/usr/share/octave/packages/statistics-1.2.3/raylinv.m is in octave-statistics 1.2.3-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 | ## 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);
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