Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/statistics-1.1.3/raylcdf.m b/octave_packages/statistics-1.1.3/raylcdf.m
new file mode 100644 (file)
index 0000000..8e57d1f
--- /dev/null
+++ b/octave_packages/statistics-1.1.3/raylcdf.m
@@ -0,0 +1,117 @@
+## 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{p} =} raylcdf (@var{x}, @var{sigma})
+## Compute the cumulative distribution function of the Rayleigh
+## distribution.
+##
+## @subheading Arguments
+##
+## @itemize @bullet
+## @item
+## @var{x} is the support. The elements of @var{x} must be non-negative.
+##
+## @item
+## @var{sigma} is the parameter of the Rayleigh distribution. The elements
+## of @var{sigma} must be positive.
+## @end itemize
+## @var{x} and @var{sigma} must be of common size or one of them must be
+## scalar.
+##
+## @subheading Return values
+##
+## @itemize @bullet
+## @item
+## @var{p} is the cumulative distribution of the Rayleigh distribution at
+## each element of @var{x} and corresponding parameter @var{sigma}.
+## @end itemize
+##
+## @subheading Examples
+##
+## @example
+## @group
+## x = 0:0.5:2.5;
+## sigma = 1:6;
+## p = raylcdf (x, sigma)
+## @end group
+##
+## @group
+## p = raylcdf (x, 0.5)
+## @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}. pages 104 and 148, McGraw-Hill, New York, second edition,
+## 1984.
+## @end enumerate
+## @end deftypefn
+
+## Author: Arno Onken <asnelt@asnelt.org>
+## Description: CDF of the Rayleigh distribution
+
+function p = raylcdf (x, sigma)
+
+  # Check arguments
+  if (nargin != 2)
+    print_usage ();
+  endif
+
+  if (! isempty (x) && ! ismatrix (x))
+    error ("raylcdf: x must be a numeric matrix");
+  endif
+  if (! isempty (sigma) && ! ismatrix (sigma))
+    error ("raylcdf: sigma must be a numeric matrix");
+  endif
+
+  if (! isscalar (x) || ! isscalar (sigma))
+    [retval, x, sigma] = common_size (x, sigma);
+    if (retval > 0)
+      error ("raylcdf: x and sigma must be of common size or scalar");
+    endif
+  endif
+
+  # Calculate cdf
+  p = 1 - exp ((-x .^ 2) ./ (2 * sigma .^ 2));
+
+  # Continue argument check
+  k = find (! (x >= 0) | ! (x < Inf) | ! (sigma > 0));
+  if (any (k))
+    p(k) = NaN;
+  endif
+
+endfunction
+
+%!test
+%! x = 0:0.5:2.5;
+%! sigma = 1:6;
+%! p = raylcdf (x, sigma);
+%! expected_p = [0.0000, 0.0308, 0.0540, 0.0679, 0.0769, 0.0831];
+%! assert (p, expected_p, 0.001);
+
+%!test
+%! x = 0:0.5:2.5;
+%! p = raylcdf (x, 0.5);
+%! expected_p = [0.0000, 0.3935, 0.8647, 0.9889, 0.9997, 1.0000];
+%! assert (p, expected_p, 0.001);