update packages

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

diff --git a/octave_packages/m/statistics/tests/hotelling_test.m b/octave_packages/m/statistics/tests/hotelling_test.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 (@var{x}, @var{m})
+## For a sample @var{x} from a multivariate normal distribution with unknown
+## mean and covariance matrix, test the null hypothesis that @code{mean
+## (@var{x}) == @var{m}}.
+##
+## Hotelling's @math{T^2} is returned in @var{tsq}.  Under the null,
+## @math{(n-p) T^2 / (p(n-1))} has an F distribution with @math{p} and
+## @math{n-p} degrees of freedom, where @math{n} and @math{p} are the
+## numbers of samples and variables, respectively.
+##
+## 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: Test for mean of a multivariate normal
+
+function [pval, Tsq] = hotelling_test (x, m)
+
+  if (nargin != 2)
+    print_usage ();
+  endif
+
+  if (isvector (x))
+    if (! isscalar (m))
+      error ("hotelling_test: if X is a vector, M must be a scalar");
+    endif
+    n = length (x);
+    p = 1;
+  elseif (ismatrix (x))
+    [n, p] = size (x);
+    if (n <= p)
+      error ("hotelling_test: X must have more rows than columns");
+    endif
+    if (isvector (m) && length (m) == p)
+      m = reshape (m, 1, p);
+    else
+      error ("hotelling_test: if X is a matrix, M must be a vector of length columns (X)");
+    endif
+  else
+    error ("hotelling_test: X must be a matrix or vector");
+  endif
+
+  d    = mean (x) - m;
+  Tsq  = n * d * (cov (x) \ d');
+  pval = 1 - fcdf ((n-p) * Tsq / (p * (n-1)), p, n-p);
+
+  if (nargout == 0)
+    printf ("  pval: %g\n", pval);
+  endif
+
+endfunction