update packages

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

diff --git a/octave_packages/m/statistics/tests/bartlett_test.m b/octave_packages/m/statistics/tests/bartlett_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{chisq}, @var{df}] =} bartlett_test (@var{x1}, @dots{})
+## Perform a Bartlett test for the homogeneity of variances in the data
+## vectors @var{x1}, @var{x2}, @dots{}, @var{xk}, where @var{k} > 1.
+##
+## Under the null of equal variances, the test statistic @var{chisq}
+## approximately follows a chi-square distribution with @var{df} degrees of
+## freedom.
+##
+## The p-value (1 minus the CDF of this distribution at @var{chisq}) 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: Bartlett test for homogeneity of variances
+
+function [pval, chisq, df] = bartlett_test (varargin)
+
+  k = nargin;
+  if (k < 2)
+    print_usage ();
+  endif
+
+  f = zeros (k, 1);
+  v = zeros (k, 1);
+
+  for i = 1 : k;
+    x = varargin{i};
+    if (! isvector (x))
+      error ("bartlett_test: all arguments must be vectors");
+    endif
+    f(i) = length (x) - 1;
+    v(i) = var (x);
+  endfor
+
+  f_tot = sum (f);
+  v_tot = sum (f .* v) / f_tot;
+  c     = 1 + (sum (1 ./ f) - 1 / f_tot) / (3 * (k - 1));
+  chisq = (f_tot * log (v_tot) - sum (f .* log (v))) / c;
+  df    = k;
+  pval  = 1 - chi2cdf (chisq, df);
+
+  if (nargout == 0)
+    printf("  pval: %g\n", pval);
+  endif
+
+endfunction