/usr/share/octave/packages/statistics-1.3.0/gevfit.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 | ## Copyright (C) 2012-2016 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{paramhat}, @var{paramci} =} gevfit (@var{data}, @var{parmguess})
## Find the maximum likelihood estimator (@var{paramhat}) of the generalized extreme value (GEV) distribution to fit @var{data}.
##
## @subheading Arguments
##
## @itemize @bullet
## @item
## @var{data} is the vector of given values.
## @item
## @var{parmguess} is an initial guess for the maximum likelihood parameter vector. If not given, this defaults to @var{k}=0 and @var{sigma}, @var{mu} determined by matching the data mean and standard deviation to their expected values.
## @end itemize
##
## @subheading Return values
##
## @itemize @bullet
## @item
## @var{parmhat} is the 3-parameter maximum-likelihood parameter vector [@var{k}; @var{sigma}; @var{mu}], where @var{k} is the shape parameter of the GEV distribution, @var{sigma} is the scale parameter of the GEV distribution, and @var{mu} is the location parameter of the GEV distribution.
## @item
## @var{paramci} has the approximate 95% confidence intervals of the parameter values based on the Fisher information matrix at the maximum-likelihood position.
##
## @end itemize
##
## @subheading Examples
##
## @example
## @group
## data = 1:50;
## [pfit, pci] = gevfit (data);
## p1 = gevcdf(data,pfit(1),pfit(2),pfit(3));
## plot(data, p1)
## @end group
## @end example
## @seealso{gevcdf, gevinv, gevlike, gevpdf, gevrnd, gevstat}
## @end deftypefn
## Author: Nir Krakauer <nkrakauer@ccny.cuny.edu>
## Description: Maximum likelihood parameter estimation for the generalized extreme value distribution
function [paramhat, paramci] = gevfit (data, paramguess)
# Check arguments
if (nargin < 1)
print_usage;
endif
if (nargin < 2) || isempty(paramguess)
paramguess = zeros (3, 1);
paramguess(2) = (sqrt(6)/pi) * std (data);
paramguess(3) = mean(data) - 0.5772156649*paramguess(2) #expectation involves Euler–Mascheroni constant
endif
#cost function to minimize
f = @(p) gevlike (p, data);
paramhat = fminunc(f, paramguess, optimset("GradObj", "on"));
if nargout > 1
[nlogL, ~, ACOV] = gevlike (paramhat, data);
param_se = sqrt(diag(inv(ACOV)));
if any(iscomplex(param_se))
warning ('gevfit: Fisher information matrix not positive definite; parameter optimization likely did not converge')
paramci = nan (3, 2);
else
paramci(:, 1) = paramhat - 1.96*param_se;
paramci(:, 2) = paramhat + 1.96*param_se;
endif
endif
endfunction
%!test
%! data = 1:50;
%! [pfit, pci] = gevfit (data);
%! expected_p = [-0.44 15.19 21.53]';
%! expected_pu = [-0.13 19.31 26.49]';
%! assert (pfit, expected_p, 0.1);
%! assert (pci(:, 2), expected_pu, 0.1);
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