Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / raylstat.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}] =} raylstat (@var{sigma})
+## Compute mean and variance of the Rayleigh distribution.
+##
+## @subheading Arguments
+##
+## @itemize @bullet
+## @item
+## @var{sigma} is the parameter of the Rayleigh distribution. The elements
+## of @var{sigma} must be positive.
+## @end itemize
+##
+## @subheading Return values
+##
+## @itemize @bullet
+## @item
+## @var{m} is the mean of the Rayleigh distribution.
+##
+## @item
+## @var{v} is the variance of the Rayleigh distribution.
+## @end itemize
+##
+## @subheading Example
+##
+## @example
+## @group
+## sigma = 1:6;
+## [m, v] = raylstat (sigma)
+## @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 Rayleigh distribution
+
+function [m, v] = raylstat (sigma)
+
+  # Check arguments
+  if (nargin != 1)
+    print_usage ();
+  endif
+
+  if (! isempty (sigma) && ! ismatrix (sigma))
+    error ("raylstat: sigma must be a numeric matrix");
+  endif
+
+  # Calculate moments
+  m = sigma .* sqrt (pi ./ 2);
+  v = (2 - pi ./ 2) .* sigma .^ 2;
+
+  # Continue argument check
+  k = find (! (sigma > 0));
+  if (any (k))
+    m(k) = NaN;
+    v(k) = NaN;
+  endif
+
+endfunction
+
+%!test
+%! sigma = 1:6;
+%! [m, v] = raylstat (sigma);
+%! expected_m = [1.2533, 2.5066, 3.7599, 5.0133, 6.2666, 7.5199];
+%! expected_v = [0.4292, 1.7168, 3.8628, 6.8673, 10.7301, 15.4513];
+%! assert (m, expected_m, 0.001);
+%! assert (v, expected_v, 0.001);