update packages

[CreaPhase.git] / octave_packages / m / statistics / tests / kolmogorov_smirnov_test.m

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+## Copyright (C) 1995-2012 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{pval}, @var{ks}] =} kolmogorov_smirnov_test (@var{x}, @var{dist}, @var{params}, @var{alt})
+## Perform a Kolmogorov-Smirnov test of the null hypothesis that the
+## sample @var{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 @var{params} contains a list of parameters of
+## @var{dist}.  For example, to test whether a sample @var{x} comes from
+## a uniform distribution on [2,4], use
+##
+## @example
+## kolmogorov_smirnov_test(x, "unif", 2, 4)
+## @end example
+##
+## @noindent
+## @var{dist} can be any string for which a function @var{dist_cdf}
+## that calculates the CDF of distribution @var{dist} exists.
+##
+## With the optional argument string @var{alt}, the alternative of
+## interest can be selected.  If @var{alt} is @code{"!="} or
+## @code{"<>"}, the null is tested against the two-sided alternative F
+## != G@.  In this case, the test statistic @var{ks} follows a two-sided
+## Kolmogorov-Smirnov distribution.  If @var{alt} is @code{">"}, the
+## one-sided alternative F > G is considered.  Similarly for @code{"<"},
+## the one-sided alternative F > G is considered.  In this case, the
+## test statistic @var{ks} has a one-sided Kolmogorov-Smirnov
+## distribution.  The default is the two-sided case.
+##
+## The p-value of the test is returned in @var{pval}.
+##
+## If no output argument is given, the p-value is displayed.
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: One-sample Kolmogorov-Smirnov test
+
+function [pval, ks] = kolmogorov_smirnov_test (x, dist, varargin)
+
+  if (nargin < 2)
+    print_usage ();
+  endif
+
+  if (! isvector (x))
+    error ("kolmogorov_smirnov_test: X must be a vector");
+  endif
+
+  n = length (x);
+  s = sort (x);
+  try
+    f = str2func (sprintf ("%scdf", dist));
+  catch
+    try
+      f = str2func (sprintf ("%s_cdf", dist));
+    catch
+      error ("kolmogorov_smirnov_test: no %scdf or %s_cdf function found",
+             dist, dist);
+    end_try_catch
+  end_try_catch
+
+  alt  = "!=";
+
+  args{1} = s;
+  nvargs = numel (varargin);
+  if (nvargs > 0)
+    if (ischar (varargin{end}))
+      alt = varargin{end};
+      args(2:nvargs) = varargin(1:end-1);
+    else
+      args(2:nvargs+1) = varargin;
+    endif
+  endif
+
+  z = reshape (feval (f, args{:}), 1, n);
+
+  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 ("kolmogorov_smirnov_test: alternative %s not recognized", alt);
+  endif
+
+  if (nargout == 0)
+    printf ("pval: %g\n", pval);
+  endif
+
+endfunction
+
+%!error <Invalid call to kolmogorov_smirnov_test>
+%!  kolmogorov_smirnov_test (1);
+%!error <kolmogorov_smirnov_test: X must be a vector>
+%!  kolmogorov_smirnov_test ({}, "unif", 2, 4);
+%!error <kolmogorov_smirnov_test: no not_a_distcdf or not_a_dist_cdf function found>
+%!  kolmogorov_smirnov_test (1, "not_a_dist");
+%!error <kolmogorov_smirnov_test: alternative bla not recognized>
+%!  kolmogorov_smirnov_test (1, "unif", 2, 4, "bla");
+%!test # for recognition of unifcdf function
+%!  assert (kolmogorov_smirnov_test (0:100, "unif", 0, 100), 1.0, eps);
+%!test # for recognition of logistic_cdf function
+%!  assert (kolmogorov_smirnov_test (0:100, "logistic"), 0);
+%!test # F < G
+%!  assert (kolmogorov_smirnov_test (50:100, "unif", 0, 50, "<"));