Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / hygestat.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}] =} hygestat (@var{t}, @var{m}, @var{n})
+## Compute mean and variance of the hypergeometric distribution.
+##
+## @subheading Arguments
+##
+## @itemize @bullet
+## @item
+## @var{t} is the total size of the population of the hypergeometric
+## distribution. The elements of @var{t} must be positive natural numbers
+##
+## @item
+## @var{m} is the number of marked items of the hypergeometric distribution.
+## The elements of @var{m} must be natural numbers
+##
+## @item
+## @var{n} is the size of the drawn sample of the hypergeometric
+## distribution. The elements of @var{n} must be positive natural numbers
+## @end itemize
+## @var{t}, @var{m}, and @var{n} must be of common size or scalar
+##
+## @subheading Return values
+##
+## @itemize @bullet
+## @item
+## @var{mn} is the mean of the hypergeometric distribution
+##
+## @item
+## @var{v} is the variance of the hypergeometric distribution
+## @end itemize
+##
+## @subheading Examples
+##
+## @example
+## @group
+## t = 4:9;
+## m = 0:5;
+## n = 1:6;
+## [mn, v] = hygestat (t, m, n)
+## @end group
+##
+## @group
+## [mn, v] = hygestat (t, m, 2)
+## @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 hypergeometric distribution
+
+function [mn, v] = hygestat (t, m, n)
+
+  # Check arguments
+  if (nargin != 3)
+    print_usage ();
+  endif
+
+  if (! isempty (t) && ! ismatrix (t))
+    error ("hygestat: t must be a numeric matrix");
+  endif
+  if (! isempty (m) && ! ismatrix (m))
+    error ("hygestat: m must be a numeric matrix");
+  endif
+  if (! isempty (n) && ! ismatrix (n))
+    error ("hygestat: n must be a numeric matrix");
+  endif
+
+  if (! isscalar (t) || ! isscalar (m) || ! isscalar (n))
+    [retval, t, m, n] = common_size (t, m, n);
+    if (retval > 0)
+      error ("hygestat: t, m and n must be of common size or scalar");
+    endif
+  endif
+
+  # Calculate moments
+  mn = (n .* m) ./ t;
+  v = (n .* (m ./ t) .* (1 - m ./ t) .* (t - n)) ./ (t - 1);
+
+  # Continue argument check
+  k = find (! (t >= 0) | ! (m >= 0) | ! (n > 0) | ! (t == round (t)) | ! (m == round (m)) | ! (n == round (n)) | ! (m <= t) | ! (n <= t));
+  if (any (k))
+    mn(k) = NaN;
+    v(k) = NaN;
+  endif
+
+endfunction
+
+%!test
+%! t = 4:9;
+%! m = 0:5;
+%! n = 1:6;
+%! [mn, v] = hygestat (t, m, n);
+%! expected_mn = [0.0000, 0.4000, 1.0000, 1.7143, 2.5000, 3.3333];
+%! expected_v = [0.0000, 0.2400, 0.4000, 0.4898, 0.5357, 0.5556];
+%! assert (mn, expected_mn, 0.001);
+%! assert (v, expected_v, 0.001);
+
+%!test
+%! t = 4:9;
+%! m = 0:5;
+%! [mn, v] = hygestat (t, m, 2);
+%! expected_mn = [0.0000, 0.4000, 0.6667, 0.8571, 1.0000, 1.1111];
+%! expected_v = [0.0000, 0.2400, 0.3556, 0.4082, 0.4286, 0.4321];
+%! assert (mn, expected_mn, 0.001);
+%! assert (v, expected_v, 0.001);