Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / gamstat.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}] =} gamstat (@var{a}, @var{b})
+## Compute mean and variance of the gamma distribution.
+##
+## @subheading Arguments
+##
+## @itemize @bullet
+## @item
+## @var{a} is the first parameter of the gamma distribution. @var{a} must be
+## positive
+##
+## @item
+## @var{b} is the second parameter of the gamma 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 gamma distribution
+##
+## @item
+## @var{v} is the variance of the gamma distribution
+## @end itemize
+##
+## @subheading Examples
+##
+## @example
+## @group
+## a = 1:6;
+## b = 1:0.2:2;
+## [m, v] = gamstat (a, b)
+## @end group
+##
+## @group
+## [m, v] = gamstat (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 gamma distribution
+
+function [m, v] = gamstat (a, b)
+
+  # Check arguments
+  if (nargin != 2)
+    print_usage ();
+  endif
+
+  if (! isempty (a) && ! ismatrix (a))
+    error ("gamstat: a must be a numeric matrix");
+  endif
+  if (! isempty (b) && ! ismatrix (b))
+    error ("gamstat: b must be a numeric matrix");
+  endif
+
+  if (! isscalar (a) || ! isscalar (b))
+    [retval, a, b] = common_size (a, b);
+    if (retval > 0)
+      error ("gamstat: a and b must be of common size or scalar");
+    endif
+  endif
+
+  # Calculate moments
+  m = a .* b;
+  v = a .* (b .^ 2);
+
+  # 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] = gamstat (a, b);
+%! expected_m = [1.00, 2.40, 4.20,  6.40,  9.00, 12.00];
+%! expected_v = [1.00, 2.88, 5.88, 10.24, 16.20, 24.00];
+%! assert (m, expected_m, 0.001);
+%! assert (v, expected_v, 0.001);
+
+%!test
+%! a = 1:6;
+%! [m, v] = gamstat (a, 1.5);
+%! expected_m = [1.50, 3.00, 4.50, 6.00,  7.50,  9.00];
+%! expected_v = [2.25, 4.50, 6.75, 9.00, 11.25, 13.50];
+%! assert (m, expected_m, 0.001);
+%! assert (v, expected_v, 0.001);