update packages

[CreaPhase.git] / octave_packages / m / statistics / tests / hotelling_test_2.m

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+## Copyright (C) 1996-2012 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{tsq}] =} hotelling_test_2 (@var{x}, @var{y})
+## For two samples @var{x} from multivariate normal distributions with
+## the same number of variables (columns), unknown means and unknown
+## equal covariance matrices, test the null hypothesis @code{mean
+## (@var{x}) == mean (@var{y})}.
+##
+## Hotelling's two-sample @math{T^2} is returned in @var{tsq}.  Under the null,
+## @tex
+## $$
+## {n_x+n_y-p-1) T^2 \over p(n_x+n_y-2)}
+## $$
+## @end tex
+## @ifnottex
+##
+## @example
+## (n_x+n_y-p-1) T^2 / (p(n_x+n_y-2))
+## @end example
+##
+## @end ifnottex
+## @noindent
+## has an F distribution with @math{p} and @math{n_x+n_y-p-1} degrees of
+## freedom, where @math{n_x} and @math{n_y} are the sample sizes and
+## @math{p} is the number of variables.
+##
+## The p-value of the test is returned in @var{pval}.
+##
+## If no output argument is given, the p-value of the test is displayed.
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: Compare means of two multivariate normals
+
+function [pval, Tsq] = hotelling_test_2 (x, y)
+
+  if (nargin != 2)
+    print_usage ();
+  endif
+
+  if (isvector (x))
+    n_x = length (x);
+    if (! isvector (y))
+      error ("hotelling_test_2: if X is a vector, Y must also be a vector");
+    else
+      n_y = length (y);
+      p   = 1;
+    endif
+  elseif (ismatrix (x))
+    [n_x, p] = size (x);
+    [n_y, q] = size (y);
+    if (p != q)
+      error ("hotelling_test_2: X and Y must have the same number of columns");
+    endif
+  else
+    error ("hotelling_test_2: X and Y must be matrices (or vectors)");
+  endif
+
+  d    = mean (x) - mean (y);
+  S    = ((n_x - 1) * cov (x) + (n_y - 1) * cov (y)) / (n_x + n_y - 2);
+  Tsq  = (n_x * n_y / (n_x + n_y)) * d * (S \ d');
+  pval = 1 - fcdf ((n_x + n_y - p - 1) * Tsq / (p * (n_x + n_y - 2)),
+                    p, n_x + n_y - p - 1);
+
+  if (nargout == 0)
+    printf ("  pval: %g\n", pval);
+  endif
+
+endfunction