/usr/share/octave/packages/statistics-1.3.0/gevpdf.m is in octave-statistics 1.3.0-1.
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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 | ## Copyright (C) 2012 Nir Krakauer <nkrakauer@ccny.cuny.edu>
##
## 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{y} =} gevpdf (@var{x}, @var{k}, @var{sigma}, @var{mu})
## Compute the probability density function of the generalized extreme value (GEV) distribution.
##
## @subheading Arguments
##
## @itemize @bullet
## @item
## @var{x} is the support.
##
## @item
## @var{k} is the shape parameter of the GEV distribution. (Also denoted gamma or xi.)
## @item
## @var{sigma} is the scale parameter of the GEV distribution. The elements
## of @var{sigma} must be positive.
## @item
## @var{mu} is the location parameter of the GEV distribution.
## @end itemize
## The inputs must be of common size, or some of them must be scalar.
##
## @subheading Return values
##
## @itemize @bullet
## @item
## @var{y} is the probability density of the GEV distribution at each
## element of @var{x} and corresponding parameter values.
## @end itemize
##
## @subheading Examples
##
## @example
## @group
## x = 0:0.5:2.5;
## sigma = 1:6;
## k = 1;
## mu = 0;
## y = gevpdf (x, k, sigma, mu)
## @end group
##
## @group
## y = gevpdf (x, k, 0.5, mu)
## @end group
## @end example
##
## @subheading References
##
## @enumerate
## @item
## Rolf-Dieter Reiss and Michael Thomas. @cite{Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields}. Chapter 1, pages 16-17, Springer, 2007.
##
## @end enumerate
## @seealso{gevcdf, gevfit, gevinv, gevlike, gevrnd, gevstat}
## @end deftypefn
## Author: Nir Krakauer <nkrakauer@ccny.cuny.edu>
## Description: PDF of the generalized extreme value distribution
function y = gevpdf (x, k, sigma, mu)
# Check arguments
if (nargin != 4)
print_usage ();
endif
if (isempty (x) || isempty (k) || isempty (sigma) || isempty (mu) || ~ismatrix (x) || ~ismatrix (k) || ~ismatrix (sigma) || ~ismatrix (mu))
error ("gevpdf: inputs must be numeric matrices");
endif
[retval, x, k, sigma, mu] = common_size (x, k, sigma, mu);
if (retval > 0)
error ("gevpdf: inputs must be of common size or scalars");
endif
z = 1 + k .* (x - mu) ./ sigma;
# Calculate pdf
y = exp(-(z .^ (-1 ./ k))) .* (z .^ (-1 - 1 ./ k)) ./ sigma;
y(z <= 0) = 0;
inds = (abs (k) < (eps^0.7)); %use a different formula if k is very close to zero
if any(inds)
z = (mu(inds) - x(inds)) ./ sigma(inds);
y(inds) = exp(z-exp(z)) ./ sigma(inds);
endif
endfunction
%!test
%! x = 0:0.5:2.5;
%! sigma = 1:6;
%! k = 1;
%! mu = 0;
%! y = gevpdf (x, k, sigma, mu);
%! expected_y = [0.367879 0.143785 0.088569 0.063898 0.049953 0.040997];
%! assert (y, expected_y, 0.001);
%!test
%! x = -0.5:0.5:2.5;
%! sigma = 0.5;
%! k = 1;
%! mu = 0;
%! y = gevpdf (x, k, sigma, mu);
%! expected_y = [0 0.735759 0.303265 0.159229 0.097350 0.065498 0.047027];
%! assert (y, expected_y, 0.001);
%!test #check for continuity for k near 0
%! x = 1;
%! sigma = 0.5;
%! k = -0.03:0.01:0.03;
%! mu = 0;
%! y = gevpdf (x, k, sigma, mu);
%! expected_y = [0.23820 0.23764 0.23704 0.23641 0.23576 0.23508 0.23438];
%! assert (y, expected_y, 0.001);
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