2).^2)<.25)).'; %! int = mean (f (smpl) ./ pdf (smpl)); %! errest = std (f (smpl) ./ pdf (smpl)) / nsamples^.5; %! trueerr = abs (2/3*pi*.25^(3/2)-int); %! fprintf("Monte Carlo integral estimate int f(x) dx = %f\n", int); %! fprintf("Monte Carlo integral error estimate %f\n", errest); %! fprintf("The actual error %f\n", trueerr); %! mesh (x,y,reshape (f([x(:), y(:)]), size(x)), "facecolor", "None"); %!demo %! ##Integrate truncated normal distribution to find normilization constant %! pdf = @(x) exp (-.5*x.^2)/(pi^.5*2^.5); %! nsamples = 1e3; %! [smpl,accept] = slicesample (1, nsamples, "pdf", pdf, "thin", 4); %! f = @(x) exp (-.5 * x .^ 2) .* (x >= -2 & x <= 2); %! x=linspace(-3,3,1000); %! area(x,f(x)); %! xlabel ('x'); %! ylabel ('f(x)'); %! int = mean (f (smpl)./pdf(smpl)); %! errest = std (f (smpl)./pdf(smpl))/nsamples^.5; %! trueerr = abs (erf (2^.5)*2^.5*pi^.5-int); %! fprintf("Monte Carlo integral estimate int f(x) dx = %f\n", int); %! fprintf("Monte Carlo integral error estimate %f\n", errest); %! fprintf("The actual error %f\n", trueerr); %!test %! start = 0.5; %! nsamples = 1e3; %! pdf = @(x) exp (-.5*(x-1).^2)/(2*pi)^.5; %! [smpl, accept] = slicesample (start, nsamples, "pdf", pdf, "thin", 2, "burnin", 0, "width", 5); %! assert (mean (smpl, 1), 1, .1); %! assert (var (smpl, 1), 1, .1); %!error slicesample (); %!error slicesample (1); %!error slicesample (1, 1); statistics-1.4.3/inst/squareform.m0000644000000000000000000001033414153320774015425 0ustar0000000000000000## Copyright (C) 2015 CarnĂ« Draug ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{z} =} squareform (@var{y}) ## @deftypefnx {Function File} {@var{y} =} squareform (@var{z}) ## @deftypefnx {Function File} {@var{z} =} squareform (@var{y}, @qcode{"tovector"}) ## @deftypefnx {Function File} {@var{y} =} squareform (@var{z}, @qcode{"tomatrix"}) ## Interchange between distance matrix and distance vector formats. ## ## Converts between an hollow (diagonal filled with zeros), square, and ## symmetric matrix and a vector with of the lower triangular part. ## ## Its target application is the conversion of the vector returned by ## @code{pdist} into a distance matrix. It performs the opposite operation ## if input is a matrix. ## ## If @var{x} is a vector, its number of elements must fit into the ## triangular part of a matrix (main diagonal excluded). In other words, ## @code{numel (@var{x}) = @var{n} * (@var{n} - 1) / 2} for some integer ## @var{n}. The resulting matrix will be @var{n} by @var{n}. ## ## If @var{x} is a distance matrix, it must be square and the diagonal entries ## of @var{x} must all be zeros. @code{squareform} will generate a warning if ## @var{x} is not symmetric. ## ## The second argument is used to specify the output type in case there ## is a single element. It will defaults to @qcode{"tomatrix"} otherwise. ## ## @seealso{pdist} ## @end deftypefn ## Author: CarnĂ« Draug function y = squareform (x, method) if (nargin < 1 || nargin > 2) print_usage (); elseif (! isnumeric (x) || ! ismatrix (x)) error ("squareform: Y or Z must be a numeric matrix or vector"); endif if (nargin == 1) ## This is ambiguous when numel (x) == 1, but that's the whole reason ## why the "method" option exists. if (isvector (x)) method = "tomatrix"; else method = "tovector"; endif endif switch (tolower (method)) case "tovector" if (! issquare (x)) error ("squareform: Z is not a square matrix"); elseif (any (diag (x) != 0)) error ("squareform: Z is not a hollow matrix, i.e., with diagonal entries all zero"); elseif (! issymmetric(x)) warning ("squareform:symmetric", "squareform: Z is not a symmetric matrix"); endif y = vec (tril (x, -1, "pack"), 2); case "tomatrix" ## the dimensions of y are the solution to the quadratic formula for: ## length (x) = (sy - 1) * (sy / 2) sy = (1 + sqrt (1 + 8 * numel (x))) / 2; if (fix (sy) != sy) error ("squareform: the numel of Y cannot form a square matrix"); endif y = zeros (sy, class (x)); y(tril (true (sy), -1)) = x; # fill lower triangular part y += y.'; # and then the upper triangular part otherwise error ("squareform: invalid METHOD '%s'", method); endswitch endfunction %!shared v, m %! v = 1:6; %! m = [0 1 2 3;1 0 4 5;2 4 0 6;3 5 6 0]; ## make sure that it can go both directions automatically %!assert (squareform (v), m) %!assert (squareform (squareform (v)), v) %!assert (squareform (m), v) ## treat row and column vectors equally %!assert (squareform (v'), m) ## handle 1 element input properly %!assert (squareform (1), [0 1;1 0]) %!assert (squareform (1, "tomatrix"), [0 1; 1 0]) %!assert (squareform (0, "tovector"), zeros (1, 0)) %!warning squareform ([0 1 2; 3 0 4; 5 6 0]); ## confirm that it respects input class %!test %! for c = {@single, @double, @uint8, @uint32, @uint64} %! f = c{1}; %! assert (squareform (f (v)), f (m)) %! assert (squareform (f (m)), f (v)) %! endfor statistics-1.4.3/inst/stepwisefit.m0000644000000000000000000001410214153320774015604 0ustar0000000000000000## Copyright (C) 2013-2021 Nir Krakauer ## Copyright (C) 2014 by Mikael Kurula ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{X_use}, @var{b}, @var{bint}, @var{r}, @var{rint}, @var{stats} =} stepwisefit (@var{y}, @var{X}, @var{penter} = 0.05, @var{premove} = 0.1, @var{method} = "corr") ## Linear regression with stepwise variable selection. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{y} is an @var{n} by 1 vector of data to fit. ## @item ## @var{X} is an @var{n} by @var{k} matrix containing the values of @var{k} potential predictors. No constant term should be included (one will always be added to the regression automatically). ## @item ## @var{penter} is the maximum p-value to enter a new variable into the regression (default: 0.05). ## @item ## @var{premove} is the minimum p-value to remove a variable from the regression (default: 0.1). ## @item ## @var{method} sets how predictors are selected at each step, either based on their correlation with the residuals ("corr", default) ## or on the p values of their regression coefficients when they are successively added ("p"). ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{X_use} contains the indices of the predictors included in the final regression model. The predictors are listed in the order they were added, so typically the first ones listed are the most significant. ## @item ## @var{b}, @var{bint}, @var{r}, @var{rint}, @var{stats} are the results of @code{[b, bint, r, rint, stats] = regress(y, [ones(size(y)) X(:, X_use)], penter);} ## @end itemize ## @subheading References ## ## @enumerate ## @item ## N. R. Draper and H. Smith (1966). @cite{Applied Regression Analysis}. Wiley. Chapter 6. ## ## @end enumerate ## @seealso{regress} ## @end deftypefn ## Author: Nir Krakauer ## Description: Linear regression with stepwise variable selection function [X_use, b, bint, r, rint, stats] = stepwisefit(y, X, penter = 0.05, premove = 0.1, method = "corr") if nargin >= 3 && isempty(penter) penter = 0.05; endif if nargin >= 4 && isempty(premove) premove = 0.1; endif #remove any rows with missing entries notnans = !any (isnan ([y X]) , 2); y = y(notnans); X = X(notnans,:); n = numel(y); #number of data points k = size(X, 2); #number of predictors X_use = []; v = 0; #number of predictor variables in regression model iter = 0; max_iters = 100; #maximum number of interations to do r = y; while 1 iter++; #decide which variable to add to regression, if any added = false; if numel(X_use) < k X_inds = zeros(k, 1, "logical"); X_inds(X_use) = 1; switch lower (method) case {"corr"} [~, i_to_add] = max(abs(corr(X(:, ~X_inds), r))); #try adding the variable with the highest correlation to the residual from current regression i_to_add = (1:k)(~X_inds)(i_to_add); #index within the original predictor set [b_new, bint_new, r_new, rint_new, stats_new] = regress(y, [ones(n, 1) X(:, [X_use i_to_add])], penter); case {"p"} z_vals=zeros(k,1); for j=1:k if ~X_inds(j) [b_j, bint_j, ~,~ ,~] = regress(y, [ones(n, 1) X(:, [X_use j])], penter); z_vals(j) = abs(b_j(end)) / (bint_j(end, 2) - b_j(end)); endif endfor [~, i_to_add] = max(z_vals); #try adding the variable with the largest z-value (smallest partial p-value) [b_new, bint_new, r_new, rint_new, stats_new] = regress(y, [ones(n, 1) X(:, [X_use i_to_add])], penter); otherwise error("stepwisefit: invalid value for method") endswitch z_new = abs(b_new(end)) / (bint_new(end, 2) - b_new(end)); if z_new > 1 #accept new variable added = true; X_use = [X_use i_to_add]; b = b_new; bint = bint_new; r = r_new; rint = rint_new; stats = stats_new; v = v + 1; endif endif #decide which variable to drop from regression, if any dropped = false; if v > 0 t_ratio = tinv(1 - premove/2, n - v - 1) / tinv(1 - penter/2, n - v - 1); #estimate the ratio between the z score corresponding to premove to that corresponding to penter [z_min, i_min] = min(abs(b(2:end)) ./ (bint(2:end, 2) - b(2:end))); if z_min < t_ratio #drop a variable dropped = true; X_use(i_min) = []; [b, bint, r, rint, stats] = regress(y, [ones(n, 1) X(:, X_use)], penter); v = v - 1; endif endif #terminate if no change in the list of regression variables if ~added && ~dropped break endif if iter >= max_iters warning('stepwisefit: maximum iteration count exceeded before convergence') break endif endwhile endfunction %!test %! % Sample data from Draper and Smith (n = 13, k = 4) %! X = [7 1 11 11 7 11 3 1 2 21 1 11 10; ... %! 26 29 56 31 52 55 71 31 54 47 40 66 68; ... %! 6 15 8 8 6 9 17 22 18 4 23 9 8; ... %! 60 52 20 47 33 22 6 44 22 26 34 12 12]'; %! y = [78.5 74.3 104.3 87.6 95.9 109.2 102.7 72.5 93.1 115.9 83.8 113.3 109.4]'; %! [X_use, b, bint, r, rint, stats] = stepwisefit(y, X); %! assert(X_use, [4 1]) %! assert(b, regress(y, [ones(size(y)) X(:, X_use)], 0.05)) %! [X_use, b, bint, r, rint, stats] = stepwisefit(y, X, 0.05, 0.1, "corr"); %! assert(X_use, [4 1]) %! assert(b, regress(y, [ones(size(y)) X(:, X_use)], 0.05)) %! [X_use, b, bint, r, rint, stats] = stepwisefit(y, X, [], [], "p"); %! assert(X_use, [4 1]) %! assert(b, regress(y, [ones(size(y)) X(:, X_use)], 0.05)) statistics-1.4.3/inst/tabulate.m0000644000000000000000000000770114153320774015046 0ustar0000000000000000## Copyright (C) 2003 Alberto Terruzzi ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{table} =} tabulate (@var{data}, @var{edges}) ## ## Compute a frequency table. ## ## For vector data, the function counts the number of ## values in data that fall between the elements in the edges vector ## (which must contain monotonically non-decreasing values). @var{table} is a ## matrix. ## The first column of @var{table} is the number of bin, the second ## is the number of instances in each class (absolute frequency). The ## third column contains the percentage of each value (relative ## frequency) and the fourth column contains the cumulative frequency. ## ## If @var{edges} is missed the width of each class is unitary, if @var{edges} ## is a scalar then represent the number of classes, or you can define the ## width of each bin. ## @var{table}(@var{k}, 2) will count the value @var{data} (@var{i}) if ## @var{edges} (@var{k}) <= @var{data} (@var{i}) < @var{edges} (@var{k}+1). ## The last bin will count the value of @var{data} (@var{i}) if ## @var{edges}(@var{k}) <= @var{data} (@var{i}) <= @var{edges} (@var{k}+1). ## Values outside the values in @var{edges} are not counted. Use -inf and inf ## in @var{edges} to include all values. ## Tabulate with no output arguments returns a formatted table in the ## command window. ## ## Example ## ## @example ## sphere_radius = [1:0.05:2.5]; ## tabulate (sphere_radius) ## @end example ## ## Tabulate returns 2 bins, the first contains the sphere with radius ## between 1 and 2 mm excluded, and the second one contains the sphere with ## radius between 2 and 3 mm. ## ## @example ## tabulate (sphere_radius, 10) ## @end example ## ## Tabulate returns ten bins. ## ## @example ## tabulate (sphere_radius, [1, 1.5, 2, 2.5]) ## @end example ## ## Tabulate returns three bins, the first contains the sphere with radius ## between 1 and 1.5 mm excluded, the second one contains the sphere with ## radius between 1.5 and 2 mm excluded, and the third contains the sphere with ## radius between 2 and 2.5 mm. ## ## @example ## bar (table (:, 1), table (:, 2)) ## @end example ## ## draw histogram. ## ## @seealso{bar, pareto} ## @end deftypefn ## Author: Alberto Terruzzi ## Version: 1.0 ## Created: 13 February 2003 function table = tabulate (varargin) if nargin < 1 || nargin > 2 print_usage; endif data = varargin{1}; if isvector (data) != 1 error ("data must be a vector."); endif n = length(data); m = min(data); M = max(data); if nargin == 1 edges = 1:1:max(data)+1; else edges = varargin{2}; end if isscalar(edges) h=(M-m)/edges; edges = [m:h:M]; end # number of classes bins=length(edges)-1; # initialize freqency table freqtable = zeros(bins,4); for k=1:1:bins; if k != bins freqtable(k,2)=length(find (data >= edges(k) & data < edges(k+1))); else freqtable(k,2)=length(find (data >= edges(k) & data <= edges(k+1))); end if k == 1 freqtable (k,4) = freqtable(k,2); else freqtable(k,4) = freqtable(k-1,4) + freqtable(k,2); end end freqtable(:,1) = edges(1:end-1)(:); freqtable(:,3) = 100*freqtable(:,2)/n; if nargout == 0 disp(" bin Fa Fr% Fc"); printf("%8g %5d %6.2f%% %5d\n",freqtable'); else table = freqtable; end endfunction statistics-1.4.3/inst/tblread.m0000644000000000000000000000602614153320774014661 0ustar0000000000000000## Copyright (C) 2008 Bill Denney ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{data}, @var{varnames}, @var{casenames}] =} tblread (@var{filename}) ## @deftypefnx {Function File} {[@var{data}, @var{varnames}, @var{casenames}] =} tblread (@var{filename}, @var{delimeter}) ## Read tabular data from an ascii file. ## ## @var{data} is read from an ascii data file named @var{filename} with ## an optional @var{delimeter}. The delimeter may be any single ## character or ## @itemize ## @item "space" " " (default) ## @item "tab" "\t" ## @item "comma" "," ## @item "semi" ";" ## @item "bar" "|" ## @end itemize ## ## The @var{data} is read starting at cell (2,2) where the ## @var{varnames} form a char matrix from the first row (starting at ## (1,2)) vertically concatenated, and the @var{casenames} form a char ## matrix read from the first column (starting at (2,1)) vertically ## concatenated. ## @seealso{tblwrite, csv2cell, cell2csv} ## @end deftypefn function [data, varnames, casenames] = tblread (f="", d=" ") ## Check arguments if nargin < 1 || nargin > 2 print_usage (); endif if isempty (f) ## FIXME: open a file dialog box in this case when a file dialog box ## becomes available error ("tblread: filename must be given") endif [d err] = tbl_delim (d); if ! isempty (err) error ("tblread: %s", err) endif d = csv2cell (f, d); data = cell2mat (d(2:end, 2:end)); varnames = strvcat (d(1,2:end)); casenames = strvcat (d(2:end,1)); endfunction ## Tests %!shared d, v, c, tblreadspacefile, tblreadtabfile %! d = [1 2;3 4]; %! v = ["a ";"bc"]; %! c = ["de";"f "]; %! tblreadspacefile = file_in_loadpath("test/tblread-space.dat"); %! tblreadtabfile = file_in_loadpath("test/tblread-tab.dat"); %!test %! [dt vt ct] = tblread (tblreadspacefile); %! assert (dt, d); %! assert (vt, v); %! assert (ct, c); %!test %! [dt vt ct] = tblread (tblreadspacefile, " "); %! assert (dt, d); %! assert (vt, v); %! assert (ct, c); %!test %! [dt vt ct] = tblread (tblreadspacefile, "space"); %! assert (dt, d); %! assert (vt, v); %! assert (ct, c); %!test %! [dt vt ct] = tblread (tblreadtabfile, "tab"); %! assert (dt, d); %! assert (vt, v); %! assert (ct, c); %!test %! [dt vt ct] = tblread (tblreadtabfile, "\t"); %! assert (dt, d); %! assert (vt, v); %! assert (ct, c); %!test %! [dt vt ct] = tblread (tblreadtabfile, '\t'); %! assert (dt, d); %! assert (vt, v); %! assert (ct, c); statistics-1.4.3/inst/tblwrite.m0000644000000000000000000001335314153320774015101 0ustar0000000000000000## Copyright (C) 2008 Bill Denney ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} tblwrite (@var{data}, @var{varnames}, @var{casenames}, @var{filename}) ## @deftypefnx {Function File} {} tblwrite (@var{data}, @var{varnames}, @var{casenames}, @var{filename}, @var{delimeter}) ## Write tabular data to an ascii file. ## ## @var{data} is written to an ascii data file named @var{filename} with ## an optional @var{delimeter}. The delimeter may be any single ## character or ## @itemize ## @item "space" " " (default) ## @item "tab" "\t" ## @item "comma" "," ## @item "semi" ";" ## @item "bar" "|" ## @end itemize ## ## The @var{data} is written starting at cell (2,2) where the ## @var{varnames} are a char matrix or cell vector written to the first ## row (starting at (1,2)), and the @var{casenames} are a char matrix ## (or cell vector) written to the first column (starting at (2,1)). ## @seealso{tblread, csv2cell, cell2csv} ## @end deftypefn function tblwrite (data, varnames, casenames, f="", d=" ") ## Check arguments if nargin < 4 || nargin > 5 print_usage (); endif varnames = __makecell__ (varnames, "varnames"); casenames = __makecell__ (casenames, "varnames"); if numel (varnames) != columns (data) error ("tblwrite: the number of rows (or cells) in varnames must equal the number of columns in data") endif if numel (varnames) != rows (data) error ("tblwrite: the number of rows (or cells) in casenames must equal the number of rows in data") endif if isempty (f) ## FIXME: open a file dialog box in this case when a file dialog box ## becomes available error ("tblread: filename must be given") endif [d err] = tbl_delim (d); if ! isempty (err) error ("tblwrite: %s", err) endif dat = cell (size (data) + 1); dat(1,2:end) = varnames; dat(2:end,1) = casenames; dat(2:end,2:end) = mat2cell (data, ones (rows (data), 1), ones (columns (data), 1));; cell2csv (f, dat, d); endfunction function x = __makecell__ (x, name) ## force x into a cell matrix if ! iscell (x) if ischar (x) ## convert varnames into a cell x = mat2cell (x, ones (rows (x), 1)); else error ("tblwrite: %s must be either a char or a cell", name) endif endif endfunction ## Tests %!shared privpath %! privpath = [fileparts(which('tblwrite')) filesep() 'private']; ## Tests for tbl_delim (private function) %!test %! addpath (privpath,'-end') %! [d err] = tbl_delim (" "); %! assert (d, " "); %! assert (err, ""); %! rmpath (privpath); ## Named delimiters %!test %! addpath (privpath,'-end') %! [d err] = tbl_delim ("space"); %! assert (d, " "); %! assert (err, ""); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! [d err] = tbl_delim ("tab"); %! assert (d, sprintf ("\t")); %! assert (err, ""); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! [d err] = tbl_delim ("comma"); %! assert (d, ","); %! assert (err, ""); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! [d err] = tbl_delim ("semi"); %! assert (d, ";"); %! assert (err, ""); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! [d err] = tbl_delim ("bar"); %! assert (d, "|"); %! assert (err, ""); %! rmpath (privpath); ## An arbitrary character %!test %! addpath (privpath,'-end') %! [d err] = tbl_delim ("x"); %! assert (d, "x"); %! assert (err, ""); %! rmpath (privpath); ## An arbitrary escape string %!test %! addpath (privpath,'-end') %! [d err] = tbl_delim ('\r'); %! assert (d, sprintf ('\r')) %! assert (err, ""); %! rmpath (privpath); ## Errors %!test %! addpath (privpath,'-end') %! [d err] = tbl_delim ("bars"); %! assert (isnan (d)); %! assert (! isempty (err)); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! [d err] = tbl_delim (""); %! assert (isnan (d)); %! assert (! isempty (err)); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! [d err] = tbl_delim (5); %! assert (isnan (d)); %! assert (! isempty (err)); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! [d err] = tbl_delim ({"."}); %! assert (isnan (d)); %! assert (! isempty (err)); %! rmpath (privpath); ## Tests for tblwrite %!shared d, v, c, tempfilename %! d = [1 2;3 4]; %! v = ["a ";"bc"]; %! c = ["de";"f "]; %! tempfilename = tempname; %!test %! tblwrite (d, v, c, tempfilename); %! [dt vt ct] = tblread (tempfilename, " "); %! assert (dt, d); %! assert (vt, v); %! assert (ct, c); %! delete (tempfilename); %!test %! tblwrite (d, v, c, tempfilename, " "); %! [dt vt ct] = tblread (tempfilename, " "); %! assert (dt, d); %! assert (vt, v); %! assert (ct, c); %! delete (tempfilename); %!test %! tblwrite (d, v, c, tempfilename, "space"); %! [dt vt ct] = tblread (tempfilename); %! assert (dt, d); %! assert (vt, v); %! assert (ct, c); %! delete (tempfilename); %!test %! tblwrite (d, v, c, tempfilename, "tab"); %! [dt vt ct] = tblread (tempfilename, "tab"); %! assert (dt, d); %! assert (vt, v); %! assert (ct, c); %! delete (tempfilename); %!test %! tblwrite (d, v, c, tempfilename, "\t"); %! [dt vt ct] = tblread (tempfilename, "\t"); %! assert (dt, d); %! assert (vt, v); %! assert (ct, c); %! delete (tempfilename); statistics-1.4.3/inst/tricdf.m0000644000000000000000000001044014153320774014512 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1997-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} tricdf (@var{x}, @var{a}, @var{b}, @var{c}) ## Compute the cumulative distribution function (CDF) at @var{x} of the ## triangular distribution with parameters @var{a}, @var{b}, and @var{c} ## on the interval [@var{a}, @var{b}]. ## @end deftypefn ## Author: Dag Lyberg ## Description: CDF of the triangle distribution function cdf = tricdf (x, a, b, c) if (nargin != 4) print_usage (); endif if (! isscalar (a) || ! isscalar (b) || ! isscalar (c)) [retval, x, a, b, c] = common_size (x, a, b, c); if (retval > 0) error ("tricdf: X, A, B, and C must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (a) || iscomplex (b) || iscomplex (c)) error ("tricdf: X, A, B, and C must not be complex"); endif if (isa (x, "single") || isa (a, "single") || isa (b, "single") || isa (c, "single")) cdf = zeros (size (x), "single"); else cdf = zeros (size (x)); endif k = isnan (x) | !(a < b) | !(c >= a) | !(c <= b) ; cdf(k) = NaN; k = (x > a) & (a < b) & (a <= c) & (c <= b); if (isscalar (a) && isscalar (b) && isscalar (c)) h = 2 / (b-a); k_temp = k & (c <= x); full_area = (c-a) * h / 2; cdf(k_temp) += full_area; k_temp = k & (a < x) & (x < c); area = (x(k_temp) - a).^2 * h / (2 * ( c - a)); cdf(k_temp) += area; k_temp = k & (b <= x); full_area = (b-c) * h / 2; cdf(k_temp) += full_area; k_temp = k & (c < x) & (x < b); area = (b-x(k_temp)).^2 * h / (2 * (b - c)); cdf(k_temp) += full_area - area; else h = 2 ./ (b-a); k_temp = k & (c <= x); full_area = (c(k_temp)-a(k_temp)) .* h(k_temp) / 2; cdf(k_temp) += full_area; k_temp = k & (a <= x) & (x < c); area = (x(k_temp) - a(k_temp)).^2 .* h(k_temp) ./ (2 * (c(k_temp) - a(k_temp))); cdf(k_temp) += area; k_temp = k & (b <= x); full_area = (b(k_temp)-c(k_temp)) .* h(k_temp) / 2; cdf(k_temp) += full_area; k_temp = k & (c <= x) & (x < b); area = (b(k_temp)-x(k_temp)).^2 .* h(k_temp) ./ (2 * (b(k_temp) - c(k_temp))); cdf(k_temp) += full_area - area; endif endfunction %!shared x,y %! x = [-1, 0, 0.1, 0.5, 0.9, 1, 2] + 1; %! y = [0, 0, 0.02, 0.5, 0.98, 1 1]; %!assert (tricdf (x, ones (1,7), 2*ones (1,7), 1.5*ones (1,7)), y, eps) %!assert (tricdf (x, 1*ones (1,7), 2, 1.5), y, eps) %!assert (tricdf (x, 1, 2*ones (1,7), 1.5), y, eps) %!assert (tricdf (x, 1, 2, 1.5*ones (1,7)), y, eps) %!assert (tricdf (x, 1, 2, 1.5), y, eps) %!assert (tricdf (x, [1, 1, NaN, 1, 1, 1, 1], 2, 1.5), [y(1:2), NaN, y(4:7)], eps) %!assert (tricdf (x, 1, 2*[1, 1, NaN, 1, 1, 1, 1], 1.5), [y(1:2), NaN, y(4:7)], eps) %!assert (tricdf (x, 1, 2, 1.5*[1, 1, NaN, 1, 1, 1, 1]), [y(1:2), NaN, y(4:7)], eps) %!assert (tricdf ([x, NaN], 1, 2, 1.5), [y, NaN], eps) ## Test class of input preserved %!assert (tricdf (single ([x, NaN]), 1, 2, 1.5), single ([y, NaN]), eps('single')) %!assert (tricdf ([x, NaN], single (1), 2, 1.5), single ([y, NaN]), eps('single')) %!assert (tricdf ([x, NaN], 1, single (2), 1.5), single ([y, NaN]), eps('single')) %!assert (tricdf ([x, NaN], 1, 2, single (1.5)), single ([y, NaN]), eps('single')) ## Test input validation %!error tricdf () %!error tricdf (1) %!error tricdf (1,2) %!error tricdf (1,2,3) %!error tricdf (1,2,3,4,5) %!error tricdf (1, ones (3), ones (2), ones (2)) %!error tricdf (1, ones (2), ones (3), ones (2)) %!error tricdf (1, ones (2), ones (2), ones (3)) %!error tricdf (i, 2, 2, 2) %!error tricdf (2, i, 2, 2) %!error tricdf (2, 2, i, 2) %!error tricdf (2, 2, 2, i) statistics-1.4.3/inst/triinv.m0000644000000000000000000000751514153320774014563 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} triinv (@var{x}, @var{a}, @var{b}, @var{c}) ## For each element of @var{x}, compute the quantile (the inverse of the CDF) ## at @var{x} of the triangular distribution with parameters ## @var{a}, @var{b}, and @var{c} on the interval [@var{a}, @var{b}]. ## @end deftypefn ## Author: Dag Lyberg ## Description: Quantile function of the triangular distribution function inv = triinv (x, a, b, c) if (nargin != 4) print_usage (); endif if (! isscalar (a) || ! isscalar (b) || ! isscalar (c)) [retval, x, a, b, c] = common_size (x, a, b, c); if (retval > 0) error ("triinv: X, A, B, and C must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (a) || iscomplex (b) || iscomplex (c)) error ("triinv: X, A, B, and C must not be complex"); endif if (isa (x, "single") || isa (a, "single") || isa (b, "single")) inv = NaN (size (x), "single"); else inv = NaN (size (x)); endif k = (x >= 0) & (x <= 1) & (a < b) & (a <= c) & (c <= b); inv(k) = 0; if (isscalar (a) && isscalar (b) && isscalar(c)) h = 2 / (b-a); w = c-a; area1 = h * w / 2; j = k & (x <= area1); inv(j) += (x(j) * 2 * w / h).^0.5 + a; w = b-c; j = k & (area1 < x) & (x < 1); inv(j) += b - ((1-x(j)) * 2 * w / h).^0.5; j = k & (x == 1); inv(j) = b; else h = 2 ./ (b-a); w = c-a; area1 = h .* w / 2; j = k & (x <= area1); inv(j) += (2 * x(j) .* (w(j) ./ h(j))).^0.5 + a(j); w = b-c; j = k & (area1 < x) & (x < 1); inv(j) += b(j) - (2 * (1-x(j)) .* (w(j) ./ h(j))).^0.5; j = k & (x == 1); inv(j) = b(j); endif endfunction %!shared x,y %! x = [-1, 0, 0.02, 0.5, 0.98, 1, 2]; %! y = [NaN, 0, 0.1, 0.5, 0.9, 1, NaN] + 1; %!assert (triinv (x, ones (1,7), 2*ones (1,7), 1.5*ones (1,7)), y, eps) %!assert (triinv (x, 1*ones (1,7), 2, 1.5), y, eps) %!assert (triinv (x, 1, 2*ones (1,7), 1.5), y, eps) %!assert (triinv (x, 1, 2, 1.5*ones (1,7)), y, eps) %!assert (triinv (x, 1, 2, 1.5), y, eps) %!assert (triinv (x, [1, 1, NaN, 1, 1, 1, 1], 2, 1.5), [y(1:2), NaN, y(4:7)], eps) %!assert (triinv (x, 1, 2*[1, 1, NaN, 1, 1, 1, 1], 1.5), [y(1:2), NaN, y(4:7)], eps) %!assert (triinv (x, 1, 2, 1.5*[1, 1, NaN, 1, 1, 1, 1]), [y(1:2), NaN, y(4:7)], eps) %!assert (triinv ([x, NaN], 1, 2, 1.5), [y, NaN], eps) ## Test class of input preserved %!assert (triinv (single ([x, NaN]), 1, 2, 1.5), single ([y, NaN]), eps('single')) %!assert (triinv ([x, NaN], single (1), 2, 1.5), single ([y, NaN]), eps('single')) %!assert (triinv ([x, NaN], 1, single (2), 1.5), single ([y, NaN]), eps('single')) %!assert (triinv ([x, NaN], 1, 2, single (1.5)), single ([y, NaN]), eps('single')) ## Test input validation %!error triinv () %!error triinv (1) %!error triinv (1,2) %!error triinv (1,2,3) %!error triinv (1,2,3,4,5) %!error triinv (1, ones (3), ones (2), ones (2)) %!error triinv (1, ones (2), ones (3), ones (2)) %!error triinv (1, ones (2), ones (2), ones (3)) %!error triinv (i, 2, 2, 2) %!error triinv (2, i, 2, 2) %!error triinv (2, 2, i, 2) %!error triinv (2, 2, 2, i) statistics-1.4.3/inst/trimmean.m0000644000000000000000000000317614153320774015063 0ustar0000000000000000## Copyright (C) 2001 Paul Kienzle ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{a} =} trimmean (@var{x}, @var{p}) ## ## Compute the trimmed mean. ## ## The trimmed mean of @var{x} is defined as the mean of @var{x} excluding the ## highest and lowest @var{p} percent of the data. ## ## For example ## ## @example ## mean ([-inf, 1:9, inf]) ## @end example ## ## is NaN, while ## ## @example ## trimmean ([-inf, 1:9, inf], 10) ## @end example ## ## excludes the infinite values, which make the result 5. ## ## @seealso{mean} ## @end deftypefn function a = trimmean(x, p, varargin) if (nargin != 2 && nargin != 3) print_usage; endif y = sort(x, varargin{:}); sz = size(x); if nargin < 3 dim = min(find(sz>1)); if isempty(dim), dim=1; endif; else dim = varargin{1}; endif idx = cell (0); for i=1:length(sz), idx{i} = 1:sz(i); end; trim = round(sz(dim)*p*0.01); idx{dim} = 1+trim : sz(dim)-trim; a = mean (y (idx{:}), varargin{:}); endfunction statistics-1.4.3/inst/tripdf.m0000644000000000000000000000736714153320774014545 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1997-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} tripdf (@var{x}, @var{a}, @var{b}, @var{c}) ## Compute the probability density function (PDF) at @var{x} of the triangular ## distribution with parameters @var{a}, @var{b}, and @var{c} on the interval ## [@var{a}, @var{b}]. ## @end deftypefn ## Author: Dag Lyberg ## Description: PDF of the triangular distribution function pdf = tripdf (x, a, b, c) if (nargin != 4) print_usage (); endif if (! isscalar (a) || ! isscalar (b) || ! isscalar (c)) [retval, x, a, b, c] = common_size (x, a, b, c); if (retval > 0) error ("tripdf: X, A, B, and C must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (a) || iscomplex (b) || iscomplex (c)) error ("tripdf: X, A, B, and C must not be complex"); endif if (isa (x, "single") || isa (a, "single") ... || isa (b, "single") || isa (c, "single")) pdf = zeros (size (x), "single"); else pdf = zeros (size (x)); endif k = isnan (x) | !(a < b) | !(c >= a) | !(c <= b) ; pdf(k) = NaN; k = (x >= a) & (x <= b) & (a < b) & (a <= c) & (c <= b); h = 2 ./ (b-a); if (isscalar (a) && isscalar (b) && isscalar (c)) j = k & (a <= x) & (x < c); pdf(j) = h * (x(j)-a) / (c-a); j = k & (x == c); pdf(j) = h; j = k & (c < x) & (x <= b); pdf(j) = h * (b-x(j)) / (b-c); else j = k & (a <= x) & (x < c); pdf(j) = h(j) .* (x(j)-a(j)) ./ (c(j)-a(j)); j = k & (x == c); pdf(j) = h(j); j = k & (c < x) & (x <= b); pdf(j) = h(j) .* (b(j)-x(j)) ./ (b(j)-c(j)); endif endfunction %!shared x,y,deps %! x = [-1, 0, 0.1, 0.5, 0.9, 1, 2] + 1; %! y = [0, 0, 0.4, 2, 0.4, 0, 0]; %! deps = 2*eps; %!assert (tripdf (x, ones (1,7), 2*ones (1,7), 1.5*ones (1,7)), y, deps) %!assert (tripdf (x, 1*ones (1,7), 2, 1.5), y, deps) %!assert (tripdf (x, 1, 2*ones (1,7), 1.5), y, deps) %!assert (tripdf (x, 1, 2, 1.5*ones (1,7)), y, deps) %!assert (tripdf (x, 1, 2, 1.5), y, deps) %!assert (tripdf (x, [1, 1, NaN, 1, 1, 1, 1], 2, 1.5), [y(1:2), NaN, y(4:7)], deps) %!assert (tripdf (x, 1, 2*[1, 1, NaN, 1, 1, 1, 1], 1.5), [y(1:2), NaN, y(4:7)], deps) %!assert (tripdf (x, 1, 2, 1.5*[1, 1, NaN, 1, 1, 1, 1]), [y(1:2), NaN, y(4:7)], deps) %!assert (tripdf ([x, NaN], 1, 2, 1.5), [y, NaN], deps) ## Test class of input preserved %!assert (tripdf (single ([x, NaN]), 1, 2, 1.5), single ([y, NaN]), eps('single')) %!assert (tripdf ([x, NaN], single (1), 2, 1.5), single ([y, NaN]), eps('single')) %!assert (tripdf ([x, NaN], 1, single (2), 1.5), single ([y, NaN]), eps('single')) %!assert (tripdf ([x, NaN], 1, 2, single (1.5)), single ([y, NaN]), eps('single')) ## Test input validation %!error tripdf () %!error tripdf (1) %!error tripdf (1,2) %!error tripdf (1,2,3) %!error tripdf (1,2,3,4,5) %!error tripdf (1, ones (3), ones (2), ones (2)) %!error tripdf (1, ones (2), ones (3), ones (2)) %!error tripdf (1, ones (2), ones (2), ones (3)) %!error tripdf (i, 2, 2, 2) %!error tripdf (2, i, 2, 2) %!error tripdf (2, 2, i, 2) %!error tripdf (2, 2, 2, i) statistics-1.4.3/inst/trirnd.m0000644000000000000000000001242714153320774014550 0ustar0000000000000000## Copyright (C) 2016 Dag Lyberg ## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} trirnd (@var{a}, @var{b}, @var{c}) ## @deftypefnx {} {} trirnd (@var{a}, @var{b}, @var{c}, @var{r}) ## @deftypefnx {} {} trirnd (@var{a}, @var{b}, @var{c}, @var{r}, @var{c}, @dots{}) ## @deftypefnx {} {} trirnd (@var{a}, @var{b}, @var{c}, [@var{sz}]) ## Return a matrix of random samples from the rectangular distribution with ## parameters @var{a}, @var{b}, and @var{c} on the interval [@var{a}, @var{b}]. ## ## When called with a single size argument, return a square matrix with ## the dimension specified. When called with more than one scalar argument the ## first two arguments are taken as the number of rows and columns and any ## further arguments specify additional matrix dimensions. The size may also ## be specified with a vector of dimensions @var{sz}. ## ## If no size arguments are given then the result matrix is the common size of ## @var{a}, @var{b} and @var{c}. ## @end deftypefn ## Author: Dag Lyberg ## Description: Random deviates from the triangular distribution function rnd = trirnd (a, b, c, varargin) if (nargin < 3) print_usage (); endif if (! isscalar (a) || ! isscalar (b) || ! isscalar (c)) [retval, a, b, c] = common_size (a, b, c); if (retval > 0) error ("trirnd: A, B, and C must be of common size or scalars"); endif endif if (iscomplex (a) || iscomplex (b) || iscomplex (c)) error ("trirnd: A, B, and C must not be complex"); endif if (nargin == 3) sz = size (a); elseif (nargin == 4) if (isscalar (varargin{1}) && varargin{1} >= 0) sz = [varargin{1}, varargin{1}]; elseif (isrow (varargin{1}) && all (varargin{1} >= 0)) sz = varargin{1}; else error ("trirnd: dimension vector must be row vector of non-negative integers"); endif elseif (nargin > 4) if (any (cellfun (@(x) (! isscalar (x) || x < 0), varargin))) error ("trirnd: dimensions must be non-negative integers"); endif sz = [varargin{:}]; endif if (! isscalar (a) && ! isequal (size (b), sz)) error ("trirnd: A, B, and C must be scalar or of size SZ"); endif if (isa (a, "single") || isa (b, "single") || isa (c, "single")) cls = "single"; else cls = "double"; endif if (isscalar (a) && isscalar (b) && isscalar (c)) if ((-Inf < a) && (a < b) && (a <= c) && (c <= b) && (b < Inf)) w = b-a; left_width = c-a; right_width = b-c; h = 2 / w; left_area = h * left_width / 2; rnd = rand (sz, cls); idx = rnd < left_area; rnd(idx) = a + (rnd(idx) * w * left_width).^0.5; rnd(~idx) = b - ((1-rnd(~idx)) * w * right_width).^0.5; else rnd = NaN (sz, cls); endif else w = b-a; left_width = c-a; right_width = b-c; h = 2 ./ w; left_area = h .* left_width / 2; rnd = rand (sz, cls); k = rnd < left_area; rnd(k) = a(k) + (rnd(k) .* w(k) .* left_width(k)).^0.5; rnd(~k) = b(~k) - ((1-rnd(~k)) .* w(~k) .* right_width(~k)).^0.5; k = ! (-Inf < a) | ! (a < b) | ! (a <= c) | ! (c <= b) | ! (b < Inf); rnd(k) = NaN; endif endfunction %!assert (size (trirnd (1,2,1.5)), [1, 1]) %!assert (size (trirnd (1*ones (2,1), 2,1.5)), [2, 1]) %!assert (size (trirnd (1*ones (2,2), 2,1.5)), [2, 2]) %!assert (size (trirnd (1, 2*ones (2,1), 1.5)), [2, 1]) %!assert (size (trirnd (1, 2*ones (2,2), 1.5)), [2, 2]) %!assert (size (trirnd (1, 2, 1.5*ones (2,1))), [2, 1]) %!assert (size (trirnd (1, 2, 1.5*ones (2,2))), [2, 2]) %!assert (size (trirnd (1, 2, 1.5, 3)), [3, 3]) %!assert (size (trirnd (1, 2, 1.5, [4 1])), [4, 1]) %!assert (size (trirnd (1, 2, 1.5, 4, 1)), [4, 1]) ## Test class of input preserved %!assert (class (trirnd (1,2,1.5)), "double") %!assert (class (trirnd (single (1),2,1.5)), "single") %!assert (class (trirnd (single ([1 1]),2,1.5)), "single") %!assert (class (trirnd (1,single (2),1.5)), "single") %!assert (class (trirnd (1,single ([2 2]),1.5)), "single") %!assert (class (trirnd (1,2,single (1.5))), "single") %!assert (class (trirnd (1,2,single ([1.5 1.5]))), "single") ## Test input validation %!error trirnd () %!error trirnd (1) %!error trirnd (1,2) %!error trirnd (ones (3), 2*ones (2), 1.5*ones (2), 2) %!error trirnd (ones (2), 2*ones (3), 1.5*ones (2), 2) %!error trirnd (ones (2), 2*ones (2), 1.5*ones (3), 2) %!error trirnd (i, 2, 1.5) %!error trirnd (1, i, 1.5) %!error trirnd (1, 2, i) %!error trirnd (1,2,1.5, -1) %!error trirnd (1,2,1.5, ones (2)) %!error trirnd (1,2,1.5, [2 -1 2]) %!error trirnd (1*ones (2),2,1.5, 3) %!error trirnd (1*ones (2),2,1.5, [3, 2]) %!error trirnd (1*ones (2),2,1.5, 3, 2) statistics-1.4.3/inst/tstat.m0000644000000000000000000000474314153320774014407 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} tstat (@var{n}) ## Compute mean and variance of the t (Student) distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{n} is the parameter of the t (Student) distribution. The elements ## of @var{n} must be positive ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the t (Student) distribution ## ## @item ## @var{v} is the variance of the t (Student) distribution ## @end itemize ## ## @subheading Example ## ## @example ## @group ## n = 3:8; ## [m, v] = tstat (n) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the t (Student) distribution function [m, v] = tstat (n) # Check arguments if (nargin != 1) print_usage (); endif if (! isempty (n) && ! ismatrix (n)) error ("tstat: n must be a numeric matrix"); endif # Calculate moments m = zeros (size (n)); v = n ./ (n - 2); # Continue argument check k = find (! (n > 1) | ! (n < Inf)); if (any (k)) m(k) = NaN; v(k) = NaN; endif k = find (! (n > 2) & (n < Inf)); if (any (k)) v(k) = Inf; endif endfunction %!test %! n = 3:8; %! [m, v] = tstat (n); %! expected_m = [0, 0, 0, 0, 0, 0]; %! expected_v = [3.0000, 2.0000, 1.6667, 1.5000, 1.4000, 1.3333]; %! assert (m, expected_m); %! assert (v, expected_v, 0.001); statistics-1.4.3/inst/ttest.m0000644000000000000000000001311114153320774014400 0ustar0000000000000000## Copyright (C) 2014 Tony Richardson ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{stats}] =} ttest (@var{x}) ## @deftypefnx {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{stats}] =} ttest (@var{x}, @var{m}) ## @deftypefnx {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{stats}] =} ttest (@var{x}, @var{y}) ## @deftypefnx {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{stats}] =} ttest (@var{x}, @var{m}, @var{Name}, @var{Value}) ## @deftypefnx {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{stats}] =} ttest (@var{x}, @var{y}, @var{Name}, @var{Value}) ## Test for mean of a normal sample with unknown variance. ## ## Perform a T-test of the null hypothesis @code{mean (@var{x}) == ## @var{m}} for a sample @var{x} from a normal distribution with unknown ## mean and unknown std deviation. Under the null, the test statistic ## @var{t} has a Student's t distribution. The default value of ## @var{m} is 0. ## ## If the second argument @var{y} is a vector, a paired-t test of the ## hypothesis @code{mean (@var{x}) = mean (@var{y})} is performed. ## ## Name-Value pair arguments can be used to set various options. ## @qcode{"alpha"} can be used to specify the significance level ## of the test (the default value is 0.05). @qcode{"tail"}, can be used ## to select the desired alternative hypotheses. If the value is ## @qcode{"both"} (default) the null is tested against the two-sided ## alternative @code{mean (@var{x}) != @var{m}}. ## If it is @qcode{"right"} the one-sided alternative @code{mean (@var{x}) ## > @var{m}} is considered. Similarly for @qcode{"left"}, the one-sided ## alternative @code{mean (@var{x}) < @var{m}} is considered. ## When argument @var{x} is a matrix, @qcode{"dim"} can be used to selection ## the dimension over which to perform the test. (The default is the ## first non-singleton dimension). ## ## If @var{h} is 0 the null hypothesis is accepted, if it is 1 the null ## hypothesis is rejected. The p-value of the test is returned in @var{pval}. ## A 100(1-alpha)% confidence interval is returned in @var{ci}. @var{stats} ## is a structure containing the value of the test statistic (@var{tstat}), ## the degrees of freedom (@var{df}) and the sample standard deviation ## (@var{sd}). ## ## @end deftypefn ## Author: Tony Richardson function [h, p, ci, stats] = ttest(x, my, varargin) % Set default arguments my_default = 0; alpha = 0.05; tail = 'both'; % Find the first non-singleton dimension of x dim = min(find(size(x)~=1)); if isempty(dim), dim = 1; end if (nargin == 1) my = my_default; end i = 1; while ( i <= length(varargin) ) switch lower(varargin{i}) case 'alpha' i = i + 1; alpha = varargin{i}; case 'tail' i = i + 1; tail = varargin{i}; case 'dim' i = i + 1; dim = varargin{i}; otherwise error('Invalid Name argument.',[]); end i = i + 1; end if ~isa(tail, 'char') error('tail argument to ttest must be a string\n',[]); end if any(and(~isscalar(my),size(x)~=size(my))) error('Arrays in paired test must be the same size.'); end % Set default values if arguments are present but empty if isempty(my) my = my_default; end % This adjustment allows everything else to remain the % same for both the one-sample t test and paired tests. x = x - my; % Calculate the test statistic value (tval) n = size(x, dim); x_bar = mean(x, dim); stats.tstat = 0; stats.df = n-1; stats.sd = std(x, 0, dim); x_bar_std = stats.sd/sqrt(n); tval = (x_bar)./x_bar_std; stats.tstat = tval; % Based on the "tail" argument determine the P-value, the critical values, % and the confidence interval. switch lower(tail) case 'both' p = 2*(1 - tcdf(abs(tval),n-1)); tcrit = -tinv(alpha/2,n-1); ci = [x_bar-tcrit*x_bar_std; x_bar+tcrit*x_bar_std] + my; case 'left' p = tcdf(tval,n-1); tcrit = -tinv(alpha,n-1); ci = [-inf*ones(size(x_bar)); my+x_bar+tcrit*x_bar_std]; case 'right' p = 1 - tcdf(tval,n-1); tcrit = -tinv(alpha,n-1); ci = [my+x_bar-tcrit*x_bar_std; inf*ones(size(x_bar))]; otherwise error('Invalid tail argument to ttest\n',[]); end % Reshape the ci array to match MATLAB shaping if and(isscalar(x_bar), dim==2) ci = ci(:)'; elseif size(x_bar,2). ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{stats}] =} ttest2 (@var{x}, @var{y}) ## @deftypefnx {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{stats}] =} ttest2 (@var{x}, @var{y}, @var{Name}, @var{Value}) ## Test for mean of a normal sample with known variance. ## ## Perform a T-test of the null hypothesis @code{mean (@var{x}) == ## @var{m}} for a sample @var{x} from a normal distribution with unknown ## mean and unknown std deviation. Under the null, the test statistic ## @var{t} has a Student's t distribution. ## ## If the second argument @var{y} is a vector, a paired-t test of the ## hypothesis @code{mean (@var{x}) = mean (@var{y})} is performed. ## ## The argument @qcode{"alpha"} can be used to specify the significance level ## of the test (the default value is 0.05). The string ## argument @qcode{"tail"}, can be used to select the desired alternative ## hypotheses. If @qcode{"alt"} is @qcode{"both"} (default) the null is ## tested against the two-sided alternative @code{mean (@var{x}) != @var{m}}. ## If @qcode{"alt"} is @qcode{"right"} the one-sided ## alternative @code{mean (@var{x}) > @var{m}} is considered. ## Similarly for @qcode{"left"}, the one-sided alternative @code{mean ## (@var{x}) < @var{m}} is considered. When @qcode{"vartype"} is @qcode{"equal"} ## the variances are assumed to be equal (this is the default). When ## @qcode{"vartype"} is @qcode{"unequal"} the variances are not assumed equal. ## When argument @var{x} is a matrix the @qcode{"dim"} argument can be ## used to selection the dimension over which to perform the test. ## (The default is the first non-singleton dimension.) ## ## If @var{h} is 0 the null hypothesis is accepted, if it is 1 the null ## hypothesis is rejected. The p-value of the test is returned in @var{pval}. ## A 100(1-alpha)% confidence interval is returned in @var{ci}. @var{stats} ## is a structure containing the value of the test statistic (@var{tstat}), ## the degrees of freedom (@var{df}) and the sample standard deviation ## (@var{sd}). ## ## @end deftypefn ## Author: Tony Richardson function [h, p, ci, stats] = ttest2(x, y, varargin) alpha = 0.05; tail = 'both'; vartype = 'equal'; % Find the first non-singleton dimension of x dim = min(find(size(x)~=1)); if isempty(dim), dim = 1; end i = 1; while ( i <= length(varargin) ) switch lower(varargin{i}) case 'alpha' i = i + 1; alpha = varargin{i}; case 'tail' i = i + 1; tail = varargin{i}; case 'vartype' i = i + 1; vartype = varargin{i}; case 'dim' i = i + 1; dim = varargin{i}; otherwise error('Invalid Name argument.',[]); end i = i + 1; end if ~isa(tail, 'char') error('Tail argument to ttest2 must be a string\n',[]); end m = size(x, dim); n = size(y, dim); x_bar = mean(x,dim)-mean(y,dim); s1_var = var(x, 0, dim); s2_var = var(y, 0, dim); switch lower(vartype) case 'equal' stats.tstat = 0; stats.df = (m + n - 2)*ones(size(x_bar)); sp_var = ((m-1)*s1_var + (n-1)*s2_var)./stats.df; stats.sd = sqrt(sp_var); x_bar_std = sqrt(sp_var*(1/m+1/n)); case 'unequal' stats.tstat = 0; se1 = sqrt(s1_var/m); se2 = sqrt(s2_var/n); sp_var = s1_var/m + s2_var/n; stats.df = ((se1.^2+se2.^2).^2 ./ (se1.^4/(m-1) + se2.^4/(n-1))); stats.sd = [sqrt(s1_var); sqrt(s2_var)]; x_bar_std = sqrt(sp_var); otherwise error('Invalid fifth (vartype) argument to ttest2\n',[]); end stats.tstat = x_bar./x_bar_std; % Based on the "tail" argument determine the P-value, the critical values, % and the confidence interval. switch lower(tail) case 'both' p = 2*(1 - tcdf(abs(stats.tstat),stats.df)); tcrit = -tinv(alpha/2,stats.df); %ci = [x_bar-tcrit*stats.sd; x_bar+tcrit*stats.sd]; ci = [x_bar-tcrit.*x_bar_std; x_bar+tcrit.*x_bar_std]; case 'left' p = tcdf(stats.tstat,stats.df); tcrit = -tinv(alpha,stats.df); ci = [-inf*ones(size(x_bar)); x_bar+tcrit.*x_bar_std]; case 'right' p = 1 - tcdf(stats.tstat,stats.df); tcrit = -tinv(alpha,stats.df); ci = [x_bar-tcrit.*x_bar_std; inf*ones(size(x_bar))]; otherwise error('Invalid fourth (tail) argument to ttest2\n',[]); end % Reshape the ci array to match MATLAB shaping if and(isscalar(x_bar), dim==2) ci = ci(:)'; stats.sd = stats.sd(:)'; elseif size(x_bar,2) ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} unidstat (@var{n}) ## Compute mean and variance of the discrete uniform distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{n} is the parameter of the discrete uniform distribution. The elements ## of @var{n} must be positive natural numbers ## @end itemize ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the discrete uniform distribution ## ## @item ## @var{v} is the variance of the discrete uniform distribution ## @end itemize ## ## @subheading Example ## ## @example ## @group ## n = 1:6; ## [m, v] = unidstat (n) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the discrete uniform distribution function [m, v] = unidstat (n) # Check arguments if (nargin != 1) print_usage (); endif if (! isempty (n) && ! ismatrix (n)) error ("unidstat: n must be a numeric matrix"); endif # Calculate moments m = (n + 1) ./ 2; v = ((n .^ 2) - 1) ./ 12; # Continue argument check k = find (! (n > 0) | ! (n < Inf) | ! (n == round (n))); if (any (k)) m(k) = NaN; v(k) = NaN; endif endfunction %!test %! n = 1:6; %! [m, v] = unidstat (n); %! expected_m = [1.0000, 1.5000, 2.0000, 2.5000, 3.0000, 3.5000]; %! expected_v = [0.0000, 0.2500, 0.6667, 1.2500, 2.0000, 2.9167]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); statistics-1.4.3/inst/unifstat.m0000644000000000000000000000645014153320774015102 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} unifstat (@var{a}, @var{b}) ## Compute mean and variance of the continuous uniform distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{a} is the first parameter of the continuous uniform distribution ## ## @item ## @var{b} is the second parameter of the continuous uniform distribution ## @end itemize ## @var{a} and @var{b} must be of common size or one of them must be scalar ## and @var{a} must be less than @var{b} ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the continuous uniform distribution ## ## @item ## @var{v} is the variance of the continuous uniform distribution ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## a = 1:6; ## b = 2:2:12; ## [m, v] = unifstat (a, b) ## @end group ## ## @group ## [m, v] = unifstat (a, 10) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the continuous uniform distribution function [m, v] = unifstat (a, b) # Check arguments if (nargin != 2) print_usage (); endif if (! isempty (a) && ! ismatrix (a)) error ("unifstat: a must be a numeric matrix"); endif if (! isempty (b) && ! ismatrix (b)) error ("unifstat: b must be a numeric matrix"); endif if (! isscalar (a) || ! isscalar (b)) [retval, a, b] = common_size (a, b); if (retval > 0) error ("unifstat: a and b must be of common size or scalar"); endif endif # Calculate moments m = (a + b) ./ 2; v = ((b - a) .^ 2) ./ 12; # Continue argument check k = find (! (-Inf < a) | ! (a < b) | ! (b < Inf)); if (any (k)) m(k) = NaN; v(k) = NaN; endif endfunction %!test %! a = 1:6; %! b = 2:2:12; %! [m, v] = unifstat (a, b); %! expected_m = [1.5000, 3.0000, 4.5000, 6.0000, 7.5000, 9.0000]; %! expected_v = [0.0833, 0.3333, 0.7500, 1.3333, 2.0833, 3.0000]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); %!test %! a = 1:6; %! [m, v] = unifstat (a, 10); %! expected_m = [5.5000, 6.0000, 6.5000, 7.0000, 7.5000, 8.0000]; %! expected_v = [6.7500, 5.3333, 4.0833, 3.0000, 2.0833, 1.3333]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); statistics-1.4.3/inst/vartest.m0000644000000000000000000001067514153320774014741 0ustar0000000000000000## Copyright (C) 2014 Tony Richardson ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{stats}] =} vartest (@var{x}, @var{y}) ## @deftypefnx {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{stats}] =} vartest (@var{x}, @var{y}, @var{Name}, @var{Value}) ## Perform a F-test for equal variances. ## ## If the second argument @var{y} is a vector, a paired-t test of the ## hypothesis @code{mean (@var{x}) = mean (@var{y})} is performed. ## ## The argument @qcode{"alpha"} can be used to specify the significance level ## of the test (the default value is 0.05). The string ## argument @qcode{"tail"}, can be used to select the desired alternative ## hypotheses. If @qcode{"alt"} is @qcode{"both"} (default) the null is ## tested against the two-sided alternative @code{mean (@var{x}) != @var{m}}. ## If @qcode{"alt"} is @qcode{"right"} the one-sided ## alternative @code{mean (@var{x}) > @var{m}} is considered. ## Similarly for @qcode{"left"}, the one-sided alternative @code{mean ## (@var{x}) < @var{m}} is considered. When @qcode{"vartype"} is @qcode{"equal"} ## the variances are assumed to be equal (this is the default). When ## @qcode{"vartype"} is @qcode{"unequal"} the variances are not assumed equal. ## When argument @var{x} is a matrix the @qcode{"dim"} argument can be ## used to selection the dimension over which to perform the test. ## (The default is the first non-singleton dimension.) ## ## If @var{h} is 0 the null hypothesis is accepted, if it is 1 the null ## hypothesis is rejected. The p-value of the test is returned in @var{pval}. ## A 100(1-alpha)% confidence interval is returned in @var{ci}. @var{stats} ## is a structure containing the value of the test statistic (@var{tstat}), ## the degrees of freedom (@var{df}) and the sample standard deviation ## (@var{sd}). ## ## @end deftypefn ## Author: Tony Richardson ## Description: Test for mean of a normal sample with known variance function [h, p, ci, stats] = vartest(x, v, varargin) % Set default arguments alpha = 0.05; tail = 'both'; % Find the first non-singleton dimension of x dim = min(find(size(x)~=1)); if isempty(dim), dim = 1; end i = 1; while ( i <= length(varargin) ) switch lower(varargin{i}) case 'alpha' i = i + 1; alpha = varargin{i}; case 'tail' i = i + 1; tail = varargin{i}; case 'dim' i = i + 1; dim = varargin{i}; otherwise error('Invalid Name argument.',[]); end i = i + 1; end if ~isa(tail, 'char') error('tail argument to vartest must be a string\n',[]); end s_var = var(x, 0, dim); df = size(x, dim) - 1; stats.chisqstat = df*s_var/v; % Based on the "tail" argument determine the P-value, the critical values, % and the confidence interval. switch lower(tail) case 'both' p = 2*min(chi2cdf(stats.chisqstat,df),1-chi2cdf(stats.chisqstat,df)); ci = [df*s_var ./ (chi2inv(1-alpha/2,df)); df*s_var ./ (chi2inv(alpha/2,df))]; case 'left' p = chi2cdf(stats.chisqstat,df); chi2crit = chi2inv(alpha,df); ci = [zeros(size(stats.chisqstat)); df*s_var ./ (chi2inv(alpha,df))]; case 'right' p = 1 - chi2cdf(stats.chisqstat,df); chi2crit = chi2inv(1-alpha,df); ci = [df*s_var ./ (chi2inv(1-alpha,df)); inf*ones(size(stats.chisqstat))]; otherwise error('Invalid fourth (tail) argument to vartest\n',[]); end % Reshape the ci array to match MATLAB shaping if and(isscalar(stats.chisqstat), dim==2) ci = ci(:)'; elseif size(stats.chisqstat,2). ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{stats}] =} vartest2 (@var{x}, @var{y}) ## @deftypefnx {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{stats}] =} vartest2 (@var{x}, @var{y}, @var{Name}, @var{Value}) ## Perform a F-test for equal variances. ## ## If the second argument @var{y} is a vector, a paired-t test of the ## hypothesis @code{mean (@var{x}) = mean (@var{y})} is performed. ## ## The argument @qcode{"alpha"} can be used to specify the significance level ## of the test (the default value is 0.05). The string ## argument @qcode{"tail"}, can be used to select the desired alternative ## hypotheses. If @qcode{"alt"} is @qcode{"both"} (default) the null is ## tested against the two-sided alternative @code{mean (@var{x}) != @var{m}}. ## If @qcode{"alt"} is @qcode{"right"} the one-sided ## alternative @code{mean (@var{x}) > @var{m}} is considered. ## Similarly for @qcode{"left"}, the one-sided alternative @code{mean ## (@var{x}) < @var{m}} is considered. When @qcode{"vartype"} is @qcode{"equal"} ## the variances are assumed to be equal (this is the default). When ## @qcode{"vartype"} is @qcode{"unequal"} the variances are not assumed equal. ## When argument @var{x} is a matrix the @qcode{"dim"} argument can be ## used to selection the dimension over which to perform the test. ## (The default is the first non-singleton dimension.) ## ## If @var{h} is 0 the null hypothesis is accepted, if it is 1 the null ## hypothesis is rejected. The p-value of the test is returned in @var{pval}. ## A 100(1-alpha)% confidence interval is returned in @var{ci}. @var{stats} ## is a structure containing the value of the test statistic (@var{tstat}), ## the degrees of freedom (@var{df}) and the sample standard deviation ## (@var{sd}). ## ## @end deftypefn ## Author: Tony Richardson ## Description: Test for mean of a normal sample with known variance function [h, p, ci, stats] = vartest2(x, y, varargin) % Set default arguments alpha = 0.05; tail = 'both'; % Find the first non-singleton dimension of x dim = min(find(size(x)~=1)); if isempty(dim), dim = 1; end i = 1; while ( i <= length(varargin) ) switch lower(varargin{i}) case 'alpha' i = i + 1; alpha = varargin{i}; case 'tail' i = i + 1; tail = varargin{i}; case 'dim' i = i + 1; dim = varargin{i}; otherwise error('Invalid Name argument.',[]); end i = i + 1; end if ~isa(tail, 'char') error('tail argument to vartest2 must be a string\n',[]); end s1_var = var(x, 0, dim); s2_var = var(y, 0, dim); stats.fstat = s1_var ./ s2_var; df1= size(x, dim) - 1; df2 = size(y, dim) - 1; % Based on the "tail" argument determine the P-value, the critical values, % and the confidence interval. switch lower(tail) case 'both' p = 2*min(fcdf(stats.fstat,df1,df2),1 - fcdf(stats.fstat,df1,df2)); fcrit = finv(1-alpha/2,df1,df2); ci = [s1_var ./ (fcrit*s2_var); fcrit*s1_var ./ s2_var]; case 'left' p = fcdf(stats.fstat,df1,df2); fcrit = finv(alpha,df1,df2); ci = [zeros(size(stats.fstat)); s1_var ./ (fcrit*s2_var)]; case 'right' p = 1 - fcdf(stats.fstat,df1,df2); fcrit = finv(1-alpha,df1,df2); ci = [s1_var ./ (fcrit*s2_var); inf*ones(size(stats.fstat))]; otherwise error('Invalid fourth (tail) argument to vartest2\n',[]); end % Reshape the ci array to match MATLAB shaping if and(isscalar(stats.fstat), dim==2) ci = ci(:)'; elseif size(stats.fstat,2). ## Author: Juan Pablo Carbajal ## -*- texinfo -*- ## @defun {@var{h} =} violin (@var{x}) ## @defunx {@var{h} =} violin (@dots{}, @var{property}, @var{value}, @dots{}) ## @defunx {@var{h} =} violin (@var{hax}, @dots{}) ## @defunx {@var{h} =} violin (@dots{}, @asis{"horizontal"}) ## Produce a Violin plot of the data @var{x}. ## ## The input data @var{x} can be a N-by-m array containg N observations of m variables. ## It can also be a cell with m elements, for the case in which the varibales ## are not uniformly sampled. ## ## The following @var{property} can be set using @var{property}/@var{value} pairs ## (default values in parenthesis). ## The value of the property can be a scalar indicating that it applies ## to all the variables in the data. ## It can also be a cell/array, indicating the property for each variable. ## In this case it should have m columns (as many as variables). ## ## @table @asis ## ## @item Color ## (@asis{"y"}) Indicates the filling color of the violins. ## ## @item Nbins ## (50) Internally, the function calls @command{hist} to compute the histogram of the data. ## This property indicates how many bins to use. See @command{help hist} ## for more details. ## ## @item SmoothFactor ## (4) The fuction performs simple kernel density estimation and automatically ## finds the bandwith of the kernel function that best approximates the histogram ## using optimization (@command{sqp}). ## The result is in general very noisy. To smooth the result the bandwidth is ## multiplied by the value of this property. The higher the value the smoother ## the violings, but values too high might remove features from the data distribution. ## ## @item Bandwidth ## (NA) If this property is given a value other than NA, it sets the bandwith of the ## kernel function. No optimization is peformed and the property @asis{SmoothFactor} ## is ignored. ## ## @item Width ## (0.5) Sets the maximum width of the violins. Violins are centered at integer axis ## values. The distance between two violin middle axis is 1. Setting a value ## higher thna 1 in this property will cause the violins to overlap. ## @end table ## ## If the string @asis{"Horizontal"} is among the input arguments, the violin ## plot is rendered along the x axis with the variables in the y axis. ## ## The returned structure @var{h} has handles to the plot elements, allowing ## customization of the visualization using set/get functions. ## ## Example: ## ## @example ## title ("Grade 3 heights"); ## axis ([0,3]); ## set (gca, "xtick", 1:2, "xticklabel", @{"girls"; "boys"@}); ## h = violin (@{randn(100,1)*5+140, randn(130,1)*8+135@}, "Nbins", 10); ## set (h.violin, "linewidth", 2) ## @end example ## ## @seealso{boxplot, hist} ## @end defun function h = violin (ax, varargin) old_hold = ishold (); # First argument is not an axis if (~ishandle (ax) || ~isscalar (ax)) x = ax; ax = gca (); else x = varargin{1}; varargin(1) = []; endif ###################### ## Parse parameters ## parser = inputParser (); parser.CaseSensitive = false; parser.FunctionName = 'violin'; parser.addParamValue ('Nbins', 50); parser.addParamValue ('SmoothFactor', 4); parser.addParamValue ('Bandwidth', NA); parser.addParamValue ('Width', 0.5); parser.addParamValue ('Color', "y"); parser.addSwitch ('Horizontal'); parser.parse (varargin{:}); res = parser.Results; c = res.Color; # Color of violins if (ischar (c)) c = c(:); endif nb = res.Nbins; # Number of bins in histogram sf = res.SmoothFactor; # Smoothing factor for kernel estimation r0 = res.Bandwidth; # User value for KDE bandwth to prevent optimization is_horiz = res.Horizontal; # Whether the plot must be rotated width = res.Width; # Width of the violins clear parser res ###################### ## Make everything a cell for code simplicity if (~iscell (x)) [N Nc] = size (x); x = mat2cell (x, N, ones (1, Nc)); else Nc = numel (x); endif try [nb, c, sf, r0, width] = to_cell (nb, c, sf, r0, width, Nc); catch err if strcmp (err.identifier, "to_cell:element_idx") n = str2num (err.message); txt = {"Nbins", "Color", "SmoothFactor", "Bandwidth", "Width"}; error ("Octave:invaid-input-arg", ... ["options should be scalars or call/array with as many values as" ... " numbers of variables in the data (wrong size of %s)."], txt{n}); else rethrow (lasterror()) endif end ## Build violins [px py mx] = cellfun (@(y,n,s,r)build_polygon(y, n, s, r), ... x, nb, sf, r0, "unif", 0); Nc = 1:numel (px); Ncc = mat2cell (Nc, 1, ones (1, Nc(end))); # get hold state old_hold = ishold (); # Draw plain violins tmp = cellfun (@(x,y,n,u, w)patch(ax, (w * x + n)(:), y(:) ,u), ... px, py, Ncc, c, width); h.violin = tmp; hold on # Overlay mean value tmp = cellfun (@(z,y)plot(ax, z, y,'.k', "markersize", 6), Ncc, mx); h.mean = tmp; # Overlay median Mx = cellfun (@median, x, "unif", 0); tmp = cellfun (@(z,y)plot(ax, z, y, 'ok'), Ncc, Mx); h.median = tmp; # Overlay 1nd and 3th quartiles LUBU = cellfun (@(x,y)abs(quantile(x,[0.25 0.75])-y), x, Mx, "unif", 0); tmp = cellfun (@(x,y,z)errorbar(ax, x, y, z(1),z(2)), Ncc, Mx, LUBU)(:); # Flatten errorbar output handles tmp2 = allchild (tmp); if (~iscell (tmp2)) tmp2 = mat2cell (tmp2, ones(length (tmp2), 1), 1); endif tmp = mat2cell (tmp, ones (length (tmp), 1), 1); tmp = cellfun (@vertcat, tmp, tmp2, "unif", 0); h.quartile = cell2mat (tmp); hold off # Rotate the plot if it is horizontal if (is_horiz) structfun (@swap_axes, h); set (ax, "ytick", Nc); else set (ax, "xtick", Nc); endif if (nargout < 1); clear h; endif # restore hold state if (old_hold) hold on endif endfunction function k = kde(x,r) k = mean (stdnormal_pdf (x / r)) / r; k /= max (k); endfunction function [px py mx] = build_polygon (x, nb, sf, r) N = size (x, 1); mx = mean (x); sx = std (x); X = (x - mx ) / sx; [count bin] = hist (X, nb); count /= max (count); Y = X - bin; if isna (r) r0 = 1.06 * N^(1/5); r = sqp (r0, @(r)sumsq (kde(Y,r) - count), [], [], 1e-3, 1e2); else sf = 1; endif sig = sf * r; ## Create violin polygon # smooth tails: extend to 1.83 sigmas, i.e. ~99% of data. xx = linspace (0, 1.83 * sig, 5); bin = [bin(1)-fliplr(xx) bin bin(end)+xx]; py = [bin; fliplr(bin)].' * sx + mx; v = kde (X-bin, sig).'; px = [v -flipud(v)]; endfunction function tf = swap_axes (h) tmp = mat2cell (h(:), ones (length (h),1), 1); % tmp = cellfun (@(x)[x; allchild(x)], tmp, "unif", 0); tmpy = cellfun(@(x)get(x, "ydata"), tmp, "unif", 0); tmpx = cellfun(@(x)get(x, "xdata"), tmp, "unif", 0); cellfun (@(h,x,y)set (h, "xdata", y, "ydata", x), tmp, tmpx, tmpy); tf = true; endfunction function varargout = to_cell (varargin) m = varargin{end}; varargin(end) = []; for i = 1:numel(varargin) x = varargin{i}; if (isscalar (x)) x = repmat (x, m, 1); endif if (iscell (x)) if (numel(x) ~= m) # no dimension equals m error ("to_cell:element_idx", "%d\n",i); endif varargout{i} = x; continue endif sz = size (x); d = find (sz == m); if (isempty (d)) # no dimension equals m error ("to_cell:element_idx", "%d\n",i); elseif (length (d) == 2) #both dims are m, choose 1st elseif (d == 1) # 2nd dimension is m --> transpose x = x.'; sz = fliplr (sz); endif varargout{i} = mat2cell (x, sz(1), ones (m,1)); endfor endfunction %!demo %! clf %! x = zeros (9e2, 10); %! for i=1:10 %! x(:,i) = (0.1 * randn (3e2, 3) * (randn (3,1) + 1) + ... %! 2 * randn (1,3))(:); %! endfor %! h = violin (x, "color", "c"); %! axis tight %! set (h.violin, "linewidth", 2); %! set (gca, "xgrid", "on"); %! xlabel ("Variables") %! ylabel ("Values") %!demo %! clf %! data = {randn(100,1)*5+140, randn(130,1)*8+135}; %! subplot (1,2,1) %! title ("Grade 3 heights - vertical"); %! set (gca, "xtick", 1:2, "xticklabel", {"girls"; "boys"}); %! violin (data, "Nbins", 10); %! axis tight %! %! subplot(1,2,2) %! title ("Grade 3 heights - horizontal"); %! set (gca, "ytick", 1:2, "yticklabel", {"girls"; "boys"}); %! violin (data, "horizontal", "Nbins", 10); %! axis tight %!demo %! clf %! data = exprnd (0.1, 500,4); %! violin (data, "nbins", {5,10,50,100}); %! axis ([0 5 0 max(data(:))]) %!demo %! clf %! data = exprnd (0.1, 500,4); %! violin (data, "color", jet(4)); %! axis ([0 5 0 max(data(:))]) %!demo %! clf %! data = repmat(exprnd (0.1, 500,1), 1, 4); %! violin (data, "width", linspace (0.1,0.5,4)); %! axis ([0 5 0 max(data(:))]) %!demo %! clf %! data = repmat(exprnd (0.1, 500,1), 1, 4); %! violin (data, "nbins", [5,10,50,100], "smoothfactor", [4 4 8 10]); %! axis ([0 5 0 max(data(:))]) statistics-1.4.3/inst/vmpdf.m0000644000000000000000000000303714153320774014357 0ustar0000000000000000## Copyright (C) 2009 Soren Hauberg ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{theta} = vmpdf (@var{x}, @var{mu}, @var{k}) ## Evaluates the Von Mises probability density function. ## ## The Von Mises distribution has probability density function ## @example ## f (@var{x}) = exp (@var{k} * cos (@var{x} - @var{mu})) / @var{Z} , ## @end example ## where @var{Z} is a normalisation constant. By default, @var{mu} is 0 and ## @var{k} is 1. ## @seealso{vmrnd} ## @end deftypefn function p = vmpdf (x, mu = 0, k = 1) ## Check input if (!isreal (x)) error ("vmpdf: first input must be real"); endif if (!isreal (mu)) error ("vmpdf: second input must be a scalar"); endif if (!isreal (k) || k <= 0) error ("vmpdf: third input must be a real positive scalar"); endif ## Evaluate PDF Z = 2 * pi * besseli (0, k); p = exp (k * cos (x-mu)) / Z; endfunction statistics-1.4.3/inst/vmrnd.m0000644000000000000000000000474014153320774014373 0ustar0000000000000000## Copyright (C) 2009 Soren Hauberg ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{theta} = vmrnd (@var{mu}, @var{k}) ## @deftypefnx{Function File} @var{theta} = vmrnd (@var{mu}, @var{k}, @var{sz}) ## Draw random angles from a Von Mises distribution with mean @var{mu} and ## concentration @var{k}. ## ## The Von Mises distribution has probability density function ## @example ## f (@var{x}) = exp (@var{k} * cos (@var{x} - @var{mu})) / @var{Z} , ## @end example ## where @var{Z} is a normalisation constant. ## ## The output, @var{theta}, is a matrix of size @var{sz} containing random angles ## drawn from the given Von Mises distribution. By default, @var{mu} is 0 ## and @var{k} is 1. ## @seealso{vmpdf} ## @end deftypefn function theta = vmrnd (mu = 0, k = 1, sz = 1) ## Check input if (!isreal (mu)) error ("vmrnd: first input must be a scalar"); endif if (!isreal (k) || k <= 0) error ("vmrnd: second input must be a real positive scalar"); endif if (isscalar (sz)) sz = [sz, sz]; elseif (!isvector (sz)) error ("vmrnd: third input must be a scalar or a vector"); endif ## Simulate! if (k < 1e-6) ## k is small: sample uniformly on circle theta = 2 * pi * rand (sz) - pi; else a = 1 + sqrt (1 + 4 * k.^2); b = (a - sqrt (2 * a)) / (2 * k); r = (1 + b^2) / (2 * b); N = prod (sz); notdone = true (N, 1); while (any (notdone)) u (:, notdone) = rand (3, N); z (notdone) = cos (pi * u (1, notdone)); f (notdone) = (1 + r * z (notdone)) ./ (r + z (notdone)); c (notdone) = k * (r - f (notdone)); notdone = (u (2, :) >= c .* (2 - c)) & (log (c) - log (u (2, :)) + 1 - c < 0); N = sum (notdone); endwhile theta = mu + sign (u (3, :) - 0.5) .* acos (f); theta = reshape (theta, sz); endif endfunction statistics-1.4.3/inst/wblplot.m0000644000000000000000000002602314153320774014726 0ustar0000000000000000## Copyright (C) 2014 Bj{\"o}rn Vennberg ## ## This program is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {wblplot.m} wblplot (@var{data},...) ## @deftypefnx {wblplot.m} {@var{handle} =} wblplot (@var{data},...) ## @deftypefnx {wblplot.m} {[@var{handle} @var{param}] =} wblplot (@var{data}) ## @deftypefnx {wblplot.m} {[@var{handle} @var{param}] =} wblplot (@var{data} , @var{censor}) ## @deftypefnx {wblplot.m} {[@var{handle} @var{param}] =} wblplot (@var{data} , @var{censor}, @var{freq}) ## @deftypefnx {wblplot.m} {[@var{handle} @var{param}] =} wblplot (@var{data} , @var{censor}, @var{freq}, @var{confint}) ## @deftypefnx {wblplot.m} {[@var{handle} @var{param}] =} wblplot (@var{data} , @var{censor}, @var{freq}, @var{confint}, @var{fancygrid}) ## @deftypefnx {wblplot.m} {[@var{handle} @var{param}] =} wblplot (@var{data} , @var{censor}, @var{freq}, @var{confint}, @var{fancygrid}, @var{showlegend}) ## ## ## @noindent ## Plot a column vector @var{data} on a Weibull probability plot using rank regression. ## ## @var{censor}: optional parameter is a column vector of same size as @var{data} ## with 1 for right censored data and 0 for exact observation. ## Pass [] when no censor data are available. ## ## @var{freq}: optional vector same size as data with the number of occurences for corresponding data. ## Pass [] when no frequency data are available. ## ## @var{confint}: optional confidence limits for ploting upper and lower ## confidence bands using beta binomial confidence bounds. If a single ## value is given this will be used such as LOW = a and HIGH = 1 - a. ## Pass [] if confidence bounds is not requested. ## ## @var{fancygrid}: optional parameter which if set to anything but 1 will turn of the the fancy gridlines. ## ## @var{showlegend}: optional parameter that when set to zero(0) turns off the legend. ## ## If one output argument is given, a @var{handle} for the data marker and plotlines are returned ## which can be used for further modification of line and marker style. ## ## If a second output argument is specified, a @var{param} vector with scale, ## shape and correlation factor is returned. ## ## @seealso{normplot, wblpdf} ## @end deftypefn ## Author: Bj{\"o}rn Vennberg ## Created: 2014-11-11 ## 2014-11-22 Updated argin check ## 2014-11-22 Code clean up, error checking ## 2014-11-23 Turn off legend box, check for zero and negative values in data. ## 2014-11-23 Censored data check and inclusion of demo samples. Help info updates. function [handle param] = wblplot (data , censor=[], freq=[], confint=[], fancygrid=1, showlegend=1) [mm nn] = size(data); if mm > 1 && nn > 1 error ("wblplot: can only handle a single data vector") elseif mm == 1 && nn > 1 data=data(:); mm = nn; end if any(data<=0) error("wblplot: data vector must be positive and non zero") end if isempty(freq) freq = ones(mm,1); N = mm; else [mmf nnf]=size(freq); if (mmf == mm && nnf == 1) || (mmf == 1 && nnf == mm) freq = freq(:); N=sum(freq); ## Total number of samples if any(freq<=0) error("wblplot: frequency vector must be positive non zero integers") end else error("wblplot: frequency must be vector of same length as data") end end if isempty(censor) censor = zeros(mm,1); else [mmc nnc]=size(censor); if (mmc == mm && nnc == 1) || (mmc == 1 && nnc == mm) censor = censor(:); else error("wblplot: censor must be a vector of same length as data") end ## Make sure censored data is sorted corectly so that no censored samples ## are processed before failures if they have the same time. if any(censor>0) ind=find(censor>0); ind2=find(data(1:end-1)==data(2:end)); if ~isempty(ind) && ~isempty(ind2) if any(ind==ind2) tmp=censor(ind2); censor(ind2)=censor(ind2+1); censor(ind2+1)=tmp; tmp=freq(ind2); freq(ind2)=freq(ind2+1); freq(ind2+1)=tmp; end end end end ## Determine the order number wbdat=zeros(length(find(censor==0)),3); Op = 0; Oi = 0; c = N; nf = 0; for k = 1 : mm if censor(k, 1) == 0 nf = nf + 1; wbdat(nf, 1) = data(k, 1); for s = 1 : freq(k, 1); Oi = Op + ((N + 1) - Op) / (1 + c); Op = Oi; c = c - 1; end wbdat(nf, 3) = Oi; else c = c - freq(k, 1); endif end ## Compute median rank a=wbdat(:, 3)./(N-wbdat(:, 3)+1); f=finv(0.5,2*(N-wbdat(:, 3)+1),2*wbdat(:, 3)); wbdat(:, 2) = a./(f+a); datx = log(wbdat(:,1)); daty = log(log(1 ./ (1 - wbdat(:,2)))); ## Rank regression poly = polyfit(datx, daty, 1); ## Shape factor beta_rry = poly(1); ## Scale factor eta_rry = exp(-(poly(2) / beta_rry)); ## Determin min-max values of view port aa=ceil(log10(max(wbdat(:,1)))); bb=log10(max(wbdat(:,1))); if aa-bb<0.2 aa=ceil(log10(max(wbdat(:,1))))+1; end xmax= 10^aa; if log10(min(wbdat(:,1)))-floor(log10(min(wbdat(:,1))))<0.2 xmin=10^(floor(log10(min(wbdat(:,1))))-1); else xmin=10^floor(log10(min(wbdat(:,1)))); end if min(wbdat(:,2))>0.20 ymin = log(log(1/(1-0.1))); elseif min(wbdat(:,2))>0.02 ymin = log(log(1/(1-0.01))); elseif min(wbdat(:,2))>0.002 ymin = log(log(1/(1-0.001))); else ymin = log(log(1/(1-0.0001))); end ymax= log(log(1/(1-0.999))); x=[0;0]; y=[0;0]; label = char('0.10','1.00','10.00','99.00'); prob = [0.001 0.01 0.1 0.99]; tick = log(log(1./(1-prob))); xbf = [xmin;xmax]; ybf = polyval(poly, log(xbf)); newplot(); x(1, 1) = xmin; x(2, 1) = xmax; if fancygrid==1 for k = 1 : 4 ## Y major grids x(1, 1) = xmin; x(2, 1) = xmax*10; y(1, 1) = log(log(1 / (1 - 10 ^ (-k)))); y(2, 1) = y(1, 1); ymajorgrid(k) = line(x,y,'LineStyle','-','Marker','none','Color',[1 0.75 0.75],'LineWidth',0.1); end ## Y Minor grids 2 - 9 x(1, 1) = xmin; x(2, 1) = xmax*10; for m = 1 : 4 for k = 1 : 8 y(1, 1) = log(log(1 / (1 - ((k + 1) / (10 ^ m))))); y(2, 1) = y(1, 1); yminorgrid(k) = line(x,y,'LineStyle','-','Marker','none','Color',[0.75 1 0.75],'LineWidth',0.1); end end ## X-axis grid y(1, 1) = ymin; y(2, 1) = ymax; for m = log10(xmin) : log10(xmax) x(1, 1) = 10 ^ m; x(2, 1) = x(1, 1); y(1, 1) = ymin; % y(2, 1) = ymax; % xmajorgrid(k) = line(x,y,'LineStyle','-','Marker','none','Color',[1 0.75 0.75]); for k = 1 : 8 ## X Minor grids - 2 - 9 x(1, 1) = (k + 1) * (10 ^ m); x(2, 1) = (k + 1) * (10 ^ m); xminorgrid(k) = line(x,y,'LineStyle','-','Marker','none','Color',[0.75 1 0.75],'LineWidth',0.1); end end end set(gca,'XScale','log'); set(gca,'YTick',tick,'YTickLabel',label); xlabel('Data','FontSize',12); ylabel('Unreliability, F(t)=1-R(t)','FontSize',12); title('Weibull Probability Plot','FontSize',12); set(gcf,'Color',[0.9,0.9,0.9]) set(gcf,'name','WblPlot') hold on h=plot(wbdat(:,1),daty,'o'); set(h,'markerfacecolor',[0,0,1]) set(h,'markersize',8) h2 = line(xbf,ybf,'LineStyle','-','Marker','none','Color',[0.25 0.25 1],'LineWidth',1); ## If requested plot beta binomial confidens bounds if ~isempty(confint) cb_high=[]; cb_low=[]; if length(confint)==1 if confint >0.5 cb_high=confint; cb_low=1-confint; else cb_high=1-confint; cb_low=confint; end else cb_high=confint(2); cb_low=confint(1); end conf=zeros(N+4,3); betainv = 1 / beta_rry; N2 = [1:N]'; N2=[0.3;0.7;N2;N2(end)+0.5;N2(end)+0.8]; ## Extend the ends a bit ypos = medianranks(0.5, N, N2); conf(:, 1) = eta_rry * log(1./ (1 - ypos)).^ betainv; conf(:, 2) = medianranks(cb_low, N, N2); conf(:, 3) = medianranks(cb_high, N, N2); confy=log(log(1./(1-conf(:,2:3)))); confu=[conf(:,1) confy]; if conf(1,1)>xmin ## Not totally correct but it looks better to extend the lines. p1=polyfit(log(conf(1:2,1)),confy(1:2,1),1); y1=polyval(p1,log(xmin)); p2=polyfit(log(conf(1:2,1)),confy(1:2,2),1); y2=polyval(p2,log(xmin)); confu=[xmin y1 y2;confu]; end if conf(end,1)= 2 param = [eta_rry beta_rry rsq]; if ~isempty(confint) handle = [h; h2; h3]; else handle = [h; h2]; end end if nargout == 1 if ~isempty(confint) handle = [h; h2; h3]; else handle = [h; h2]; end end endfunction function [ ret ] = medianranks (alpha, n, ii) a=ii./(n-ii+1); f=finv(alpha,2*(n-ii+1),2*ii); ret=a./(f+a); endfunction %!demo %! x=[16 34 53 75 93 120]; %! wblplot(x); %!demo %! x=[2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67]'; %! c=[0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1]'; %! [h p]=wblplot(x,c) %!demo %! x=[16, 34, 53, 75, 93, 120, 150, 191, 240 ,339]; %! [h p]=wblplot(x,[],[],0.05) %! ## Benchmark Reliasoft eta = 146.2545 beta 1.1973 rho = 0.9999 %!demo %! x=[46 64 83 105 123 150 150]; %! c=[0 0 0 0 0 0 1]; %! f=[1 1 1 1 1 1 4]; %! wblplot(x,c,f,0.05); %!demo %! x=[46 64 83 105 123 150 150]; %! c=[0 0 0 0 0 0 1]; %! f=[1 1 1 1 1 1 4]; %! ## Subtract 30.92 from x to simulate a 3 parameter wbl with gamma = 30.92 %! wblplot(x-30.92,c,f,0.05); ## Get current figure visibility so it can be restored after tests %!shared visibility_setting %! visibility_setting = get (0, "DefaultFigureVisible"); %!test %! set (0, "DefaultFigureVisible", "off"); %! x=[16, 34, 53, 75, 93, 120, 150, 191, 240 ,339]; %! [h p]=wblplot(x,[],[],0.05); %! assert(numel(h), 4) %! assert(p(1), 146.2545, 1E-4) %! assert(p(2), 1.1973, 1E-4) %! assert(p(3), 0.9999, 5E-5) %! set (0, "DefaultFigureVisible", visibility_setting); statistics-1.4.3/inst/wblstat.m0000644000000000000000000000667714153320774014740 0ustar0000000000000000## Copyright (C) 2006, 2007 Arno Onken ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{m}, @var{v}] =} wblstat (@var{scale}, @var{shape}) ## Compute mean and variance of the Weibull distribution. ## ## @subheading Arguments ## ## @itemize @bullet ## @item ## @var{scale} is the scale parameter of the Weibull distribution. ## @var{scale} must be positive ## ## @item ## @var{shape} is the shape parameter of the Weibull distribution. ## @var{shape} must be positive ## @end itemize ## @var{scale} and @var{shape} must be of common size or one of them must be ## scalar ## ## @subheading Return values ## ## @itemize @bullet ## @item ## @var{m} is the mean of the Weibull distribution ## ## @item ## @var{v} is the variance of the Weibull distribution ## @end itemize ## ## @subheading Examples ## ## @example ## @group ## scale = 3:8; ## shape = 1:6; ## [m, v] = wblstat (scale, shape) ## @end group ## ## @group ## [m, v] = wblstat (6, shape) ## @end group ## @end example ## ## @subheading References ## ## @enumerate ## @item ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, ## 2001. ## ## @item ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic ## Processes}. McGraw-Hill, New York, second edition, 1984. ## @end enumerate ## @end deftypefn ## Author: Arno Onken ## Description: Moments of the Weibull distribution function [m, v] = wblstat (scale, shape) # Check arguments if (nargin != 2) print_usage (); endif if (! isempty (scale) && ! ismatrix (scale)) error ("wblstat: scale must be a numeric matrix"); endif if (! isempty (shape) && ! ismatrix (shape)) error ("wblstat: shape must be a numeric matrix"); endif if (! isscalar (scale) || ! isscalar (shape)) [retval, scale, shape] = common_size (scale, shape); if (retval > 0) error ("wblstat: scale and shape must be of common size or scalar"); endif endif # Calculate moments m = scale .* gamma (1 + 1 ./ shape); v = (scale .^ 2) .* gamma (1 + 2 ./ shape) - m .^ 2; # Continue argument check k = find (! (scale > 0) | ! (scale < Inf) | ! (shape > 0) | ! (shape < Inf)); if (any (k)) m(k) = NaN; v(k) = NaN; endif endfunction %!test %! scale = 3:8; %! shape = 1:6; %! [m, v] = wblstat (scale, shape); %! expected_m = [3.0000, 3.5449, 4.4649, 5.4384, 6.4272, 7.4218]; %! expected_v = [9.0000, 3.4336, 2.6333, 2.3278, 2.1673, 2.0682]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); %!test %! shape = 1:6; %! [m, v] = wblstat (6, shape); %! expected_m = [ 6.0000, 5.3174, 5.3579, 5.4384, 5.5090, 5.5663]; %! expected_v = [36.0000, 7.7257, 3.7920, 2.3278, 1.5923, 1.1634]; %! assert (m, expected_m, 0.001); %! assert (v, expected_v, 0.001); statistics-1.4.3/inst/wishpdf.m0000644000000000000000000000542214153320774014707 0ustar0000000000000000## Copyright (C) 2013 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License along with Octave; see the file COPYING. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} @var{y} = wishpdf (@var{W}, @var{Sigma}, @var{df}, @var{log_y}=false) ## Compute the probability density function of the Wishart distribution ## ## Inputs: A @var{p} x @var{p} matrix @var{W} where to find the PDF. The @var{p} x @var{p} positive definite matrix @var{Sigma} and scalar degrees of freedom parameter @var{df} characterizing the Wishart distribution. (For the density to be finite, need @var{df} > (@var{p} - 1).) ## If the flag @var{log_y} is set, return the log probability density -- this helps avoid underflow when the numerical value of the density is very small ## ## Output: @var{y} is the probability density of Wishart(@var{Sigma}, @var{df}) at @var{W}. ## ## @seealso{wishrnd, iwishpdf} ## @end deftypefn ## Author: Nir Krakauer ## Description: Compute the probability density function of the Wishart distribution function [y] = wishpdf(W, Sigma, df, log_y=false) if (nargin < 3) print_usage (); endif p = size(Sigma, 1); if (df <= (p - 1)) error('df too small, no finite densities exist') endif #calculate the logarithm of G_d(df/2), the multivariate gamma function g = (p * (p-1) / 4) * log(pi); for i = 1:p g = g + log(gamma((df + (1 - i))/2)); #using lngamma_gsl(.) from the gsl package instead of log(gamma(.)) might help avoid underflow/overflow endfor C = chol(Sigma); #use formulas for determinant of positive definite matrix for better efficiency and numerical accuracy logdet_W = 2*sum(log(diag(chol(W)))); logdet_Sigma = 2*sum(log(diag(C))); y = -(df*p)/2 * log(2) - (df/2)*logdet_Sigma - g + ((df - p - 1)/2)*logdet_W - trace(chol2inv(C)*W)/2; if ~log_y y = exp(y); endif endfunction ##test results cross-checked against dwish function in R MCMCpack library %!assert(wishpdf(4, 3, 3.1), 0.07702496, 1E-7); %!assert(wishpdf([2 -0.3;-0.3 4], [1 0.3;0.3 1], 4), 0.004529741, 1E-7); %!assert(wishpdf([6 2 5; 2 10 -5; 5 -5 25], [9 5 5; 5 10 -8; 5 -8 22], 5.1), 4.474865e-10, 1E-15); %% Test input validation %!error wishpdf () %!error wishpdf (1, 2) %!error wishpdf (1, 2, 0) %!error wishpdf (1, 2) statistics-1.4.3/inst/wishrnd.m0000644000000000000000000000645714153320774014732 0ustar0000000000000000## Copyright (C) 2013-2019 Nir Krakauer ## ## This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License along with Octave; see the file COPYING. If not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} [@var{W}[, @var{D}]] = wishrnd (@var{Sigma}, @var{df}[, @var{D}][, @var{n}=1]) ## Return a random matrix sampled from the Wishart distribution with given parameters ## ## Inputs: the @var{p} x @var{p} positive definite matrix @var{Sigma} (or the lower-triangular Cholesky factor @var{D} of @var{Sigma}) and scalar degrees of freedom parameter @var{df}. ## @var{df} can be non-integer as long as @var{df} > @var{p} ## ## Output: a random @var{p} x @var{p} matrix @var{W} from the Wishart(@var{Sigma}, @var{df}) distribution. If @var{n} > 1, then @var{W} is @var{p} x @var{p} x @var{n} and holds @var{n} such random matrices. (Optionally, the lower-triangular Cholesky factor @var{D} of @var{Sigma} is also returned.) ## ## Averaged across many samples, the mean of @var{W} should approach @var{df}*@var{Sigma}, and the variance of each element @var{W}_ij should approach @var{df}*(@var{Sigma}_ij^2 + @var{Sigma}_ii*@var{Sigma}_jj) ## ## Reference: Yu-Cheng Ku and Peter Bloomfield (2010), Generating Random Wishart Matrices with Fractional Degrees of Freedom in OX, http://www.gwu.edu/~forcpgm/YuChengKu-030510final-WishartYu-ChengKu.pdf ## ## @seealso{iwishrnd, wishpdf} ## @end deftypefn ## Author: Nir Krakauer ## Description: Sample from the Wishart distribution function [W, D] = wishrnd(Sigma, df, D, n=1) if (nargin < 2) print_usage (); endif if nargin < 3 || isempty(D) try D = chol(Sigma, 'lower'); catch error('wishrnd: Cholesky decomposition failed; Sigma probably not positive definite') end_try_catch endif p = size(D, 1); if df < p df = floor(df); #distribution not defined for small noninteger df df_isint = 1; else #check for integer degrees of freedom df_isint = (df == floor(df)); endif if ~df_isint [ii, jj] = ind2sub([p, p], 1:(p*p)); endif if n > 1 W = nan(p, p, n); endif for i = 1:n if df_isint Z = D * randn(p, df); else Z = diag(sqrt(chi2rnd(df - (0:(p-1))))); #fill diagonal #note: chi2rnd(x) is equivalent to 2*randg(x/2), but the latter seems to offer no performance advantage Z(ii > jj) = randn(p*(p-1)/2, 1); #fill lower triangle with normally distributed variates Z = D * Z; endif W(:, :, i) = Z*Z'; endfor endfunction %!assert(size (wishrnd (1,2)), [1, 1]); %!assert(size (wishrnd (1,2,[])), [1, 1]); %!assert(size (wishrnd (1,2,1)), [1, 1]); %!assert(size (wishrnd ([],2,1)), [1, 1]); %!assert(size (wishrnd ([3 1; 1 3], 2.00001, [], 1)), [2, 2]); %!assert(size (wishrnd (eye(2), 2, [], 3)), [2, 2, 3]); %% Test input validation %!error wishrnd () %!error wishrnd (1) %!error wishrnd ([1; 1], 2) statistics-1.4.3/inst/ztest.m0000644000000000000000000001021514153320774014410 0ustar0000000000000000## Copyright (C) 2014 Tony Richardson ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{z}, @var{zcrit}] =} ztest (@var{x}, @var{m}, @var{s}) ## @deftypefnx {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{z}, @var{zcrit}] =} ztest (@var{x}, @var{m}, @var{s}, @var{Name}, @var{Value}) ## Test for mean of a normal sample with known variance. ## ## Perform a Z-test of the null hypothesis @code{mean (@var{x}) == @var{m}} ## for a sample @var{x} from a normal distribution with unknown ## mean and known std deviation @var{s}. Under the null, the test statistic ## @var{z} follows a standard normal distribution. ## ## Name-Value pair arguments can be used to set various options. ## @qcode{"alpha"} can be used to specify the significance level ## of the test (the default value is 0.05). @qcode{"tail"}, can be used ## to select the desired alternative hypotheses. If the value is ## @qcode{"both"} (default) the null is tested against the two-sided ## alternative @code{mean (@var{x}) != @var{m}}. ## If it is @qcode{"right"} the one-sided alternative @code{mean (@var{x}) ## > @var{m}} is considered. Similarly for @qcode{"left"}, the one-sided ## alternative @code{mean (@var{x}) < @var{m}} is considered. ## When argument @var{x} is a matrix, @qcode{"dim"} can be used to selection ## the dimension over which to perform the test. (The default is the ## first non-singleton dimension.) ## ## If @var{h} is 0 the null hypothesis is accepted, if it is 1 the null ## hypothesis is rejected. The p-value of the test is returned in @var{pval}. ## A 100(1-alpha)% confidence interval is returned in @var{ci}. The test statistic ## value is returned in @var{z} and the z critical value in @var{zcrit}. ## ## @end deftypefn ## Author: Tony Richardson function [h, p, ci, zval, zcrit] = ztest(x, m, sigma, varargin) alpha = 0.05; tail = 'both'; % Find the first non-singleton dimension of x dim = min(find(size(x)~=1)); if isempty(dim), dim = 1; end i = 1; while ( i <= length(varargin) ) switch lower(varargin{i}) case 'alpha' i = i + 1; alpha = varargin{i}; case 'tail' i = i + 1; tail = varargin{i}; case 'dim' i = i + 1; dim = varargin{i}; otherwise error('Invalid Name argument.',[]); end i = i + 1; end if ~isa(tail, 'char') error('tail argument to ztest must be a string\n',[]); end % Calculate the test statistic value (zval) n = size(x, dim); x_bar = mean(x, dim); x_bar_std = sigma/sqrt(n); zval = (x_bar - m)./x_bar_std; % Based on the "tail" argument determine the P-value, the critical values, % and the confidence interval. switch lower(tail) case 'both' p = 2*(1 - normcdf(abs(zval))); zcrit = -norminv(alpha/2); ci = [x_bar-zcrit*x_bar_std; x_bar+zcrit*x_bar_std]; case 'left' p = normcdf(zval); zcrit = -norminv(alpha); ci = [-inf*ones(size(x_bar)); x_bar+zcrit*x_bar_std]; case 'right' p = 1 - normcdf(zval); zcrit = -norminv(alpha); ci = [x_bar-zcrit*x_bar_std; inf*ones(size(x_bar))]; otherwise error('Invalid fifth (tail) argument to ztest\n',[]); end % Reshape the ci array to match MATLAB shaping if and(isscalar(x_bar), dim==2) ci = ci(:)'; elseif size(x_bar,2)> Statistics Distributions stdnormal_rnd hygecdf hygeinv cauchy_inv discrete_rnd wienrnd nbinpdf unidrnd wblrnd geoinv hygepdf logncdf cauchy_pdf finv chi2pdf empirical_pdf geornd unidinv betacdf fpdf fcdf unifcdf discrete_inv stdnormal_inv stdnormal_pdf exprnd normcdf discrete_cdf poissinv empirical_rnd wblcdf laplace_cdf stdnormal_cdf gampdf laplace_pdf laplace_rnd expcdf unifinv nbinrnd betapdf trnd geocdf laplace_inv tcdf unidpdf normrnd binocdf poisscdf tinv discrete_pdf empirical_inv norminv gamcdf unifpdf empirical_cdf nbincdf logistic_inv frnd chi2cdf cauchy_cdf lognpdf normpdf logistic_cdf betarnd wblinv chi2inv hygernd poisspdf kolmogorov_smirnov_cdf logistic_rnd exppdf binopdf lognrnd logninv binoinv geopdf betainv cauchy_rnd poissrnd gamrnd nbininv expinv chi2rnd wblpdf tpdf logistic_pdf binornd unidcdf gaminv unifrnd Models logistic_regression Hypothesis testing kolmogorov_smirnov_test_2 t_test_2 hotelling_test wilcoxon_test chisquare_test_independence hotelling_test_2 bartlett_test run_test t_test welch_test anova var_test manova sign_test u_test cor_test mcnemar_test chisquare_test_homogeneity z_test prop_test_2 f_test_regression kolmogorov_smirnov_test kruskal_wallis_test z_test_2 t_test_regression Descriptive statistics mad corr probit corrcoef kendall var lscov quantile logit mean range ranks statistics cloglog mode std prctile crosstab moment cov median spearman kurtosis zscore run_count skewness iqr ols runlength Other center ismissing rmmissing Plots qqplot ppplot histc Clustering meansq gls statistics-1.4.3/install-conditionally/README0000644000000000000000000000121614153320774017301 0ustar0000000000000000This directory contains functions currently or previously available in core Octave. Of these functions, only those not present in the local Octave version will be installed by the package. Under this directory: Only statistics functions available in some core Octave versions should be added. (Functions with different names than (former) core Octave functions should be placed under inst/ .) If functions are added, they should also be added to the file utils/functions_to_install. Newer function versions than contained in core Octave can be developed, but this should only be done for functions removed (or scheduled for removal) from core Octave. statistics-1.4.3/install-conditionally/base/0000755000000000000000000000000014153320774017333 5ustar0000000000000000statistics-1.4.3/install-conditionally/base/center.m0000644000000000000000000000615414153320774020777 0ustar0000000000000000## Copyright (C) 1995-2017 Kurt Hornik ## Copyright (C) 2009 VZLU Prague ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} center (@var{x}) ## @deftypefnx {} {} center (@var{x}, @var{dim}) ## Center data by subtracting its mean. ## ## If @var{x} is a vector, subtract its mean. ## ## If @var{x} is a matrix, do the above for each column. ## ## If the optional argument @var{dim} is given, operate along this dimension. ## ## Programming Note: @code{center} has obvious application for normalizing ## statistical data. It is also useful for improving the precision of general ## numerical calculations. Whenever there is a large value that is common ## to a batch of data, the mean can be subtracted off, the calculation ## performed, and then the mean added back to obtain the final answer. ## @seealso{zscore} ## @end deftypefn ## Author: KH ## Description: Center by subtracting means function retval = center (x, dim) if (nargin != 1 && nargin != 2) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("center: X must be a numeric vector or matrix"); endif if (isinteger (x)) x = double (x); endif nd = ndims (x); sz = size (x); if (nargin != 2) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) error ("center: DIM must be an integer and a valid dimension"); endif endif n = size (x, dim); if (n == 0) retval = x; else ## FIXME: Use bsxfun, rather than broadcasting, until broadcasting ## supports diagonal and sparse matrices (Bugs #41441, #35787). retval = bsxfun (@minus, x, mean (x, dim)); ## retval = x - mean (x, dim); # automatic broadcasting endif endfunction %!assert (center ([1,2,3]), [-1,0,1]) %!assert (center (single ([1,2,3])), single ([-1,0,1])) %!assert (center (int8 ([1,2,3])), [-1,0,1]) %!assert (center (logical ([1, 0, 0, 1])), [0.5, -0.5, -0.5, 0.5]) %!assert (center (ones (3,2,0,2)), zeros (3,2,0,2)) %!assert (center (ones (3,2,0,2, "single")), zeros (3,2,0,2, "single")) %!assert (center (magic (3)), [3,-4,1;-2,0,2;-1,4,-3]) %!assert (center ([1 2 3; 6 5 4], 2), [-1 0 1; 1 0 -1]) %!assert (center (1, 3), 0) ## Test input validation %!error center () %!error center (1, 2, 3) %!error center (1, ones (2,2)) %!error center (1, 1.5) %!error center (1, 0) statistics-1.4.3/install-conditionally/base/cloglog.m0000644000000000000000000000263614153320774021146 0ustar0000000000000000## Copyright (C) 1995-2017 Kurt Hornik ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} cloglog (@var{x}) ## Return the complementary log-log function of @var{x}. ## ## The complementary log-log function is defined as ## @tex ## $$ ## {\rm cloglog}(x) = - \log (- \log (x)) ## $$ ## @end tex ## @ifnottex ## ## @example ## cloglog (x) = - log (- log (@var{x})) ## @end example ## ## @end ifnottex ## @end deftypefn ## Author: KH ## Description: Complementary log-log function function y = cloglog (x) if (nargin != 1) print_usage (); endif y = - log (- log (x)); endfunction %!assert (cloglog (0), -Inf) %!assert (cloglog (1), Inf) %!assert (cloglog (1/e), 0) ## Test input validation %!error cloglog () %!error cloglog (1, 2) statistics-1.4.3/install-conditionally/base/corr.m0000644000000000000000000000601214153320774020455 0ustar0000000000000000## Copyright (C) 1996-2017 John W. Eaton ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} corr (@var{x}) ## @deftypefnx {} {} corr (@var{x}, @var{y}) ## Compute matrix of correlation coefficients. ## ## If each row of @var{x} and @var{y} is an observation and each column is ## a variable, then the @w{(@var{i}, @var{j})-th} entry of ## @code{corr (@var{x}, @var{y})} is the correlation between the ## @var{i}-th variable in @var{x} and the @var{j}-th variable in @var{y}. ## @tex ## $$ ## {\rm corr}(x,y) = {{\rm cov}(x,y) \over {\rm std}(x) \, {\rm std}(y)} ## $$ ## @end tex ## @ifnottex ## ## @example ## corr (@var{x},@var{y}) = cov (@var{x},@var{y}) / (std (@var{x}) * std (@var{y})) ## @end example ## ## @end ifnottex ## If called with one argument, compute @code{corr (@var{x}, @var{x})}, ## the correlation between the columns of @var{x}. ## @seealso{cov} ## @end deftypefn ## Author: Kurt Hornik ## Created: March 1993 ## Adapted-By: jwe function retval = corr (x, y = []) if (nargin < 1 || nargin > 2) print_usage (); endif ## Input validation is done by cov.m. Don't repeat tests here ## Special case, scalar is always 100% correlated with itself if (isscalar (x)) if (isa (x, "single")) retval = single (1); else retval = 1; endif return; endif ## No check for division by zero error, which happens only when ## there is a constant vector and should be rare. if (nargin == 2) c = cov (x, y); s = std (x)' * std (y); retval = c ./ s; else c = cov (x); s = sqrt (diag (c)); retval = c ./ (s * s'); endif endfunction %!test %! x = rand (10); %! cc1 = corr (x); %! cc2 = corr (x, x); %! assert (size (cc1) == [10, 10] && size (cc2) == [10, 10]); %! assert (cc1, cc2, sqrt (eps)); %!test %! x = [1:3]'; %! y = [3:-1:1]'; %! assert (corr (x, y), -1, 5*eps); %! assert (corr (x, flipud (y)), 1, 5*eps); %! assert (corr ([x, y]), [1 -1; -1 1], 5*eps); %!test %! x = single ([1:3]'); %! y = single ([3:-1:1]'); %! assert (corr (x, y), single (-1), 5*eps); %! assert (corr (x, flipud (y)), single (1), 5*eps); %! assert (corr ([x, y]), single ([1 -1; -1 1]), 5*eps); %!assert (corr (5), 1) %!assert (corr (single (5)), single (1)) ## Test input validation %!error corr () %!error corr (1, 2, 3) %!error corr ([1; 2], ["A", "B"]) %!error corr (ones (2,2,2)) %!error corr (ones (2,2), ones (2,2,2)) statistics-1.4.3/install-conditionally/base/corrcoef.m0000644000000000000000000001516314153320774021321 0ustar0000000000000000## Copyright (C) 2016-2017 Guillaume Flandin ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {@var{r} =} corrcoef (@var{x}) ## @deftypefnx {} {@var{r} =} corrcoef (@var{x}, @var{y}) ## @deftypefnx {} {[@var{r}, @var{p}] =} corrcoef (@dots{}) ## @deftypefnx {} {[@var{r}, @var{p}, @var{lci}, @var{hci}] =} corrcoef (@dots{}) ## @deftypefnx {} {[@dots{}] =} corrcoef (@dots{}, @var{param}, @var{value}, @dots{}) ## Compute a matrix of correlation coefficients. ## ## @var{x} is an array where each column contains a variable and each row is ## an observation. ## ## If a second input @var{y} (of the same size as @var{x}) is given then ## calculate the correlation coefficients between @var{x} and @var{y}. ## ## @var{r} is a matrix of Pearson's product moment correlation coefficients for ## each pair of variables. ## ## @var{p} is a matrix of pair-wise p-values testing for the null hypothesis of ## a correlation coefficient of zero. ## ## @var{lci} and @var{hci} are matrices containing, respectively, the lower and ## higher bounds of the 95% confidence interval of each correlation ## coefficient. ## ## @var{param}, @var{value} are pairs of optional parameters and values. ## Valid options are: ## ## @table @asis ## @item @qcode{"alpha"} ## Confidence level used for the definition of the bounds of the confidence ## interval, @var{lci} and @var{hci}. Default is 0.05, i.e., 95% confidence ## interval. ## ## @item @qcode{"rows"} ## Determine processing of NaN values. Acceptable values are @qcode{"all"}, ## @qcode{"complete"}, and @qcode{"pairwise"}. Default is @qcode{"all"}. ## With @qcode{"complete"}, only the rows without NaN values are considered. ## With @qcode{"pairwise"}, the selection of NaN-free rows is made for each ## pair of variables. ## ## @end table ## ## @seealso{corr, cov, cor_test} ## @end deftypefn ## FIXME: It would be good to add a definition of the calculation method ## for a Pearson product moment correlation to the documentation. function [r, p, lci, hci] = corrcoef (x, varargin) if (nargin == 0) print_usage (); endif alpha = 0.05; rows = "all"; if (nargin > 1) ## Check for numeric y argument if (isnumeric (varargin{1})) x = [x(:), varargin{1}(:)]; varargin(1) = []; endif ## Check for Parameter/Value arguments for i = 1:2:numel (varargin) if (! ischar (varargin{i})) error ("corrcoef: parameter %d must be a string", i); endif parameter = varargin{i}; if (numel (varargin) < i+1) error ('corrcoef: parameter "%s" missing value', parameter); endif value = varargin{i+1}; switch (tolower (parameter)) case "alpha" if (isnumeric (value) && isscalar (value) && value >= 0 && value <= 1) alpha = value; else error ('corrcoef: "alpha" must be a number between 0 and 1'); endif case "rows" if (! ischar (value)) error ('corrcoef: "rows" value must be a string'); endif value = tolower (value); switch (value) case {"all", "complete", "pairwise"} rows = value; otherwise error ('corrcoef: "rows" must be "all", "complete", or "pairwise".'); endswitch otherwise error ('corrcoef: Unknown option "%s"', parameter); endswitch endfor endif if (strcmp (rows, "complete")) x(any (isnan (x), 2), :) = []; endif if (isempty (x) || isscalar (x)) r = p = lci = hci = NaN; return; endif ## Flags for calculation pairwise = strcmp (rows, "pairwise"); calc_pval = nargout > 1; if (isrow (x)) x = x(:); endif [m, n] = size (x); r = eye (n); if (calc_pval) p = eye (n); endif if (strcmp (rows, "pairwise")) mpw = m * ones (n); endif for i = 1:n if (! pairwise && any (isnan (x(:,i)))) r(i,i) = NaN; if (nargout > 1) p(i,i) = NaN; endif endif for j = i+1:n xi = x(:,i); xj = x(:,j); if (pairwise) idx = any (isnan ([xi xj]), 2); xi(idx) = xj(idx) = []; mpw(i,j) = mpw(j,i) = m - nnz (idx); endif r(i,j) = r(j,i) = corr (xi, xj); if (calc_pval) T = cor_test (xi, xj, "!=", "pearson"); p(i,j) = p(j,i) = T.pval; endif endfor endfor if (nargout > 2) if (pairwise) m = mpw; endif CI = sqrt (2) * erfinv (1-alpha) ./ sqrt (m-3); lci = tanh (atanh (r) - CI); hci = tanh (atanh (r) + CI); endif endfunction %!test %! x = rand (5); %! r = corrcoef (x); %! assert (size (r) == [5, 5]); %!test %! x = [1 2 3]; %! r = corrcoef (x); %! assert (size (r) == [1, 1]); %!test %! x = []; %! r = corrcoef (x); %! assert (isnan (r)); %!test %! x = [NaN]; %! r = corrcoef (x); %! assert (isnan (r)); %!test %! x = [1]; %! r = corrcoef (x); %! assert (isnan (r)); %!test %! x = [NaN NaN]; %! r = corrcoef (x); %! assert (size(r) == [1, 1] && isnan (r)); %!test %! x = rand (5); %! [r, p] = corrcoef (x); %! assert (size (r) == [5, 5] && size (p) == [5 5]); %!test %! x = rand (5,1); %! y = rand (5,1); %! R1 = corrcoef (x, y); %! R2 = corrcoef ([x, y]); %! assert (R1, R2); %!test %! x = [1;2;3]; %! y = [1;2;3]; %! r = corrcoef (x, y); %! assert (r, ones (2,2)); %!test %! x = [1;2;3]; %! y = [3;2;1]; %! r = corrcoef (x, y); %! assert (r, [1, -1; -1, 1]); %!test %! x = [1;2;3]; %! y = [1;1;1]; %! r = corrcoef (x, y); %! assert (r, [1, NaN; NaN, 1]); %!test %!error corrcoef () %!error corrcoef (1, 2, 3) %!error corrcoef (1, 2, "alpha") %!error <"alpha" must be a number> corrcoef (1,2, "alpha", "1") %!error <"alpha" must be a number> corrcoef (1,2, "alpha", ones (2,2)) %!error <"alpha" must be a number between 0 and 1> corrcoef (1,2, "alpha", -1) %!error <"alpha" must be a number between 0 and 1> corrcoef (1,2, "alpha", 2) %!error <"rows" must be "all"...> corrcoef (1,2, "rows", "foobar") %!error corrcoef (1,2, "foobar", 1) statistics-1.4.3/install-conditionally/base/cov.m0000644000000000000000000004230614153320774020305 0ustar0000000000000000## Copyright (C) 1995-2017 Kurt Hornik ## Copyright (C) 2017 Nicholas R. Jankowski ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} cov (@var{x}) ## @deftypefnx {} {} cov (@var{x}, @var{opt}) ## @deftypefnx {} {} cov (@var{x}, @var{y}) ## @deftypefnx {} {} cov (@var{x}, @var{y}, @var{opt}) ## @deftypefnx {} {} cov (@var{x}, @var{y}, @var{opt}, @var{NaN-option}) ## Compute the covariance matrix. ## ## If each row of @var{x} and @var{y} is an observation, and each column is ## a variable, then the @w{(@var{i}, @var{j})-th} entry of ## @code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th ## variable in @var{x} and the @var{j}-th variable in @var{y}. ## @tex ## $$ ## \sigma_{ij} = {1 \over N-1} \sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y}) ## $$ ## where $\bar{x}$ and $\bar{y}$ are the mean values of @var{x} and @var{y}. ## @end tex ## @ifnottex ## ## @example ## cov (@var{x}) = 1/(N-1) * SUM_i (@var{x}(i) - mean(@var{x})) * (@var{y}(i) - mean(@var{y})) ## @end example ## ## where @math{N} is the length of the @var{x} and @var{y} vectors. ## ## @end ifnottex ## ## If called with one argument, compute @code{cov (@var{x}, @var{x})}, the ## covariance between the columns of @var{x}. ## ## If called with two vector arguments, compute ## @code{cov (@var{x}, @var{y})}, the covariance between two random variables ## @var{x} and @var{y}. The output will be the 2 by 2 covariance matrix. ## ## If called with two matrix arguments, the matrices are treated as vectors and ## covariance is computed as @code{cov (@var{x}(:), @var{y}(:))}. The output ## will be the 2 by 2 covariance matrix. ## ## The optional argument @var{opt} determines the type of normalization to use. ## Valid values are ## ## @table @asis ## @item 0: ## normalize with @math{N-1}, provides the best unbiased estimator of the ## covariance [default] ## ## @item 1: ## normalize with @math{N}, this provides the second moment around the mean ## @end table ## ## The optional argument @var{NaN-option} controls how @code{cov} deals with NaN ## values in the data. The three valid values are ## ## @table @asis ## @item includenan: ## leave NaN values in @var{x} and @var{y}. Output will follow the normal ## rules for handling NaN values in arithemtic operations [default] ## ## @item omitnans: ## rows containing NaN values are trimmed from both @var{x} and @var{y} prior ## to calculating the covariance. (A NaN in one variable will that row from ## both @var{x} and @var{y}.) ## ## @item partialnans: ## rows containing NaN values are ignored from both @var{x} and @var{y} ## independently when for each @var{i}-th and @var{j}-th covariance ## calculation. This may result in a different number of observations, ## @math{N}, being used to calculated each element of the covariance matrix. ## @end table ## ## Compatibility Note: This version of @code{cov} attempts to maintain full ## compatibility with @sc{matlab}'s cov function by treating @var{x} and ## @var{y} as two univariate distributions regardless of shape, resulting in ## a 2x2 output matrix. Previous versions of cov in Octave treated rows ## of @var{x} and @var{y} as multivariate random variables. Code relying on ## Octave's previous definition will need to be changed when running this newer ## version of @code{cov}. ## @seealso{corr} ## @end deftypefn ## Author: KH ## Author: Nicholas Jankowski ## Description: Compute covariances function c = cov (x, varargin) %%input sorting switch nargin case 1 [y, opt, handlenan] = deal ({"no_y", 0, "includenan"}{:}); case 4 [y, opt, handlenan] = deal (varargin{:}); case {2,3} [y, opt, handlenan] = deal ({"no_y", 0, "includenan"}{:}); for vararg_idx = 1 : (nargin-1) v = varargin{vararg_idx}; if ischar (v) if (vararg_idx == 1 && nargin == 3) error ('cov: NaN handling string must be the last input'); else handlenan = v; endif else if (isscalar(v) && (v == 0 || v == 1)) opt = v; elseif (vararg_idx ~= 2) y = v; else print_usage(); endif endif endfor otherwise print_usage(); endswitch ## check sorted X if ~((isnumeric (x) || islogical (x)) && (ndims (x) == 2)) error ("cov: X must be a numeric 2-D matrix or vector"); endif ##vector x needs to be column for calulations, flip before any nantrimming if (isrow (x)) x = x'; endif if ~(strcmp (y, "no_y")) ## check sorted Y assuming one is given if ~((isnumeric (y) || islogical (y)) && (ndims (y) == 2)) error ("cov: Y must be a numeric 2-D matrix or vector"); endif if (numel (x) ~= numel (y)) error ("cov: X and Y must have the same number of elements"); endif endif ## check sorted opt if (opt ~= 0 && opt ~= 1) error ("cov: normalization factor OPT must be either 0 or 1"); endif ## check sorted NaN handling switch, correct for spelling, adjust x and y switch handlenan case {"includenan"} ## okay, do nothing case {"omitrows", "omitrow"} handlenan = "omitrows"; if (strcmp (y, "no_y")) #trim out rows with nans from x x = x(~any (isnan (x), 2), :); else nan_locs = any (isnan ([x(:), y(:)]), 2); x = x(~nan_locs); y = y(~nan_locs); endif case {"partialrows", "partialrow"} handlenan = "partialrows"; if ~(strcmp (y, "no_y")) ##no need to handle anything differently for single input x_nan_locs = any (isnan (x(:)), 2); y_nan_locs = any (isnan (y(:)), 2); both_nan_locs = any (isnan ([x(:), y(:)]), 2); x_xytrim = x(~both_nan_locs); y_xytrim = y(~both_nan_locs); x = x(~x_nan_locs); y = y(~y_nan_locs); endif otherwise error (["cov: unknown NaN handling parameter, '", handlenan, "'"]); endswitch ## opt being single shouldn't affect output if (isa (opt, "single")) opt = double (opt); endif ## end input sorting/checking ## Primary handling difference is whether there are one or two inputs. if (strcmp (y, "no_y")) ## Special case, scalar has zero covariance if (isscalar (x)) if isnan (x) c = NaN; else c = 0; endif if (isa (x, "single")) c = single (c); endif return; elseif (isempty (x)) %not scalar x, check if empty sx = size (x); if all (sx == 0) c = NaN; elseif (sx(1) > 0) c = []; else c = NaN (sx(2)); endif if (isa (x, "single")) c = single (c); endif return; else %not scalar x, not empty, no y, generate covariance matrix if strcmp (handlenan, 'partialrows') ## if 'partialrows', need to calc each element separately with 'omitrows' ## c(i,j) is cov(x(:,i),x(:,j),'omitrows) ## TODO: find more efficient method. maybe can flatten recursion szx = size (x); for rw = 1:szx(1) for cl = 1:szx(2) c(rw,cl) = (cov (x(:,rw), x(:,cl), 'omitrows'))(2); endfor endfor return else ## if some elements are NaN, they propagate through calc as needed n = rows (x); x = center (x, 1); if n == 1 c = x' * x; %% to handle case of omitrows trimming to 1 row else c = x' * x / (n - 1 + opt); %will preserve single type endif return; endif endif else %there is a y if (isscalar (x)) if (isnan (x) || isnan (y)) c = NaN (2, 2); if ~isnan (x) c(1,1) = 0; elseif ~isnan (y) c(2,2) = 0; endif if (isa (x, "single") || isa (y, "single") ) c = single (c); endif return; else %scalar but neither a nan... both should be numbers... if (isa (x, "single") || isa (y, "single") ) c = single ([0 0; 0 0]); else c = [0 0; 0 0]; endif return; endif else % matrix or vector handled the same way, generate 2x2 covariance matrix if (isempty (x) || isempty (y)) if (isa (x, "single") || isa (y, "single") ) c = single (NaN (2, 2)); else c = NaN (2, 2); endif return; endif if (~strcmp (handlenan, 'partialrows')) denom = numel(x) - 1 + opt; x = center (x(:), 1); y = center (y(:), 1); c1 = x' * x; c23 = x' * y; c4 = y' * y; c = [c1, c23; c23, c4] ./ denom; return; else ## 'partialrows': handle each element separatley denom_xy = numel (x_xytrim) - 1 + opt; x_xytrim = center (x_xytrim(:), 1); y_xytrim = center (y_xytrim(:), 1); c23 = (x_xytrim' * y_xytrim) ./ denom_xy; denom_x = numel(x) - 1 + opt; x = center (x(:), 1); c1 = (x' * x) ./ denom_x; denom_y = numel(y) - 1 + opt; y = center (y(:), 1); c4 = (y' * y) ./ denom_y; c = [c1, c23; c23, c4]; return; endif endif endif endfunction %!test %! x = rand (10); %! cx1 = cov (x); %! cx2 = cov (x, x); %! assert (size (cx1) == [10, 10] && size (cx2) == [2, 2]); %! assert (cx2 - cx2(1), zeros (2, 2), eps); %!test %! x = [1:3]'; %! y = [3:-1:1]'; %! assert (cov (x, y), [1 -1; -1 1]); %! assert (cov (x, flipud (y)), ones (2, 2)); %! assert (cov ([x, y]), [1 -1; -1 1]); %!test %! x = single ([1:3]'); %! y = single ([3:-1:1]'); %! assert (cov (x, y), single ([1 -1; -1 1])); %! assert (cov (x, flipud (y)), single (ones (2, 2))); %! assert (cov ([x, y]), single ([1 -1; -1 1])); %!test %! x = [0 2 4]; %! y = [3 2 1]; %! z = [4 -2; -2 1]; %! assert (cov (x, y), z); %! assert (cov (single (x), y), single (z)); %! assert (cov (x, single (y)), single (z)); %! assert (cov (single (x), single (y)), single (z)); %!test %! x = [1:5]; %! c = cov (x); %! assert (c, 2.5); %!test %! x = [1:5]; %! c = cov (x, 0); %! assert (c, 2.5); %! c = cov (x, 1); %! assert (c, 2); %! c = cov (x, single (1)); %! assert (c, double (2)); %!test %! x = [5 0 3 7; 1 -5 7 3; 4 9 8 10]; %! b = [13/3 53/6 -3 17/3; 53/6 151/3 6.5 145/6; -3 6.5 7 1; 17/3 145/6 1 37/3]; %! assert (cov (x), b, 50*eps); %!test %! x = [3 6 4]; %! y = [7 12 -9]; %! assert (cov (x, y), [7, 20.5; 20.5, 361]./3, 50*eps); %!test %! x = [2 0 -9; 3 4 1]; %! y = [5 2 6; -4 4 9]; %! assert (cov (x, y), [66.5, -20.8; -20.8, 58.4]./3, 50*eps); %!test %! x = [1 3 -7; 3 9 2; -5 4 6]; %! assert (cov (x, 1), [104 46 -92; 46 62 47; -92 47 266]./9, 50*eps); %!test %! x = [1 0; 1 0]; %! y = [1 2; 1 1]; %! assert (cov (x, y), [1/3 -1/6; -1/6 0.25], 50*eps); %! assert (cov (x, y(:)), [1/3 -1/6; -1/6 0.25], 50*eps); %! assert (cov (x, y(:)'), [1/3 -1/6; -1/6 0.25], 50*eps); %! assert (cov (x', y(:)), [1/3 1/6; 1/6 0.25], 50*eps); %! assert (cov (x(:), y), [1/3 -1/6; -1/6 0.25], 50*eps); %! assert (cov (x(:)', y), [1/3 -1/6; -1/6 0.25], 50*eps); %!assert (cov (5), 0) %!assert (cov (single (5)), single (0)) %!assert (cov (1, 3), zeros (2, 2)) %!assert (cov (5, 0), 0) %!assert (cov (5, 1), 0) %!assert (cov (5, 2), zeros (2, 2)) %!assert (cov (5, 99), zeros (2, 2)) %!assert (cov (logical(0), logical(0)), double(0)) %!assert (cov (0, logical(0)), double(0)) %!assert (cov (logical(0), 0), double(0)) %!assert (cov (logical([0 1; 1 0]), logical([0 1; 1 0])), double ([1 1;1 1]./3)) ## Test empty and NaN handling (bug #48690) ## TODO: verify compatibily for matlab > 2016b !assert (cov ([]), NaN) %!assert (cov (single ([])), single (NaN)) %!assert (cov ([], []), NaN (2, 2)) %!assert (cov (single ([]), single([])), single (NaN (2, 2))) %!assert (cov ([], single ([])), single (NaN (2, 2))) %!assert (cov (single ([]), []), single (NaN (2, 2))) %!assert (cov (ones(2, 0)), []) %!assert (cov (ones(0, 2)), NaN (2, 2)) %!assert (cov (ones(0, 6)), NaN (6, 6)) %!assert (cov (ones(2, 0), []), NaN (2, 2)) %!assert (cov (NaN), NaN) %!assert (cov (NaN, NaN), NaN (2, 2)) %!assert (cov (5, NaN), [0, NaN; NaN, NaN]) %!assert (cov (NaN, 5), [NaN, NaN; NaN, 0]) %!assert (cov (single (NaN)), single (NaN)) %!assert (cov (NaN (2, 2)), NaN (2, 2)) %!assert (cov (single (NaN (2, 2))), single (NaN (2, 2))) %!assert (cov (NaN(2, 9)), NaN(9, 9)) %!assert (cov (NaN(9, 2)), NaN(2, 2)) %!assert (cov ([NaN, 1, 2, NaN]), NaN) %!assert (cov ([1, NaN, 2, NaN]), NaN) ## Test nan handling parameter, 1 input %!test %! x = [1 3 -7; NaN 9 NaN; -5 4 6]; %! y1 = [NaN NaN NaN;NaN 31/3 NaN;NaN NaN NaN]; %! y2 = [28 NaN -15;NaN NaN NaN;-15 NaN 103/3]; %! y3 = [18 -3 -39; -3 0.5 6.5; -39 6.5 84.5]; %! assert (cov (x), y1, 50*eps); %! assert (cov (x'), y2, 50*eps); %! assert (cov (x, 'includenan'), y1, 50*eps); %! assert (cov (x', 'includenan'), y2, 50*eps); %! assert (cov (x, 'omitrows'), y3, 50*eps); %! assert (cov (x', 'omitrows'), zeros(3, 3), 50*eps); %! y3(2,2) = 31/3; %! assert (cov (x, 'partialrows'), y3, 50*eps); %! y2(isnan (y2)) = 0; %! assert (cov (x', 'partialrows'), y2, 50*eps); ## Test nan handling parameter, 2 inputs %!test %! x = magic (3); %! x(1) = NaN; %! y = magic (3)'; %! assert (cov (x, y), [NaN, NaN; NaN, 7.5]); %! assert (cov (x', y), [NaN, NaN; NaN, 7.5]); %! assert (cov (x, y'), [NaN, NaN; NaN, 7.5]); %! assert (cov (x', y'), [NaN, NaN; NaN, 7.5]); %! assert (cov (x, y, 'omitrows'), [57/8 303/56; 303/56 57/8]); %! assert (cov (x', y, 'omitrows'), [57/8 57/8; 57/8 57/8]); %! assert (cov (x, y', 'omitrows'), [57/8 57/8; 57/8 57/8]); %! assert (cov (x', y', 'omitrows'), [57/8 303/56; 303/56 57/8]); %! assert (cov (x, y, 'partialrows'), [57/8 303/56; 303/56 7.5]); %! assert (cov (x', y, 'partialrows'), [57/8 57/8; 57/8 7.5]); %! assert (cov (x, y', 'partialrows'), [57/8 57/8; 57/8 7.5]); %! assert (cov (x', y', 'partialrows'), [57/8 303/56; 303/56 7.5]); %! assert (cov (y, x), [7.5, NaN; NaN, NaN]); %! assert (cov (y', x), [7.5, NaN; NaN, NaN]); %! assert (cov (y, x'), [7.5, NaN; NaN, NaN]); %! assert (cov (y', x'), [7.5, NaN; NaN, NaN]); %! assert (cov (y, x, 'omitrows'), [57/8 303/56; 303/56 57/8]); %! assert (cov (y', x, 'omitrows'), [57/8 57/8; 57/8 57/8]); %! assert (cov (y, x', 'omitrows'), [57/8 57/8; 57/8 57/8]); %! assert (cov (y', x', 'omitrows'), [57/8 303/56; 303/56 57/8]); %! assert (cov (y, x, 'partialrows'), [7.5 303/56; 303/56 57/8]); %! assert (cov (y', x, 'partialrows'), [7.5 57/8; 57/8 57/8]); %! assert (cov (y, x', 'partialrows'), [7.5 57/8; 57/8 57/8]); %! assert (cov (y', x', 'partialrows'), [7.5 303/56; 303/56 57/8]); ## Test nan handling parameter, 2 inputs, vectors %!test %! x = [1:5]; %! y = [10:-2:2]; %! assert (cov (x, y), [2.5 -5; -5 10]); %! assert (cov ([x NaN], [y 1]), [NaN NaN; NaN, 73/6], 50*eps); %! assert (cov ([x NaN], [y 1], 'omitrows'), [2.5 -5; -5 10],50*eps); %! assert (cov ([x NaN], [y 1], 'partialrows'), [2.5 -5; -5 73/6],50*eps); %! assert (cov ([x 1], [y NaN]), [8/3 NaN; NaN, NaN],50*eps); %! assert (cov ([x 1], [y NaN], 'omitrows'), [2.5 -5; -5 10],50*eps); %! assert (cov ([x 1], [y NaN], 'partialrows'), [8/3 -5; -5 10],50*eps); %! assert (cov ([NaN x], [y NaN], 'omitrows'), [5/3 -10/3; -10/3 20/3],50*eps); %! assert (cov ([NaN x], [y NaN], 'partialrows'), [2.5 -10/3; -10/3 10],50*eps); ## Test nan handling parameter, one matrix trimmed to vector %!test %! x = magic(3); %! y = magic (3) - 2; %! assert (cov (x, y), [7.5 7.5; 7.5 7.5]); %! x(3:4) = NaN; %! assert (cov (x), [NaN, NaN, NaN; NaN, NaN, NaN; NaN, NaN, 7]); %! assert (cov (x, 'omitrows'), zeros (3, 3)); %! assert (cov (x, 'partialrows'), [12.5 0 -2.5; 0 8 -10; -2.5 -10 7]); %! assert (cov (x, y), [NaN, NaN; NaN, 7.5]); %! assert (cov (x, y, 'omitrows'), [46/7, 46/7; 46/7, 46/7], 50*eps); %! assert (cov (x, y, 'partialrows'), [46/7, 46/7; 46/7, 7.5], 50*eps); %! assert (cov (y, x), [7.5, NaN; NaN, NaN]); %! assert (cov (y, x, 'omitrows'), [46/7, 46/7; 46/7, 46/7], 50*eps); %! assert (cov (y, x, 'partialrows'), [7.5, 46/7; 46/7, 46/7], 50*eps); ## Test input validation %!error cov () %!error cov (1, 2, 3, 4) %!error cov (5,[1 2]) %!error cov ([1; 2], ["A", "B"]) %!error cov (ones (2, 2, 2)) %!error cov (ones (2, 2), ones (2, 2, 2)) %!error cov (ones (2, 2), ones (3, 2)) %!error cov (1, []) %!error cov (ones (1, 0, 2)) %!error cov ([1, 2],ones(1, 0, 2)) %!error cov (1, 2, []) %!error cov (1, 2, 1, []) statistics-1.4.3/install-conditionally/base/crosstab.m0000644000000000000000000001073714153320774021341 0ustar0000000000000000## Copyright (C) 2021 Stefano Guidoni ## Copyright (C) 2018 John Donoghue ## Copyright (C) 1995-2017 Kurt Hornik ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {@var{t} =} crosstab (@var{x1}, @var{x2}) ## @deftypefnx {Function File} @ ## {@var{t} =} crosstab (@var{x1}, ..., @var{xn}) ## @deftypefnx {Function File} @ ## {[@var{t}, @var{chi-2}, @var{p}, @var{labels}] =} crosstab (...) ## Create a cross-tabulation (contingency table) @var{t} from data vectors. ## ## The inputs @var{x1}, @var{x2}, ... @var{xn} must be vectors of equal length ## with a data type of numeric, logical, char, or string (cell array). ## ## As additional return values @code{crosstab} returns the chi-square statistics ## @var{chi-2}, its p-value @var{p} and a cell array @var{labels}, containing ## the labels of each input argument. ## ## Currently @var{chi-2} and @var{p} are available only for 1 or 2-dimensional ## @var{t}, with @code{crosstab} returning a NaN value for both @var{chi-2} and ## @var{p} for 3-dimensional, or more, @var{t}. ## @end deftypefn ## ## @seealso{grp2idx,tabulate} function [t, chi2, p, labels] = crosstab (varargin) ## check input if (nargin < 2) print_usage (); endif v_length = length (varargin{1}); for i = 1 : nargin if ((! isvector (varargin{i})) || (v_length != length (varargin{i}))) error ("crosstab: x1, x2 ... xn must be vectors of the same length"); endif endfor ## main - begin v_reshape = []; # vector of the dimensions of t X = []; # matrix of the indexed input values labels = {}; # cell array of labels for k = 1 : nargin [g, gn] = grp2idx (varargin{k}); X = [X, g]; for h = 1 : length (gn) labels{h, k} = gn{h, 1}; endfor v_reshape(k) = length (unique (varargin{k})); endfor v = unique (X(:, nargin)); t = []; ## core logic, this employs a recursive function "crosstab_recursive" ## given (x1, x2, x3, ... xn) as inputs ## t(i,j,k,...) = sum (x1(:) == v1(i) & x2(:) == v2(j) & ...) for i = 1 : length (v) t = [t, (crosstab_recursive (nargin - 1,... (X(:, nargin) == v(i) | isnan (v(i)) * isnan (X(:, nargin)))))]; endfor t = reshape(t, v_reshape); # build the nargin-dimensional matrix ## additional statistics if (length (v_reshape) == 2) [p, chi2] = chisquare_test_independence(t); elseif (length (v_reshape) > 2) ## FIXME! ## chisquare_test_independence works with 2D matrices only warning ("crosstab: chi-square test only available for 2D results"); p = NaN; # placeholder chi2 = NaN; # placeholder endif ## main - end ## function: crosstab_recursive ## while there are input vectors, let's do iterations over them function t_partial = crosstab_recursive (x_idx, t_parent) y = X(:, x_idx); w = unique (y); t_partial = []; if (x_idx == 1) ## we have reached the last vector, ## let the computation begin for j = 1 : length (w) t_partial = [t_partial, ... sum(t_parent & (y == w(j) | isnan (w(j)) * isnan (y)));]; endfor else ## if there are more vectors, ## just add data and pass it through to the next iteration for j = 1 : length (w) t_partial = [t_partial, ... (crosstab_recursive (x_idx - 1, ... (t_parent & (y == w(j) | isnan (w(j)) * isnan (y)))))]; endfor endif endfunction endfunction ## Test input validation %!error crosstab () %!error crosstab (1) %!error crosstab (ones (2), [1 1]) %!error crosstab ([1 1], ones (2)) %!error crosstab ([1], [1 1]) %!error crosstab ([1 1], [1]) statistics-1.4.3/install-conditionally/base/gls.m0000644000000000000000000000756314153320774020311 0ustar0000000000000000## Copyright (C) 1996-2017 John W. Eaton ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {[@var{beta}, @var{v}, @var{r}] =} gls (@var{y}, @var{x}, @var{o}) ## Generalized least squares model. ## ## Perform a generalized least squares estimation for the multivariate model ## @tex ## $y = x b + e$ ## with $\bar{e} = 0$ and cov(vec($e$)) = $(s^2)o$, ## @end tex ## @ifnottex ## @w{@math{y = x*b + e}} with @math{mean (e) = 0} and ## @math{cov (vec (e)) = (s^2) o}, ## @end ifnottex ## where ## @tex ## $y$ is a $t \times p$ matrix, $x$ is a $t \times k$ matrix, $b$ is a $k ## \times p$ matrix, $e$ is a $t \times p$ matrix, and $o$ is a $tp \times ## tp$ matrix. ## @end tex ## @ifnottex ## @math{y} is a @math{t} by @math{p} matrix, @math{x} is a @math{t} by ## @math{k} matrix, @math{b} is a @math{k} by @math{p} matrix, @math{e} ## is a @math{t} by @math{p} matrix, and @math{o} is a @math{t*p} by ## @math{t*p} matrix. ## @end ifnottex ## ## @noindent ## Each row of @var{y} and @var{x} is an observation and each column a ## variable. The return values @var{beta}, @var{v}, and @var{r} are ## defined as follows. ## ## @table @var ## @item beta ## The GLS estimator for @math{b}. ## ## @item v ## The GLS estimator for @math{s^2}. ## ## @item r ## The matrix of GLS residuals, @math{r = y - x*beta}. ## @end table ## @seealso{ols} ## @end deftypefn ## Author: Teresa Twaroch ## Created: May 1993 ## Adapted-By: jwe function [beta, v, r] = gls (y, x, o) if (nargin != 3) print_usage (); endif if (! (isnumeric (x) && isnumeric (y) && isnumeric (o))) error ("gls: X, Y, and O must be numeric matrices or vectors"); endif if (ndims (x) != 2 || ndims (y) != 2 || ndims (o) != 2) error ("gls: X, Y and O must be 2-D matrices or vectors"); endif [rx, cx] = size (x); [ry, cy] = size (y); [ro, co] = size (o); if (rx != ry) error ("gls: number of rows of X and Y must be equal"); endif if (! issquare (o) || ro != ry*cy) error ("gls: matrix O must be square matrix with rows = rows (Y) * cols (Y)"); endif if (isinteger (x)) x = double (x); endif if (isinteger (y)) y = double (y); endif if (isinteger (o)) o = double (o); endif ## Start of algorithm o ^= -1/2; z = kron (eye (cy), x); z = o * z; y1 = o * reshape (y, ry*cy, 1); u = z' * z; r = rank (u); if (r == cx*cy) b = inv (u) * z' * y1; else b = pinv (z) * y1; endif beta = reshape (b, cx, cy); if (isargout (2) || isargout (3)) r = y - x * beta; if (isargout (2)) v = (reshape (r, ry*cy, 1))' * (o^2) * reshape (r, ry*cy, 1) / (rx*cy - r); endif endif endfunction %!test %! x = [1:5]'; %! y = 3*x + 2; %! x = [x, ones(5,1)]; %! o = diag (ones (5,1)); %! assert (gls (y,x,o), [3; 2], 50*eps); ## Test input validation %!error gls () %!error gls (1) %!error gls (1, 2) %!error gls (1, 2, 3, 4) %!error gls ([true, true], [1, 2], ones (2)) %!error gls ([1, 2], [true, true], ones (2)) %!error gls ([1, 2], [1, 2], true (2)) %!error gls (ones (2,2,2), ones (2,2), ones (4,4)) %!error gls (ones (2,2), ones (2,2,2), ones (4,4)) %!error gls (ones (2,2), ones (2,2), ones (4,4,4)) %!error gls (ones (1,2), ones (2,2), ones (2,2)) %!error gls (ones (2,2), ones (2,2), ones (2,2)) statistics-1.4.3/install-conditionally/base/histc.m0000644000000000000000000001212614153320774020625 0ustar0000000000000000## Copyright (C) 2009-2017 Søren Hauberg ## Copyright (C) 2009 VZLU Prague ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {@var{n} =} histc (@var{x}, @var{edges}) ## @deftypefnx {} {@var{n} =} histc (@var{x}, @var{edges}, @var{dim}) ## @deftypefnx {} {[@var{n}, @var{idx}] =} histc (@dots{}) ## Compute histogram counts. ## ## When @var{x} is a vector, the function counts the number of elements of ## @var{x} that fall in the histogram bins defined by @var{edges}. This ## must be a vector of monotonically increasing values that define the edges ## of the histogram bins. ## @tex ## $n(k)$ ## @end tex ## @ifnottex ## @code{@var{n}(k)} ## @end ifnottex ## contains the number of elements in @var{x} for which ## @tex ## $@var{edges}(k) <= @var{x} < @var{edges}(k+1)$. ## @end tex ## @ifnottex ## @code{@var{edges}(k) <= @var{x} < @var{edges}(k+1)}. ## @end ifnottex ## The final element of @var{n} contains the number of elements of @var{x} ## exactly equal to the last element of @var{edges}. ## ## When @var{x} is an @math{N}-dimensional array, the computation is carried ## out along dimension @var{dim}. If not specified @var{dim} defaults to the ## first non-singleton dimension. ## ## When a second output argument is requested an index matrix is also returned. ## The @var{idx} matrix has the same size as @var{x}. Each element of ## @var{idx} contains the index of the histogram bin in which the ## corresponding element of @var{x} was counted. ## @seealso{hist} ## @end deftypefn function [n, idx] = histc (x, edges, dim) if (nargin < 2 || nargin > 3) print_usage (); endif if (! isreal (x)) error ("histc: X argument must be real-valued, not complex"); endif num_edges = numel (edges); if (num_edges == 0) warning ("histc: empty EDGES specified\n"); n = idx = []; return; endif if (! isreal (edges)) error ("histc: EDGES must be real-valued, not complex"); else ## Make sure 'edges' is sorted edges = edges(:); if (! issorted (edges) || edges(1) > edges(end)) warning ("histc: edge values not sorted on input"); edges = sort (edges); endif endif nd = ndims (x); sz = size (x); if (nargin < 3) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (!(isscalar (dim) && dim == fix (dim)) || !(1 <= dim && dim <= nd)) error ("histc: DIM must be an integer and a valid dimension"); endif endif nsz = sz; nsz(dim) = num_edges; ## the splitting point is 3 bins if (num_edges <= 3) ## This is the O(M*N) algorithm. ## Allocate the histogram n = zeros (nsz); ## Allocate 'idx' if (nargout > 1) idx = zeros (sz); endif ## Prepare indices idx1 = cell (1, dim-1); for k = 1:length (idx1) idx1{k} = 1:sz(k); endfor idx2 = cell (length (sz) - dim); for k = 1:length (idx2) idx2{k} = 1:sz(k+dim); endfor ## Compute the histograms for k = 1:num_edges-1 b = (edges(k) <= x & x < edges(k+1)); n(idx1{:}, k, idx2{:}) = sum (b, dim); if (nargout > 1) idx(b) = k; endif endfor b = (x == edges(end)); n(idx1{:}, num_edges, idx2{:}) = sum (b, dim); if (nargout > 1) idx(b) = num_edges; endif else ## This is the O(M*log(N) + N) algorithm. ## Look-up indices. idx = lookup (edges, x); ## Zero invalid ones (including NaNs). x < edges(1) are already zero. idx(! (x <= edges(end))) = 0; iidx = idx; ## In case of matrix input, we adjust the indices. if (! isvector (x)) nl = prod (sz(1:dim-1)); nn = sz(dim); nu = prod (sz(dim+1:end)); if (nl != 1) iidx = (iidx-1) * nl; iidx += reshape (kron (ones (1, nn*nu), 1:nl), sz); endif if (nu != 1) ne =length (edges); iidx += reshape (kron (nl*ne*(0:nu-1), ones (1, nl*nn)), sz); endif endif ## Select valid elements. iidx = iidx(idx != 0); ## Call accumarray to sum the indexed elements. n = accumarray (iidx(:), 1, nsz); endif endfunction %!test %! x = linspace (0, 10, 1001); %! n = histc (x, 0:10); %! assert (n, [repmat(100, 1, 10), 1]); %!test %! x = repmat (linspace (0, 10, 1001), [2, 1, 3]); %! n = histc (x, 0:10, 2); %! assert (n, repmat ([repmat(100, 1, 10), 1], [2, 1, 3])); %!error histc () %!error histc (1) %!error histc (1, 2, 3, 4) %!error histc ([1:10 1+i], 2) %!warning histc (1:10, []); %!error histc (1, 1, 3) statistics-1.4.3/install-conditionally/base/iqr.m0000644000000000000000000000535314153320774020312 0ustar0000000000000000## Copyright (C) 1995-2017 Kurt Hornik ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} iqr (@var{x}) ## @deftypefnx {} {} iqr (@var{x}, @var{dim}) ## Return the interquartile range, i.e., the difference between the upper ## and lower quartile of the input data. ## ## If @var{x} is a matrix, do the above for first non-singleton dimension of ## @var{x}. ## ## If the optional argument @var{dim} is given, operate along this dimension. ## ## As a measure of dispersion, the interquartile range is less affected by ## outliers than either @code{range} or @code{std}. ## @seealso{range, std} ## @end deftypefn ## Author KH ## Description: Interquartile range function y = iqr (x, dim) if (nargin != 1 && nargin != 2) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("iqr: X must be a numeric vector or matrix"); endif nd = ndims (x); sz = size (x); nel = numel (x); if (nargin != 2) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (!(isscalar (dim) && dim == fix (dim)) || !(1 <= dim && dim <= nd)) error ("iqr: DIM must be an integer and a valid dimension"); endif endif ## This code is a bit heavy, but is needed until empirical_inv ## can take a matrix, rather than just a vector argument. n = sz(dim); sz(dim) = 1; if (isa (x, "single")) y = zeros (sz, "single"); else y = zeros (sz); endif stride = prod (sz(1:dim-1)); for i = 1 : nel / n; offset = i; offset2 = 0; while (offset > stride) offset -= stride; offset2 += 1; endwhile offset += offset2 * stride * n; rng = [0 : n-1] * stride + offset; y(i) = diff (empirical_inv ([1/4, 3/4], x(rng))); endfor endfunction %!assert (iqr (1:101), 50) %!assert (iqr (single (1:101)), single (50)) ## FIXME: iqr throws horrible error when running across a dimension that is 1. %!test %! x = [1:100]'; %! assert (iqr (x, 1), 50); %! assert (iqr (x', 2), 50); %!error iqr () %!error iqr (1, 2, 3) %!error iqr (1) %!error iqr (['A'; 'B']) %!error iqr (1:10, 3) statistics-1.4.3/install-conditionally/base/ismissing.m0000644000000000000000000001025514153320774021521 0ustar0000000000000000######################################################################## ## ## Copyright (C) 1995-2021 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or . ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{TF} =} ismissing (@var{A}) ## @deftypefnx {} {@var{TF} =} ismissing (@var{A}, @var{indicator}) ## ## Find missing data in a matrix or a string array. ## ## Given an input vector, matrix or array of cell strings @var{A}, ## @code{ismissing} returns a logical vector or matrix @var{TF} with the same ## dimensions as @var{A}, where @code{true} values match missing values in the ## input data. ## ## The optional input @var{indicator} is an array of values, which represent ## missing values in the input data. The values which represent missing data by ## default depend on the data type of @var{A}: ## ## @itemize ## @item ## @code{NaN}: @code{single}, @code{double}. ## ## @item ## @code{' '} (white space): @code{char}. ## ## @item ## @code{@{''@}}: string cells. ## @end itemize ## ## @end deftypefn ## ## @seealso{all, any, isempty, isnan, rmmissing} function TF = ismissing (A, indicator) ## check "indicator" if (nargin != 2) indicator = []; else if (! isvector (indicator)) error ("ismissing: invalid format for 'indicator'"); endif if ((isnumeric (A) && ! isnumeric (indicator)) || (ischar (A) && ! ischar (indicator)) || (iscellstr (A) && ! (iscellstr (indicator) || ischar (indicator)))) error ("ismissing: 'indicator' and 'A' must have the same data type"); endif ## if A is an array of cell strings and indicator just a string, ## convert indicator to a cell string with one element if (iscellstr (A) && ischar (indicator) && ! iscellstr (indicator)) tmpstr = indicator; indicator = {}; indicator = {tmpstr}; endif endif ## main logic if (iscellstr (A) && isempty (indicator)) TF = false (1, length (A)); ## remove all empty strings for iter = 1 : length (A) if (isempty (A{iter})) TF(iter) = true; endif endfor elseif (ismatrix (A) && isempty (indicator)) if (isnumeric (A)) ## numeric matrix: just remove the NaNs TF = isnan (A); elseif (ischar (A)) ## char matrix: remove the white spaces TF = isspace (A); else error ("ismissing: unsupported data type"); endif TF = logical (TF); elseif (! isempty (indicator)) ## special cases with custom values for missing data [r, c] = size (A); TF = false (r, c); if (iscellstr (A)) for iter = 1 : length (indicator) TF(find (strcmp (A, indicator(iter)))) = true; endfor elseif (ismatrix (A)) for iter = 1 : length (indicator) TF(find (A == indicator(iter))) = true; endfor else error ("ismissing: unsupported data format"); endif else error ("ismissing: unsupported data format"); endif endfunction %!assert (ismissing ([1,NaN,3]), [false,true,false]) %!assert (ismissing ('abcd f'), [false,false,false,false,true,false]) %!assert (ismissing ({'xxx','','xyz'}), [false,true,false]) %!assert (ismissing ([1,2;NaN,2]), [false,false;true,false]) ## Test input validation %!error ismissing (); %!error ismissing ({1, 2, 3}); %!error ismissing ([1 2; 3 4], [5 1; 2 0]); %!error ismissing ([1 2; 3 4], "abc"); %!error ismissing ({"", "", ""}, 1); %!error ismissing ({1, 2, 3}); statistics-1.4.3/install-conditionally/base/kendall.m0000644000000000000000000000721114153320774021124 0ustar0000000000000000## Copyright (C) 1995-2017 Kurt Hornik ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} kendall (@var{x}) ## @deftypefnx {} {} kendall (@var{x}, @var{y}) ## @cindex Kendall's Tau ## Compute Kendall's ## @tex ## $\tau$. ## @end tex ## @ifnottex ## @var{tau}. ## @end ifnottex ## ## For two data vectors @var{x}, @var{y} of common length @math{N}, Kendall's ## @tex ## $\tau$ ## @end tex ## @ifnottex ## @var{tau} ## @end ifnottex ## is the correlation of the signs of all rank differences of ## @var{x} and @var{y}; i.e., if both @var{x} and @var{y} have distinct ## entries, then ## ## @tex ## $$ \tau = {1 \over N(N-1)} \sum_{i,j} {\rm sign}(q_i-q_j) \, {\rm sign}(r_i-r_j) $$ ## @end tex ## @ifnottex ## ## @example ## @group ## 1 ## @var{tau} = ------- SUM sign (@var{q}(i) - @var{q}(j)) * sign (@var{r}(i) - @var{r}(j)) ## N (N-1) i,j ## @end group ## @end example ## ## @end ifnottex ## @noindent ## in which the ## @tex ## $q_i$ and $r_i$ ## @end tex ## @ifnottex ## @var{q}(i) and @var{r}(i) ## @end ifnottex ## are the ranks of @var{x} and @var{y}, respectively. ## ## If @var{x} and @var{y} are drawn from independent distributions, ## Kendall's ## @tex ## $\tau$ ## @end tex ## @ifnottex ## @var{tau} ## @end ifnottex ## is asymptotically normal with mean 0 and variance ## @tex ## ${2 (2N+5) \over 9N(N-1)}$. ## @end tex ## @ifnottex ## @code{(2 * (2N+5)) / (9 * N * (N-1))}. ## @end ifnottex ## ## @code{kendall (@var{x})} is equivalent to @code{kendall (@var{x}, ## @var{x})}. ## @seealso{ranks, spearman} ## @end deftypefn ## Author: KH ## Description: Kendall's rank correlation tau function tau = kendall (x, y = []) if (nargin < 1 || nargin > 2) print_usage (); endif if ( ! (isnumeric (x) || islogical (x)) || ! (isnumeric (y) || islogical (y))) error ("kendall: X and Y must be numeric matrices or vectors"); endif if (ndims (x) != 2 || ndims (y) != 2) error ("kendall: X and Y must be 2-D matrices or vectors"); endif if (isrow (x)) x = x.'; endif [n, c] = size (x); if (nargin == 2) if (isrow (y)) y = y.'; endif if (rows (y) != n) error ("kendall: X and Y must have the same number of observations"); else x = [x, y]; endif endif if (isa (x, "single") || isa (y, "single")) cls = "single"; else cls = "double"; endif r = ranks (x); m = sign (kron (r, ones (n, 1, cls)) - kron (ones (n, 1, cls), r)); tau = corr (m); if (nargin == 2) tau = tau(1 : c, (c + 1) : columns (x)); endif endfunction %!test %! x = [1:2:10]; %! y = [100:10:149]; %! assert (kendall (x,y), 1, 5*eps); %! assert (kendall (x,fliplr (y)), -1, 5*eps); %!assert (kendall (logical (1)), 1) %!assert (kendall (single (1)), single (1)) ## Test input validation %!error kendall () %!error kendall (1, 2, 3) %!error kendall (['A'; 'B']) %!error kendall (ones (2,1), ['A'; 'B']) %!error kendall (ones (2,2,2)) %!error kendall (ones (2,2), ones (2,2,2)) %!error kendall (ones (2,2), ones (3,2)) statistics-1.4.3/install-conditionally/base/kurtosis.m0000644000000000000000000001227214153320774021400 0ustar0000000000000000## Copyright (C) 2013-2017 Julien Bect ## Copyright (C) 1996-2016 John W. Eaton ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} kurtosis (@var{x}) ## @deftypefnx {} {} kurtosis (@var{x}, @var{flag}) ## @deftypefnx {} {} kurtosis (@var{x}, @var{flag}, @var{dim}) ## Compute the sample kurtosis of the elements of @var{x}. ## ## The sample kurtosis is defined as ## @tex ## $$ ## \kappa_1 = {{{1\over N}\, ## \sum_{i=1}^N (x_i - \bar{x})^4} \over \sigma^4}, ## $$ ## where $N$ is the length of @var{x}, $\bar{x}$ its mean, and $\sigma$ ## its (uncorrected) standard deviation. ## @end tex ## @ifnottex ## ## @example ## @group ## mean ((@var{x} - mean (@var{x})).^4) ## k1 = ------------------------ ## std (@var{x}).^4 ## @end group ## @end example ## ## @end ifnottex ## ## @noindent ## The optional argument @var{flag} controls which normalization is used. ## If @var{flag} is equal to 1 (default value, used when @var{flag} is omitted ## or empty), return the sample kurtosis as defined above. If @var{flag} is ## equal to 0, return the @w{"bias-corrected"} kurtosis coefficient instead: ## @tex ## $$ ## \kappa_0 = 3 + {\scriptstyle N - 1 \over \scriptstyle (N - 2)(N - 3)} \, ## \left( (N + 1)\, \kappa_1 - 3 (N - 1) \right) ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## N - 1 ## k0 = 3 + -------------- * ((N + 1) * k1 - 3 * (N - 1)) ## (N - 2)(N - 3) ## @end group ## @end example ## ## where @math{N} is the length of the @var{x} vector. ## ## @end ifnottex ## The bias-corrected kurtosis coefficient is obtained by replacing the sample ## second and fourth central moments by their unbiased versions. It is an ## unbiased estimate of the population kurtosis for normal populations. ## ## If @var{x} is a matrix, or more generally a multi-dimensional array, return ## the kurtosis along the first non-singleton dimension. If the optional ## @var{dim} argument is given, operate along this dimension. ## ## @seealso{var, skewness, moment} ## @end deftypefn ## Author: KH ## Created: 29 July 1994 ## Adapted-By: jwe function y = kurtosis (x, flag, dim) if (nargin < 1) || (nargin > 3) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("kurtosis: X must be a numeric vector or matrix"); endif if (nargin < 2 || isempty (flag)) flag = 1; # default: do not use the "bias corrected" version else if (! isscalar (flag) || (flag != 0 && flag != 1)) error ("kurtosis: FLAG must be 0 or 1"); endif endif nd = ndims (x); sz = size (x); if (nargin < 3) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) error ("kurtosis: DIM must be an integer and a valid dimension"); endif endif n = size (x, dim); sz(dim) = 1; x = center (x, dim); # center also promotes integer, logical to double v = var (x, 1, dim); # normalize with 1/N y = sum (x .^ 4, dim); idx = (v != 0); y(idx) = y(idx) ./ (n * v(idx) .^ 2); y(! idx) = NaN; ## Apply bias correction to the second and fourth central sample moment if (flag == 0) if (n > 3) C = (n - 1) / ((n - 2) * (n - 3)); y = 3 + C * ((n + 1) * y - 3 * (n - 1)); else y(:) = NaN; endif endif endfunction %!test %! x = [-1; 0; 0; 0; 1]; %! y = [x, 2*x]; %! assert (kurtosis (y), [2.5, 2.5], sqrt (eps)); %!assert (kurtosis ([-3, 0, 1]) == kurtosis ([-1, 0, 3])) %!assert (kurtosis (ones (3, 5)), NaN (1, 5)) %!assert (kurtosis (1, [], 3), NaN) %!assert (kurtosis ([1:5 10; 1:5 10], 0, 2), 5.4377317925288901 * [1; 1], 8 * eps) %!assert (kurtosis ([1:5 10; 1:5 10], 1, 2), 2.9786509002956195 * [1; 1], 8 * eps) %!assert (kurtosis ([1:5 10; 1:5 10], [], 2), 2.9786509002956195 * [1; 1], 8 * eps) ## Test behavior on single input %!assert (kurtosis (single ([1:5 10])), single (2.9786513), eps ("single")) %!assert (kurtosis (single ([1 2]), 0), single (NaN)) ## Verify no "divide-by-zero" warnings %!test %! warning ("on", "Octave:divide-by-zero", "local"); %! lastwarn (""); # clear last warning %! kurtosis (1); %! assert (lastwarn (), ""); ## Test input validation %!error kurtosis () %!error kurtosis (1, 2, 3) %!error kurtosis (['A'; 'B']) %!error kurtosis (1, 2) %!error kurtosis (1, [1 0]) %!error kurtosis (1, [], ones (2,2)) %!error kurtosis (1, [], 1.5) %!error kurtosis (1, [], 0) statistics-1.4.3/install-conditionally/base/logit.m0000644000000000000000000000272614153320774020636 0ustar0000000000000000## Copyright (C) 1995-2017 Kurt Hornik ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} logit (@var{p}) ## Compute the logit for each value of @var{p} ## ## The logit is defined as ## @tex ## $$ ## {\rm logit}(p) = \log\Big({p \over 1-p}\Big) ## $$ ## @end tex ## @ifnottex ## ## @example ## logit (@var{p}) = log (@var{p} / (1-@var{p})) ## @end example ## ## @end ifnottex ## @seealso{probit, logistic_cdf} ## @end deftypefn ## Author: KH ## Description: Logit transformation function y = logit (p) if (nargin != 1) print_usage (); endif y = logistic_inv (p); endfunction %!test %! p = [0.01:0.01:0.99]; %! assert (logit (p), log (p ./ (1-p)), 25*eps); %!assert (logit ([-1, 0, 0.5, 1, 2]), [NaN, -Inf, 0, +Inf, NaN]) ## Test input validation %!error logit () %!error logit (1, 2) statistics-1.4.3/install-conditionally/base/lscov.m0000644000000000000000000001543614153320774020650 0ustar0000000000000000## Copyright (C) 2014-2017 Nir Krakauer ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {@var{x} =} lscov (@var{A}, @var{b}) ## @deftypefnx {} {@var{x} =} lscov (@var{A}, @var{b}, @var{V}) ## @deftypefnx {} {@var{x} =} lscov (@var{A}, @var{b}, @var{V}, @var{alg}) ## @deftypefnx {} {[@var{x}, @var{stdx}, @var{mse}, @var{S}] =} lscov (@dots{}) ## ## Compute a generalized linear least squares fit. ## ## Estimate @var{x} under the model @var{b} = @var{A}@var{x} + @var{w}, ## where the noise @var{w} is assumed to follow a normal distribution ## with covariance matrix @math{{\sigma^2} V}. ## ## If the size of the coefficient matrix @var{A} is n-by-p, the ## size of the vector/array of constant terms @var{b} must be n-by-k. ## ## The optional input argument @var{V} may be a n-by-1 vector of positive ## weights (inverse variances), or a n-by-n symmetric positive semidefinite ## matrix representing the covariance of @var{b}. If @var{V} is not ## supplied, the ordinary least squares solution is returned. ## ## The @var{alg} input argument, a guidance on solution method to use, is ## currently ignored. ## ## Besides the least-squares estimate matrix @var{x} (p-by-k), the function ## also returns @var{stdx} (p-by-k), the error standard deviation of ## estimated @var{x}; @var{mse} (k-by-1), the estimated data error covariance ## scale factors (@math{\sigma^2}); and @var{S} (p-by-p, or p-by-p-by-k if k ## > 1), the error covariance of @var{x}. ## ## Reference: @nospell{Golub and Van Loan} (1996), ## @cite{Matrix Computations (3rd Ed.)}, Johns Hopkins, Section 5.6.3 ## ## @seealso{ols, gls, lsqnonneg} ## @end deftypefn ## Author: Nir Krakauer function [x, stdx, mse, S] = lscov (A, b, V = [], alg) if (nargin < 2 || (rows (A) != rows (b))) print_usage (); endif n = rows (A); p = columns (A); k = columns (b); if (! isempty (V)) if (rows (V) != n || ! any (columns (V) == [1 n])) error ("lscov: V should be a square matrix or a vector with the same number of rows as A"); endif if (isvector (V)) ## n-by-1 vector of inverse variances v = diag (sqrt (V)); A = v * A; b = v * b; else ## n-by-n covariance matrix try ## ordinarily V will be positive definite B = chol (V)'; catch ## if V is only positive semidefinite, use its ## eigendecomposition to find a factor B such that V = B*B' [B, lambda] = eig (V); image_dims = (diag (lambda) > 0); B = B(:, image_dims) * sqrt (lambda(image_dims, image_dims)); end_try_catch A = B \ A; b = B \ b; endif endif pinv_A = pinv (A); #pseudoinverse x = pinv_A * b; if (isargout (3)) dof = n - p; #degrees of freedom remaining after fit SSE = sumsq (b - A * x); mse = SSE / dof; endif s = pinv_A * pinv_A'; stdx = sqrt (diag (s) * mse); if (isargout (4)) if (k == 1) S = mse * s; else S = NaN (p, p, k); for i = 1:k S(:, :, i) = mse(i) * s; endfor endif endif endfunction %!test <49040> %! ## Longley data from the NIST Statistical Reference Dataset %! Z = [ 60323 83.0 234289 2356 1590 107608 1947 %! 61122 88.5 259426 2325 1456 108632 1948 %! 60171 88.2 258054 3682 1616 109773 1949 %! 61187 89.5 284599 3351 1650 110929 1950 %! 63221 96.2 328975 2099 3099 112075 1951 %! 63639 98.1 346999 1932 3594 113270 1952 %! 64989 99.0 365385 1870 3547 115094 1953 %! 63761 100.0 363112 3578 3350 116219 1954 %! 66019 101.2 397469 2904 3048 117388 1955 %! 67857 104.6 419180 2822 2857 118734 1956 %! 68169 108.4 442769 2936 2798 120445 1957 %! 66513 110.8 444546 4681 2637 121950 1958 %! 68655 112.6 482704 3813 2552 123366 1959 %! 69564 114.2 502601 3931 2514 125368 1960 %! 69331 115.7 518173 4806 2572 127852 1961 %! 70551 116.9 554894 4007 2827 130081 1962 ]; %! ## Results certified by NIST using 500 digit arithmetic %! ## b and standard error in b %! V = [ -3482258.63459582 890420.383607373 %! 15.0618722713733 84.9149257747669 %! -0.358191792925910E-01 0.334910077722432E-01 %! -2.02022980381683 0.488399681651699 %! -1.03322686717359 0.214274163161675 %! -0.511041056535807E-01 0.226073200069370 %! 1829.15146461355 455.478499142212 ]; %! rsd = 304.854073561965; %! y = Z(:,1); X = [ones(rows(Z),1), Z(:,2:end)]; %! alpha = 0.05; %! [b, stdb, mse] = lscov (X, y); %! assert(b, V(:,1), 3e-6); %! assert(stdb, V(:,2), -1.e-5); %! assert(sqrt (mse), rsd, -1E-6); %!test %! ## Adapted from example in Matlab documentation %! x1 = [.2 .5 .6 .8 1.0 1.1]'; %! x2 = [.1 .3 .4 .9 1.1 1.4]'; %! X = [ones(size(x1)) x1 x2]; %! y = [.17 .26 .28 .23 .27 .34]'; %! [b, se_b, mse, S] = lscov(X, y); %! assert(b, [0.1203 0.3284 -0.1312]', 1E-4); %! assert(se_b, [0.0643 0.2267 0.1488]', 1E-4); %! assert(mse, 0.0015, 1E-4); %! assert(S, [0.0041 -0.0130 0.0075; -0.0130 0.0514 -0.0328; 0.0075 -0.0328 0.0221], 1E-4); %! w = [1 1 1 1 1 .1]'; %! [bw, sew_b, msew] = lscov (X, y, w); %! assert(bw, [0.1046 0.4614 -0.2621]', 1E-4); %! assert(sew_b, [0.0309 0.1152 0.0814]', 1E-4); %! assert(msew, 3.4741e-004, -1E-4); %! V = .2*ones(length(x1)) + .8*diag(ones(size(x1))); %! [bg, sew_b, mseg] = lscov (X, y, V); %! assert(bg, [0.1203 0.3284 -0.1312]', 1E-4); %! assert(sew_b, [0.0672 0.2267 0.1488]', 1E-4); %! assert(mseg, 0.0019, 1E-4); %! y2 = [y 2*y]; %! [b2, se_b2, mse2, S2] = lscov (X, y2); %! assert(b2, [b 2*b], 2*eps); %! assert(se_b2, [se_b 2*se_b], eps); %! assert(mse2, [mse 4*mse], eps); %! assert(S2(:, :, 1), S, eps); %! assert(S2(:, :, 2), 4*S, eps); %!test %! ## Artificial example with positive semidefinite weight matrix %! x = (0:0.2:2)'; %! y = round(100*sin(x) + 200*cos(x)); %! X = [ones(size(x)) sin(x) cos(x)]; %! V = eye(numel(x)); %! V(end, end-1) = V(end-1, end) = 1; %! [b, seb, mseb, S] = lscov (X, y, V); %! assert(b, [0 100 200]', 0.2); statistics-1.4.3/install-conditionally/base/mad.m0000644000000000000000000000656514153320774020266 0ustar0000000000000000## Copyright (C) 2017-2018 Rik Wehbring ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} mad (@var{x}) ## @deftypefnx {} {} mad (@var{x}, @var{opt}) ## @deftypefnx {} {} mad (@var{x}, @var{opt}, @var{dim}) ## Compute the mean or median absolute deviation of the elements of @var{x}. ## ## The mean absolute deviation is defined as ## ## @example ## @var{mad} = mean (abs (@var{x} - mean (@var{x}))) ## @end example ## ## The median absolute deviation is defined as ## ## @example ## @var{mad} = median (abs (@var{x} - median (@var{x}))) ## @end example ## ## If @var{x} is a matrix, compute @code{mad} for each column and return ## results in a row vector. For a multi-dimensional array, the calculation is ## done over the first non-singleton dimension. ## ## The optional argument @var{opt} determines whether mean or median absolute ## deviation is calculated. The default is 0 which corresponds to mean ## absolute deviation; A value of 1 corresponds to median absolute deviation. ## ## If the optional argument @var{dim} is given, operate along this dimension. ## ## As a measure of dispersion, @code{mad} is less affected by outliers than ## @code{std}. ## @seealso{bounds, range, iqr, std, mean, median} ## @end deftypefn function retval = mad (x, opt = 0, dim) if (nargin < 1 || nargin > 3) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("mad: X must be a numeric vector or matrix"); endif if (isempty (opt)) opt = 0; elseif (! isscalar (opt) || (opt != 0 && opt != 1)) error ("mad: OPT must be 0 or 1"); endif sz = size (x); if (nargin < 3) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) error ("mad: DIM must be an integer and a valid dimension"); endif endif if (opt == 0) fcn = @mean; else fcn = @median; endif retval = fcn (abs (x - fcn (x, dim)), dim); endfunction %!assert (mad ([0 0 1 2 100]), 31.76) %!assert (mad (single ([0 0 1 2 100])), single (31.76)) %!assert (mad ([0 0 1 2 100]'), 31.76) %!assert (mad ([0 0 1 2 100], 1), 1) %!assert (mad (single ([0 0 1 2 100]), 1), single (1)) %!assert (mad ([0 0 1 2 100]', 1), 1) %!assert (mad (magic (4)), [4, 4, 4, 4]) %!assert (mad (magic (4), [], 2), [6; 2; 2; 6]) %!assert (mad (magic (4), 1), [2.5, 3.5, 3.5, 2.5]) %!assert (mad (magic (4), 1, 2), [5.5; 1.5; 1.5; 5.5]) ## Test input validation %!error mad () %!error mad (1, 2, 3, 4) %!error mad (['A'; 'B']) %!error mad (1, 2) %!error mad (1, [], ones (2,2)) %!error mad (1, [], 1.5) %!error mad (1, [], 0) statistics-1.4.3/install-conditionally/base/mean.m0000644000000000000000000002176514153320774020444 0ustar0000000000000000## Copyright (C) 1995-2017 Kurt Hornik ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} mean (@var{x}) ## @deftypefnx {} {} mean (@var{x}, @var{dim}) ## @deftypefnx {} {} mean (@var{x}, @var{opt}) ## @deftypefnx {} {} mean (@var{x}, @var{dim}, @var{opt}) ## Compute the mean of the elements of the vector @var{x}. ## ## The mean is defined as ## ## @tex ## $$ {\rm mean}(x) = \bar{x} = {1\over N} \sum_{i=1}^N x_i $$ ## where $N$ is the number of elements of @var{x}. ## ## @end tex ## @ifnottex ## ## @example ## mean (@var{x}) = SUM_i @var{x}(i) / N ## @end example ## ## where @math{N} is the length of the @var{x} vector. ## ## @end ifnottex ## If @var{x} is a matrix, compute the mean for each column and return them ## in a row vector. ## ## If the optional argument @var{dim} is given, operate along this dimension. ## ## The optional argument @var{opt} selects the type of mean to compute. ## The following options are recognized: ## ## @table @asis ## @item @qcode{"a"} ## Compute the (ordinary) arithmetic mean. [default] ## ## @item @qcode{"g"} ## Compute the geometric mean. ## ## @item @qcode{"h"} ## Compute the harmonic mean. ## @end table ## ## Both @var{dim} and @var{opt} are optional. If both are supplied, either ## may appear first. ## @seealso{median, mode} ## @end deftypefn ## Author: KH ## Description: Compute arithmetic, geometric, and harmonic mean function retval = mean (x, opt1, opt2) if (nargin < 1 || nargin > 3) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("mean: X must be a numeric vector or matrix"); endif need_dim = false; if (nargin == 1) opt = "a"; need_dim = true; elseif (nargin == 2) if (ischar (opt1)) opt = opt1; need_dim = true; else dim = opt1; opt = "a"; endif elseif (nargin == 3) if (ischar (opt1)) opt = opt1; dim = opt2; elseif (ischar (opt2)) opt = opt2; dim = opt1; else error ("mean: OPT must be a string"); endif else print_usage (); endif nd = ndims (x); sz = size (x); if (need_dim) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) error ("mean: DIM must be an integer and a valid dimension"); endif endif n = size (x, dim); if (isempty (x)) %% codepath for Matlab compatibility. empty x produces NaN output, but %% for ndim > 2, output depends on size of x and whether DIM is set. if ((nd == 2) && (max (sz) < 2) && need_dim) retval = NaN; else if (~need_dim) sz(dim) = 1; else sz (find ((sz ~= 1), 1)) = 1; endif retval = NaN (sz); endif if (isa (x, "single")) retval = single (retval); endif elseif (strcmp (opt, "a")) retval = sum (x, dim) / n; elseif (strcmp (opt, "g")) if (all (x(:) >= 0)) retval = exp (sum (log (x), dim) ./ n); else error ("mean: X must not contain any negative values"); endif elseif (strcmp (opt, "h")) retval = n ./ sum (1 ./ x, dim); else error ("mean: option '%s' not recognized", opt); endif endfunction %!test %! x = -10:10; %! y = x'; %! z = [y, y+10]; %! assert (mean (x), 0); %! assert (mean (y), 0); %! assert (mean (z), [0, 10]); ## Test small numbers %!assert (mean (repmat (0.1, 1, 1000), "g"), 0.1, 20*eps) %!assert (mean (magic (3), 1), [5, 5, 5]) %!assert (mean (magic (3), 2), [5; 5; 5]) %!assert (mean ([2 8], "g"), 4) %!assert (mean ([4 4 2], "h"), 3) %!assert (mean (logical ([1 0 1 1])), 0.75) %!assert (mean (single ([1 0 1 1])), single (0.75)) %!assert (mean ([1 2], 3), [1 2]) ##tests for empty input Matlab compatibility (bug #48690) %!assert (mean ([]), NaN) %!assert (mean (single([])), single(NaN)) %!assert (mean (ones (0, 0, 0, 0)), NaN (1, 0, 0, 0)) %!assert (mean (ones (0, 0, 0, 1)), NaN (1, 0, 0, 1)) %!assert (mean (ones (0, 0, 0, 2)), NaN (1, 0, 0, 2)) %!assert (mean (ones (0, 0, 1, 0)), NaN (1, 0, 1, 0)) %!assert (mean (ones (0, 0, 1, 1)), NaN (1, 1, 1, 1)) %!assert (mean (ones (0, 0, 1, 2)), NaN (1, 0, 1, 2)) %!assert (mean (ones (0, 0, 2, 0)), NaN (1, 0, 2, 0)) %!assert (mean (ones (0, 0, 2, 1)), NaN (1, 0, 2, 1)) %!assert (mean (ones (0, 0, 2, 2)), NaN (1, 0, 2, 2)) %!assert (mean (ones (0, 1, 0, 0)), NaN (1, 1, 0, 0)) %!assert (mean (ones (0, 1, 0, 1)), NaN (1, 1, 0, 1)) %!assert (mean (ones (0, 1, 0, 2)), NaN (1, 1, 0, 2)) %!assert (mean (ones (0, 1, 1, 0)), NaN (1, 1, 1, 0)) %!assert (mean (ones (0, 1, 1, 1)), NaN (1, 1, 1, 1)) %!assert (mean (ones (0, 1, 1, 2)), NaN (1, 1, 1, 2)) %!assert (mean (ones (0, 1, 2, 0)), NaN (1, 1, 2, 0)) %!assert (mean (ones (0, 1, 2, 1)), NaN (1, 1, 2, 1)) %!assert (mean (ones (0, 1, 2, 2)), NaN (1, 1, 2, 2)) %!assert (mean (ones (0, 2, 0, 0)), NaN (1, 2, 0, 0)) %!assert (mean (ones (0, 2, 0, 1)), NaN (1, 2, 0, 1)) %!assert (mean (ones (0, 2, 0, 2)), NaN (1, 2, 0, 2)) %!assert (mean (ones (0, 2, 1, 0)), NaN (1, 2, 1, 0)) %!assert (mean (ones (0, 2, 1, 1)), NaN (1, 2, 1, 1)) %!assert (mean (ones (0, 2, 1, 2)), NaN (1, 2, 1, 2)) %!assert (mean (ones (0, 2, 2, 0)), NaN (1, 2, 2, 0)) %!assert (mean (ones (0, 2, 2, 1)), NaN (1, 2, 2, 1)) %!assert (mean (ones (0, 2, 2, 2)), NaN (1, 2, 2, 2)) %!assert (mean (ones (1, 0, 0, 0)), NaN (1, 1, 0, 0)) %!assert (mean (ones (1, 0, 0, 1)), NaN (1, 1, 0, 1)) %!assert (mean (ones (1, 0, 0, 2)), NaN (1, 1, 0, 2)) %!assert (mean (ones (1, 0, 1, 0)), NaN (1, 1, 1, 0)) %!assert (mean (ones (1, 0, 1, 1)), NaN (1, 1, 1, 1)) %!assert (mean (ones (1, 0, 1, 2)), NaN (1, 1, 1, 2)) %!assert (mean (ones (1, 0, 2, 0)), NaN (1, 1, 2, 0)) %!assert (mean (ones (1, 0, 2, 1)), NaN (1, 1, 2, 1)) %!assert (mean (ones (1, 0, 2, 2)), NaN (1, 1, 2, 2)) %!assert (mean (ones (1, 1, 0, 0)), NaN (1, 1, 1, 0)) %!assert (mean (ones (1, 1, 0, 1)), NaN (1, 1, 1, 1)) %!assert (mean (ones (1, 1, 0, 2)), NaN (1, 1, 1, 2)) %!assert (mean (ones (1, 1, 1, 0)), NaN (1, 1, 1, 1)) %!assert (mean (ones (1, 1, 2, 0)), NaN (1, 1, 1, 0)) %!assert (mean (ones (1, 2, 0, 0)), NaN (1, 1, 0, 0)) %!assert (mean (ones (1, 2, 0, 1)), NaN (1, 1, 0, 1)) %!assert (mean (ones (1, 2, 0, 2)), NaN (1, 1, 0, 2)) %!assert (mean (ones (1, 2, 1, 0)), NaN (1, 1, 1, 0)) %!assert (mean (ones (1, 2, 2, 0)), NaN (1, 1, 2, 0)) %!assert (mean (ones (2, 0, 0, 0)), NaN (1, 0, 0, 0)) %!assert (mean (ones (2, 0, 0, 1)), NaN (1, 0, 0, 1)) %!assert (mean (ones (2, 0, 0, 2)), NaN (1, 0, 0, 2)) %!assert (mean (ones (2, 0, 1, 0)), NaN (1, 0, 1, 0)) %!assert (mean (ones (2, 0, 1, 1)), NaN (1, 0, 1, 1)) %!assert (mean (ones (2, 0, 1, 2)), NaN (1, 0, 1, 2)) %!assert (mean (ones (2, 0, 2, 0)), NaN (1, 0, 2, 0)) %!assert (mean (ones (2, 0, 2, 1)), NaN (1, 0, 2, 1)) %!assert (mean (ones (2, 0, 2, 2)), NaN (1, 0, 2, 2)) %!assert (mean (ones (2, 1, 0, 0)), NaN (1, 1, 0, 0)) %!assert (mean (ones (2, 1, 0, 1)), NaN (1, 1, 0, 1)) %!assert (mean (ones (2, 1, 0, 2)), NaN (1, 1, 0, 2)) %!assert (mean (ones (2, 1, 1, 0)), NaN (1, 1, 1, 0)) %!assert (mean (ones (2, 1, 2, 0)), NaN (1, 1, 2, 0)) %!assert (mean (ones (2, 2, 0, 0)), NaN (1, 2, 0, 0)) %!assert (mean (ones (2, 2, 0, 1)), NaN (1, 2, 0, 1)) %!assert (mean (ones (2, 2, 0, 2)), NaN (1, 2, 0, 2)) %!assert (mean (ones (2, 2, 1, 0)), NaN (1, 2, 1, 0)) %!assert (mean (ones (2, 2, 2, 0)), NaN (1, 2, 2, 0)) %!assert (mean (ones (1, 1, 0, 0, 0)), NaN (1, 1, 1, 0, 0)) %!assert (mean (ones (1, 1, 1, 1, 0)), NaN (1, 1, 1, 1, 1)) %!assert (mean (ones (2, 1, 1, 1, 0)), NaN (1, 1, 1, 1, 0)) %!assert (mean (ones (1, 2, 1, 1, 0)), NaN (1, 1, 1, 1, 0)) %!assert (mean (ones (1, 3, 0, 2)), NaN (1, 1, 0, 2)) %!assert (mean (single (ones (1, 3, 0, 2))), single (NaN (1, 1, 0, 2))) %!assert (mean ([], 1), NaN (1, 0)) %!assert (mean ([], 2), NaN (0, 1)) %!assert (mean ([], 3), []) %!assert (mean (ones (1, 0), 1), NaN (1, 0)) %!assert (mean (ones (1, 0), 2), NaN) %!assert (mean (ones (1, 0), 3), NaN (1, 0)) %!assert (mean (ones (0, 1), 1), NaN) %!assert (mean (ones (0, 1), 2), NaN (0, 1)) %!assert (mean (ones (0, 1), 3), NaN (0, 1)) ## Test input validation %!error mean () %!error mean (1, 2, 3, 4) %!error mean ({1:5}) %!error mean (1, 2, 3) %!error mean (1, ones (2, 2)) %!error mean (1, 1.5) %!error mean (1, 0) %!error mean ([1 -1], "g") %!error