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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{x} =} raylinv (@var{p}, @var{sigma})
+## Compute the quantile of the Rayleigh distribution. The quantile is the
+## inverse of the cumulative distribution function.
+##
+## @subheading Arguments
+##
+## @itemize @bullet
+## @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.
+##
+## @subheading Return values
+##
+## @itemize @bullet
+## @item
+## @var{x} is the quantile of the Rayleigh distribution at each element of
+## @var{p} and corresponding parameter @var{sigma}.
+## @end itemize
+##
+## @subheading Examples
+##
+## @example
+## @group
+## p = 0:0.1:0.5;
+## sigma = 1:6;
+## x = raylinv (p, sigma)
+## @end group
+##
+## @group
+## x = raylinv (p, 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: Quantile of the Rayleigh distribution
+
+function x = raylinv (p, sigma)
+
+  # Check arguments
+  if (nargin != 2)
+    print_usage ();
+  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);