Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / betastat.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{m}, @var{v}] =} betastat (@var{a}, @var{b})
+## Compute mean and variance of the beta distribution.
+##
+## @subheading Arguments
+##
+## @itemize @bullet
+## @item
+## @var{a} is the first parameter of the beta distribution. @var{a} must be
+## positive
+##
+## @item
+## @var{b} is the second parameter of the beta distribution. @var{b} must be
+## positive
+## @end itemize
+## @var{a} and @var{b} must be of common size or one of them must be scalar
+##
+## @subheading Return values
+##
+## @itemize @bullet
+## @item
+## @var{m} is the mean of the beta distribution
+##
+## @item
+## @var{v} is the variance of the beta distribution
+## @end itemize
+##
+## @subheading Examples
+##
+## @example
+## @group
+## a = 1:6;
+## b = 1:0.2:2;
+## [m, v] = betastat (a, b)
+## @end group
+##
+## @group
+## [m, v] = betastat (a, 1.5)
+## @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 beta distribution
+
+function [m, v] = betastat (a, b)
+
+  # Check arguments
+  if (nargin != 2)
+    print_usage ();
+  endif
+
+  if (! isempty (a) && ! ismatrix (a))
+    error ("betastat: a must be a numeric matrix");
+  endif
+  if (! isempty (b) && ! ismatrix (b))
+    error ("betastat: b must be a numeric matrix");
+  endif
+
+  if (! isscalar (a) || ! isscalar (b))
+    [retval, a, b] = common_size (a, b);
+    if (retval > 0)
+      error ("betastat: a and b must be of common size or scalar");
+    endif
+  endif
+
+  # Calculate moments
+  m = a ./ (a + b);
+  v = (a .* b) ./ (((a + b) .^ 2) .* (a + b + 1));
+
+  # Continue argument check
+  k = find (! (a > 0) | ! (a < Inf) | ! (b > 0) | ! (b < Inf));
+  if (any (k))
+    m(k) = NaN;
+    v(k) = NaN;
+  endif
+
+endfunction
+
+%!test
+%! a = 1:6;
+%! b = 1:0.2:2;
+%! [m, v] = betastat (a, b);
+%! expected_m = [0.5000, 0.6250, 0.6818, 0.7143, 0.7353, 0.7500];
+%! expected_v = [0.0833, 0.0558, 0.0402, 0.0309, 0.0250, 0.0208];
+%! assert (m, expected_m, 0.001);
+%! assert (v, expected_v, 0.001);
+
+%!test
+%! a = 1:6;
+%! [m, v] = betastat (a, 1.5);
+%! expected_m = [0.4000, 0.5714, 0.6667, 0.7273, 0.7692, 0.8000];
+%! expected_v = [0.0686, 0.0544, 0.0404, 0.0305, 0.0237, 0.0188];
+%! assert (m, expected_m, 0.001);
+%! assert (v, expected_v, 0.001);