update packages

[CreaPhase.git] / octave_packages / m / statistics / tests / kolmogorov_smirnov_test_2.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}, @var{d}] =} kolmogorov_smirnov_test_2 (@var{x}, @var{y}, @var{alt})
+## Perform a 2-sample Kolmogorov-Smirnov test of the null hypothesis
+## that the samples @var{x} and @var{y} come from the same (continuous)
+## distribution.  I.e., if F and G are the CDFs corresponding to the
+## @var{x} and @var{y} samples, respectively, then the null is that F ==
+## G.
+##
+## 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}.
+##
+## The third returned value, @var{d}, is the test statistic, the maximum
+## vertical distance between the two cumulative distribution functions.
+##
+## If no output argument is given, the p-value is displayed.
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: Two-sample Kolmogorov-Smirnov test
+
+function [pval, ks, d] = kolmogorov_smirnov_test_2 (x, y, alt)
+
+  if (nargin < 2 || nargin > 3)
+    print_usage ();
+  endif
+
+  if (! (isvector (x) && isvector (y)))
+    error ("kolmogorov_smirnov_test_2: both X and Y must be vectors");
+  endif
+
+  if (nargin == 2)
+    alt = "!=";
+  else
+    if (! ischar (alt))
+      error ("kolmogorov_smirnov_test_2: ALT must be a string");
+    endif
+  endif
+
+  n_x = length (x);
+  n_y = length (y);
+  n   = n_x * n_y / (n_x + n_y);
+  x   = reshape (x, n_x, 1);
+  y   = reshape (y, n_y, 1);
+  [s, i] = sort ([x; y]);
+  count (find (i <= n_x)) = 1 / n_x;
+  count (find (i > n_x)) = - 1 / n_y;
+
+  z = cumsum (count);
+  ds = diff (s);
+  if (any (ds == 0))
+    ## There are some ties, so keep only those changes.
+    warning ("cannot compute correct p-values with ties");
+    elems = [find(ds); n_x+n_y];
+    z = z(elems);
+  endif
+
+  if (strcmp (alt, "!=") || strcmp (alt, "<>"))
+    d    = max (abs (z));
+    ks   = sqrt (n) * d;
+    pval = 1 - kolmogorov_smirnov_cdf (ks);
+  elseif (strcmp (alt, ">"))
+    d    = max (z);
+    ks   = sqrt (n) * d;
+    pval = exp (-2 * ks^2);
+  elseif (strcmp (alt, "<"))
+    d    = min (z);
+    ks   = -sqrt (n) * d;
+    pval = exp (-2 * ks^2);
+  else
+    error ("kolmogorov_smirnov_test_2: option %s not recognized", alt);
+  endif
+
+  if (nargout == 0)
+    printf ("  pval: %g\n", pval);
+  endif
+
+endfunction