Mercurial > octave-nkf
view scripts/statistics/tests/kolmogorov_smirnov_test.m @ 3426:f8dde1807dee
[project @ 2000-01-13 08:40:00 by jwe]
author | jwe |
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date | Thu, 13 Jan 2000 08:40:53 +0000 |
parents | 781c930425fd |
children | d8b731d3f7a3 |
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## Copyright (C) 1995, 1996, 1997 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 2, 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 file. If not, write to the Free Software Foundation, ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. ## usage: ## [pval, ks] = kolmogorov_smirnov_test (x, dist [, params] [, alt]) ## ## ## Performs a Kolmogorov-Smirnov test of the null hypothesis that the ## sample x comes from the (continuous) distribution dist. I.e., if F ## and G are the CDFs corresponding to the sample and dist, respectively, ## then the null is that F == G. ## ## The optional argument params contains a list of parameters of dist. ## E.g., to test whether a sample x comes from a uniform distribution on ## [2,4], use `kolmogorov_smirnov_test(x, "uniform", 2, 4)'. ## ## With the optional argument string alt, the alternative of interest ## can be selected. If alt is "!=" or "<>", the null is tested against ## the two-sided alternative F != G. In this case, the test statistic ## ks follows a two-sided Kolmogorov-Smirnov distribution. ## If alt is ">", the one-sided alternative F > G is considered, ## similarly for "<". In this case, the test statistic ks has a ## one-sided Kolmogorov-Smirnov distribution. ## The default is the two-sided case. ## ## pval is the p-value of the test. ## ## If no output argument is given, the p-value is displayed. ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> ## Description: One-sample Kolmogorov-Smirnov test function [pval, ks] = kolmogorov_smirnov_test (x, dist, ...) if (nargin < 2) error (sprintf (["usage:\n\t", ... "[pval, ks] = ", ... "kolmogorov_smirnov_test (x, dist, [, params] [, alt])"])); endif if (! is_vector (x)) error ("kolmogorov_smirnov_test: x must be a vector."); endif n = length (x); s = sort (x); f = sprintf ("%s_cdf", dist); alt = "!="; if (nargin == 2) z = reshape (feval (f, s), 1, n); else args = ""; for k = 1 : (nargin-2); tmp = va_arg (); if isstr (tmp) alt = tmp; else args = sprintf ("%s, %g", args, tmp); endif endfor z = reshape (eval (sprintf ("%s(s%s);", f, args)), 1, n); endif if (strcmp (alt, "!=") || strcmp (alt, "<>")) ks = sqrt(n) * max(max([abs(z - (0:(n-1))/n); abs(z - (1:n)/n)])); pval = 1 - kolmogorov_smirnov_cdf (ks); elseif (strcmp (alt, ">")) ks = sqrt(n) * max (max ([z - (0:(n-1))/n; z - (1:n)/n])); pval = exp(- 2 * ks^2); elseif (strcmp (alt, "<")) ks = - sqrt(n) * min (min ([z - (0:(n-1))/n; z - (1:n)/n])); pval = exp(- 2 * ks^2); else error (sprintf (["kolmogorov_smirnov_test: ", ... "alternative %s not recognized"], alt)); endif if (nargout == 0) printf ("pval: %g\n", pval); endif endfunction