Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / fstat.m

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+## Copyright (C) 2006, 2007 Arno Onken <asnelt@asnelt.org>
+##
+## This program 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.
+##
+## This program 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
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{mn}, @var{v}] =} fstat (@var{m}, @var{n})
+## Compute mean and variance of the F distribution.
+##
+## @subheading Arguments
+##
+## @itemize @bullet
+## @item
+## @var{m} is the first parameter of the F distribution. The elements
+## of @var{m} must be positive
+##
+## @item
+## @var{n} is the second parameter of the F distribution. The
+## elements of @var{n} must be positive
+## @end itemize
+## @var{m} and @var{n} must be of common size or one of them must be scalar
+##
+## @subheading Return values
+##
+## @itemize @bullet
+## @item
+## @var{mn} is the mean of the F distribution. The mean is undefined for
+## @var{n} not greater than 2
+##
+## @item
+## @var{v} is the variance of the F distribution. The variance is undefined
+## for @var{n} not greater than 4
+## @end itemize
+##
+## @subheading Examples
+##
+## @example
+## @group
+## m = 1:6;
+## n = 5:10;
+## [mn, v] = fstat (m, n)
+## @end group
+##
+## @group
+## [mn, v] = fstat (m, 5)
+## @end group
+## @end example
+##
+## @subheading References
+##
+## @enumerate
+## @item
+## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics
+## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC,
+## 2001.
+##
+## @item
+## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic
+## Processes}. McGraw-Hill, New York, second edition, 1984.
+## @end enumerate
+## @end deftypefn
+
+## Author: Arno Onken <asnelt@asnelt.org>
+## Description: Moments of the F distribution
+
+function [mn, v] = fstat (m, n)
+
+  # Check arguments
+  if (nargin != 2)
+    print_usage ();
+  endif
+
+  if (! isempty (m) && ! ismatrix (m))
+    error ("fstat: m must be a numeric matrix");
+  endif
+  if (! isempty (n) && ! ismatrix (n))
+    error ("fstat: n must be a numeric matrix");
+  endif
+
+  if (! isscalar (m) || ! isscalar (n))
+    [retval, m, n] = common_size (m, n);
+    if (retval > 0)
+      error ("fstat: m and n must be of common size or scalar");
+    endif
+  endif
+
+  # Calculate moments
+  mn = n ./ (n - 2);
+  v = (2 .* (n .^ 2) .* (m + n - 2)) ./ (m .* ((n - 2) .^ 2) .* (n - 4));
+
+  # Continue argument check
+  k = find (! (m > 0) | ! (m < Inf) | ! (n > 2) | ! (n < Inf));
+  if (any (k))
+    mn(k) = NaN;
+    v(k) = NaN;
+  endif
+
+  k = find (! (n > 4));
+  if (any (k))
+    v(k) = NaN;
+  endif
+
+endfunction
+
+%!test
+%! m = 1:6;
+%! n = 5:10;
+%! [mn, v] = fstat (m, n);
+%! expected_mn = [1.6667, 1.5000, 1.4000, 1.3333, 1.2857, 1.2500];
+%! expected_v = [22.2222, 6.7500, 3.4844, 2.2222, 1.5869, 1.2153];
+%! assert (mn, expected_mn, 0.001);
+%! assert (v, expected_v, 0.001);
+
+%!test
+%! m = 1:6;
+%! [mn, v] = fstat (m, 5);
+%! expected_mn = [1.6667, 1.6667, 1.6667, 1.6667, 1.6667, 1.6667];
+%! expected_v = [22.2222, 13.8889, 11.1111, 9.7222, 8.8889, 8.3333];
+%! assert (mn, expected_mn, 0.001);
+%! assert (v, expected_v, 0.001);