--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/statistics/inst/raylcdf.m	Sun Oct 01 15:38:31 2006 +0000
@@ -0,0 +1,114 @@
+## Copyright (C) 2006 Arno Onken
+##
+## 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 2 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, write to the Free Software
+## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{p} =} raylcdf (@var{x}, @var{sigma})
+## Calculates the cumulative distribution function of the Rayleigh
+## distribution.
+##
+## Arguments are
+##
+## @itemize
+## @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.
+##
+## Return values are
+##
+## @itemize
+## @item
+## @var{p} is the cumulative distribution of the Rayleigh distribution at
+## each element of @var{x} and corresponding parameter @var{sigma}.
+## @end itemize
+##
+## Examples:
+##
+## @example
+## x = 0:0.5:2.5;
+## sigma = 1:6;
+## p = raylcdf (x, sigma)
+##
+## p = raylcdf (x, 0.5)
+## @end example
+##
+## References:
+##
+## @enumerate
+## @item
+## W. L. Martinez and A. R. Martinez. @cite{Computational Statistics
+## Handbook with MATLAB.} Chapman & Hall/CRC, pages 547-557, 2001.
+##
+## @item
+## Wikipedia contributors. Rayleigh distribution. @cite{Wikipedia, The Free
+## Encyclopedia.}
+## @uref{http://en.wikipedia.org/w/index.php?title=Rayleigh_distribution&oldid=69294908},
+## August 2006.
+## @end enumerate
+## @end deftypefn
+
+## Author: Arno Onken <whyly@gmx.net>
+## Description: CDF of the Rayleigh distribution
+
+function p = raylcdf (x, sigma)
+
+  # Check arguments
+  if (nargin != 2)
+    usage ("p = raylcdf (x, sigma)");
+  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);

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/statistics/inst/raylinv.m	Sun Oct 01 15:38:31 2006 +0000
@@ -0,0 +1,120 @@
+## Copyright (C) 2006 Arno Onken
+##
+## 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 2 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, write to the Free Software
+## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{x} =} raylinv (@var{p}, @var{sigma})
+## Calculates the quantile of the Rayleigh distribution. The quantile is the
+## inverse of the cumulative distribution function.
+##
+## Arguments are
+##
+## @itemize
+## @item
+## @var{p} is the cumulative distribution. The elements of @var{p} must be
+## probabilities.
+##
+## @item
+## @var{sigma} is the parameter of the Rayleigh distribution. The elements
+## of @var{sigma} must be positive.
+## @end itemize
+## @var{p} and @var{sigma} must be of common size or one of them must be
+## scalar.
+##
+## Return values are
+##
+## @itemize
+## @item
+## @var{x} is the quantile of the Rayleigh distribution at each element of
+## @var{p} and corresponding parameter @var{sigma}.
+## @end itemize
+##
+## Examples:
+##
+## @example
+## p = 0:0.1:0.5;
+## sigma = 1:6;
+## x = raylinv (p, sigma)
+##
+## x = raylinv (p, 0.5)
+## @end example
+##
+## References:
+##
+## @enumerate
+## @item
+## W. L. Martinez and A. R. Martinez. @cite{Computational Statistics
+## Handbook with MATLAB.} Chapman & Hall/CRC, pages 547-557, 2001.
+##
+## @item
+## Wikipedia contributors. Rayleigh distribution. @cite{Wikipedia, The Free
+## Encyclopedia.}
+## @uref{http://en.wikipedia.org/w/index.php?title=Rayleigh_distribution&oldid=69294908},
+## August 2006.
+## @end enumerate
+## @end deftypefn
+
+## Author: Arno Onken <whyly@gmx.net>
+## Description: Quantile of the Rayleigh distribution
+
+function x = raylinv (p, sigma)
+
+  # Check arguments
+  if (nargin != 2)
+    usage ("x = raylinv (p, sigma)");
+  endif
+
+  if (! isempty (p) && ! ismatrix (p))
+    error ("raylinv: p must be a numeric matrix");
+  endif
+  if (! isempty (sigma) && ! ismatrix (sigma))
+    error ("raylinv: sigma must be a numeric matrix");
+  endif
+
+  if (! isscalar (p) || ! isscalar (sigma))
+    [retval, p, sigma] = common_size (p, sigma);
+    if (retval > 0)
+      error ("raylinv: p and sigma must be of common size or scalar");
+    endif
+  endif
+
+  # Calculate quantile
+  x = sqrt (-2 .* log (1 - p) .* sigma .^ 2);
+
+  k = find (p == 1);
+  if (any (k))
+    x (k) = Inf;
+  endif
+
+  # Continue argument check
+  k = find (! (p >= 0) | ! (p <= 1) | ! (sigma > 0));
+  if (any (k))
+    x (k) = NaN;
+  endif
+
+endfunction
+
+%!test
+%! p = 0:0.1:0.5;
+%! sigma = 1:6;
+%! x = raylinv (p, sigma);
+%! expected_x = [0.0000, 0.9181, 2.0041, 3.3784, 5.0538, 7.0645];
+%! assert (x, expected_x, 0.001);
+
+%!test
+%! p = 0:0.1:0.5;
+%! x = raylinv (p, 0.5);
+%! expected_x = [0.0000, 0.2295, 0.3340, 0.4223, 0.5054, 0.5887];
+%! assert (x, expected_x, 0.001);

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/statistics/inst/raylpdf.m	Sun Oct 01 15:38:31 2006 +0000
@@ -0,0 +1,113 @@
+## Copyright (C) 2006 Arno Onken
+##
+## 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 2 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, write to the Free Software
+## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{y} =} raylpdf (@var{x}, @var{sigma})
+## Calculates the probability density function of the Rayleigh distribution.
+##
+## Arguments are
+##
+## @itemize
+## @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.
+##
+## Return values are
+##
+## @itemize
+## @item
+## @var{y} is the probability density of the Rayleigh distribution at each
+## element of @var{x} and corresponding parameter @var{sigma}.
+## @end itemize
+##
+## Examples:
+##
+## @example
+## x = 0:0.5:2.5;
+## sigma = 1:6;
+## y = raylpdf (x, sigma)
+##
+## y = raylpdf (x, 0.5)
+## @end example
+##
+## References:
+##
+## @enumerate
+## @item
+## W. L. Martinez and A. R. Martinez. @cite{Computational Statistics
+## Handbook with MATLAB.} Chapman & Hall/CRC, pages 547-557, 2001.
+##
+## @item
+## Wikipedia contributors. Rayleigh distribution. @cite{Wikipedia, The Free
+## Encyclopedia.}
+## @uref{http://en.wikipedia.org/w/index.php?title=Rayleigh_distribution&oldid=69294908},
+## August 2006.
+## @end enumerate
+## @end deftypefn
+
+## Author: Arno Onken <whyly@gmx.net>
+## Description: PDF of the Rayleigh distribution
+
+function y = raylpdf (x, sigma)
+
+  # Check arguments
+  if (nargin != 2)
+    usage ("y = raylpdf (x, sigma)");
+  endif
+
+  if (! isempty (x) && ! ismatrix (x))
+    error ("raylpdf: x must be a numeric matrix");
+  endif
+  if (! isempty (sigma) && ! ismatrix (sigma))
+    error ("raylpdf: sigma must be a numeric matrix");
+  endif
+
+  if (! isscalar (x) || ! isscalar (sigma))
+    [retval, x, sigma] = common_size (x, sigma);
+    if (retval > 0)
+      error ("raylpdf: x and sigma must be of common size or scalar");
+    endif
+  endif
+
+  # Calculate pdf
+  y = x .* exp ((-x .^ 2) ./ (2 .* sigma .^ 2)) ./ (sigma .^ 2);
+
+  # Continue argument check
+  k = find (! (x >= 0) | ! (x < Inf) | ! (sigma > 0));
+  if (any (k))
+    y (k) = NaN;
+  endif
+
+endfunction
+
+%!test
+%! x = 0:0.5:2.5;
+%! sigma = 1:6;
+%! y = raylpdf (x, sigma);
+%! expected_y = [0.0000, 0.1212, 0.1051, 0.0874, 0.0738, 0.0637];
+%! assert (y, expected_y, 0.001);
+
+%!test
+%! x = 0:0.5:2.5;
+%! y = raylpdf (x, 0.5);
+%! expected_y = [0.0000, 1.2131, 0.5413, 0.0667, 0.0027, 0.0000];
+%! assert (y, expected_y, 0.001);

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/statistics/inst/raylrnd.m	Sun Oct 01 15:38:31 2006 +0000
@@ -0,0 +1,152 @@
+## Copyright (C) 2006 Arno Onken
+##
+## 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 2 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, write to the Free Software
+## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{x} =} raylrnd (@var{sigma})
+## @deftypefnx {Function File} {@var{x} =} raylrnd (@var{sigma}, @var{sz})
+## @deftypefnx {Function File} {@var{x} =} raylrnd (@var{sigma}, @var{r}, @var{c})
+## Returns a matrix of random samples from the Rayleigh distribution.
+##
+## Arguments are
+##
+## @itemize
+## @item
+## @var{sigma} is the parameter of the Rayleigh distribution. The elements
+## of @var{sigma} must be positive.
+##
+## @item
+## @var{sz} is the size of the matrix to be generated. @var{sz} must be a
+## vector of non-negative integers.
+##
+## @item
+## @var{r} is the number of rows of the matrix to be generated. @var{r} must
+## be a non-negative integer.
+##
+## @item
+## @var{c} is the number of columns of the matrix to be generated. @var{c}
+## must be a non-negative integer.
+## @end itemize
+##
+## Return values are
+##
+## @itemize
+## @item
+## @var{x} is a matrix of random samples from the Rayleigh distribution with
+## corresponding parameter @var{sigma}. If neither @var{sz} nor @var{r} and
+## @var{c} are specified, then @var{x} is of the same size as @{sigma}.
+## @end itemize
+##
+## Examples:
+##
+## @example
+## sigma = 1:6;
+## x = raylrnd (sigma)
+##
+## sz = [2, 3];
+## x = raylrnd (0.5, sz)
+##
+## r = 2;
+## c = 3;
+## x = raylrnd (0.5, r, c)
+## @end example
+##
+## References:
+##
+## @enumerate
+## @item
+## W. L. Martinez and A. R. Martinez. @cite{Computational Statistics
+## Handbook with MATLAB.} Chapman & Hall/CRC, pages 547-557, 2001.
+##
+## @item
+## Wikipedia contributors. Rayleigh distribution. @cite{Wikipedia, The Free
+## Encyclopedia.}
+## @uref{http://en.wikipedia.org/w/index.php?title=Rayleigh_distribution&oldid=69294908},
+## August 2006.
+## @end enumerate
+## @end deftypefn
+
+## Author: Arno Onken <whyly@gmx.net>
+## Description: Random samples from the Rayleigh distribution
+
+function x = raylrnd (sigma, r, c)
+
+  # Check arguments
+  if (nargin == 1)
+    sz = size (sigma);
+  elseif (nargin == 2)
+    if (! isvector (r) || any ((r < 0) | round (r) != r))
+      error ("raylrnd: sz must be a vector of non-negative integers")
+    end
+    sz = r(:)';
+    if (! isscalar (sigma) && ! isempty (sigma) && (length (size (sigma)) != length (sz) || any (size (sigma) != sz)))
+      error ("raylrnd: sigma must be scalar or of size sz");
+    endif
+  elseif (nargin == 3)
+    if (! isscalar (r) || any ((r < 0) | round (r) != r))
+      error ("raylrnd: r must be a non-negative integer")
+    end
+    if (! isscalar (c) || any ((c < 0) | round (c) != c))
+      error ("raylrnd: c must be a non-negative integer")
+    end
+    sz = [r, c];
+    if (! isscalar (sigma) && ! isempty (sigma) && (length (size (sigma)) != length (sz) || any (size (sigma) != sz)))
+      error ("raylrnd: sigma must be scalar or of size [r, c]");
+    endif
+  else
+    usage ("x = raylrnd (sigma [, sz |, r, c])");
+  endif
+
+  if (! isempty (sigma) && ! ismatrix (sigma))
+    error ("raylrnd: sigma must be a numeric matrix");
+  endif
+
+  if (isempty (sigma))
+    x = [];
+  elseif (isscalar (sigma) && ! (sigma > 0))
+    x = NaN .* ones (sz); 
+  else
+    # Draw random samples
+    x = sqrt (-2 .* log (1 - rand (sz)) .* sigma .^ 2);
+
+    # Continue argument check
+    k = find (! (sigma > 0));
+    if (any (k))
+      x (k) = NaN;
+    endif
+  endif
+
+endfunction
+
+%!test
+%! sigma = 1:6;
+%! x = raylrnd (sigma);
+%! assert (size (x), size (sigma));
+%! assert (all (x >= 0));
+
+%!test
+%! sigma = 0.5;
+%! sz = [2, 3];
+%! x = raylrnd (sigma, sz);
+%! assert (size (x), sz);
+%! assert (all (x >= 0));
+
+%!test
+%! sigma = 0.5;
+%! r = 2;
+%! c = 3;
+%! x = raylrnd (sigma, r, c);
+%! assert (size (x), [r c]);
+%! assert (all (x >= 0));

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/statistics/inst/raylstat.m	Sun Oct 01 15:38:31 2006 +0000
@@ -0,0 +1,94 @@
+## Copyright (C) 2006 Arno Onken
+##
+## 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 2 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, write to the Free Software
+## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{m}, @var{v}] =} raylstat (@var{sigma})
+## Returns mean and variance of the Rayleigh distribution.
+##
+## Arguments are
+##
+## @itemize
+## @item
+## @var{sigma} is the parameter of the Rayleigh distribution. The elements
+## of @var{sigma} must be positive.
+## @end itemize
+##
+## Return values are
+##
+## @itemize
+## @item
+## @var{m} is the mean of the Rayleigh distribution.
+##
+## @item
+## @var{v} is the variance of the Rayleigh distribution.
+## @end itemize
+##
+## Example:
+##
+## @example
+## sigma = 1:6;
+## [m, v] = raylstat (sigma)
+## @end example
+##
+## References:
+##
+## @enumerate
+## @item
+## W. L. Martinez and A. R. Martinez. @cite{Computational Statistics
+## Handbook with MATLAB.} Chapman & Hall/CRC, pages 547-557, 2001.
+##
+## @item
+## Wikipedia contributors. Rayleigh distribution. @cite{Wikipedia, The Free
+## Encyclopedia.}
+## @uref{http://en.wikipedia.org/w/index.php?title=Rayleigh_distribution&oldid=69294908},
+## August 2006.
+## @end enumerate
+## @end deftypefn
+
+## Author: Arno Onken <whyly@gmx.net>
+## Description: Moments of the Rayleigh distribution
+
+function [m, v] = raylstat (sigma)
+
+  # Check arguments
+  if (nargin != 1)
+    usage ("[m, v] = raylstat (sigma)");
+  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);