442 lines
11 KiB
Matlab
442 lines
11 KiB
Matlab
function rnd = gamrnd(a, b, method)
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% This function produces independent random variates from the Gamma distribution.
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%
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% INPUTS
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% - a [double] n*1 vector of positive parameters.
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% - b [double] n*1 vector of positive parameters.
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% - method [struct] Specifies which algorithms must be used.
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%
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% OUTPUT
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% - rnd [double] n*1 vector of independent variates from the gamma(a,b) distribution.
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% rnd(i) is gamma distributed with mean a(i)b(i) and variance a(i)b(i)^2.
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%
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% REMARKS
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% The third input is a structure with two fields named `large` and `small`.
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% These fields define the algorithms to be used if a>1 (large) or a<1 (small).
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% Copyright © 2006-2021 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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%>
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%> Set defaults
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%> ------------
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if nargin<2
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b = ones(size(a));
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end
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if nargin<3
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method = struct('large', 'Cheng', 'small', 'Johnk');
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end
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%>
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%> Check inputs
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%> ------------
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[ma,na] = size(a);
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[mb,nb] = size(b);
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if ma~=mb || na~=nb
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error('gamrnd:: Input arguments must have the same size.');
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end
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if na~=1
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error('gamrnd:: Input arguments must be column vectors.');
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end
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if (any(a<0)) || (any(b<0)) || (any(a==Inf)) || (any(b==Inf))
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error('gamrnd:: Input arguments must be finite and positive.');
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end
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%>
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%> Inititialize output
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%> -------------------
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rnd = NaN(ma,1);
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% Get indices of integer (idx) and non integer (ddx) for the first hyperparameter a.
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[~, idx, ddx] = isint(a);
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if ~isempty(idx)
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% If the first hyperparameter (a) is an integer we can use the
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% exponential random number generator or rely in a Gaussian
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% approximation.
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sdx = find(a(idx)<30);
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ldx = find(a(idx)>=30);
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if ~isempty(sdx)
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% Exact sampling using random deviates from an exponential distribution.
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for i=1:length(sdx)
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rnd(idx(sdx(i))) = sum(exprnd(ones(a(idx(sdx(i))),1)))*b(idx(sdx(i)));
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end
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end
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if ~isempty(ldx)
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% Gaussian approximation.
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rnd(idx(ldx)) = sqrt(a(idx(ldx))).* b(idx(ldx)) .* randn(length(ldx), 1) + a(idx(ldx)) .* b(idx(ldx));
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end
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end
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if ~isempty(ddx)
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% The first hyperparameter is not an integer.
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sdx = find(a(ddx)<1); % Indices for small a.
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ldx = find(a(ddx)>1); % Indices for large a.
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if ~isempty(sdx)
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switch method.small
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case 'Weibull-rejection'
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rnd(ddx(sdx)) = gamrnd.weibull_rejection(a(ddx(sdx)),b(ddx(sdx)));
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case 'Johnk'
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rnd(ddx(sdx)) = gamrnd.johnk(a(ddx(sdx)),b(ddx(sdx)));
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case 'Berman'
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rnd(ddx(sdx)) = gamrnd.berman(a(ddx(sdx)),b(ddx(sdx)));
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case 'Ahrens-Dieter'
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rnd(ddx(sdx)) = gamrnd.ahrens_dieter(a(ddx(sdx)),b(ddx(sdx)));
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case 'Best'
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rnd(ddx(sdx)) = gamrnd.best_1983(a(ddx(sdx)),b(ddx(sdx)));
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otherwise
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error('Unknown algorithm for gamrnd.')
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end
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end
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if ~isempty(ldx)
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switch method.large
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case 'Knuth'
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rnd(ddx) = gamrnd.knuth(a(ddx),b(ddx));
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case 'Best'
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rnd(ddx(ldx)) = gamrnd.best_1978(a(ddx(ldx)),b(ddx(ldx)));
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case 'Cheng'
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rnd(ddx(ldx)) = gamrnd.cheng(a(ddx(ldx)),b(ddx(ldx)));
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otherwise
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error('Unknown algorithm for gamrnd.')
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end
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end
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end
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return % --*-- Unit tests --*--
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%@test:1
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if ~isoctave && ~user_has_matlab_license('statistics_toolbox')
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method = struct('small', 'Weibull-rejection', 'large', 'Knuth');
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n = 1000000;
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m = 100;
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a = 0.1;
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b = 1.0;
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try
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mu = 0;
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s2 = 0;
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levels = .01:.01:10;
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ecdf = zeros(length(levels),1);
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for i = 1:m
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x = gamrnd(ones(n, 1)*a, ones(n,1)*b, method);
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mu = mu + mean(x);
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s2 = s2 + var(x);
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for j=1:length(levels)
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ecdf(j) = ecdf(j)+sum(x<levels(j))/n;
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end
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end
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mu = mu/m;
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s2 = s2/m;
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ecdf = ecdf/m;
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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t(2) = abs(mu-a*b)<1e-3;
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t(3) = abs(s2-a*b^2)<1e-3;
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t(4) = max(abs(ecdf-gamcdf(transpose(levels), a, b)))<1e-3;
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end
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T = all(t);
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else
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t = true(4, 1);
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T = true;
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end
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%@eof:1
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%@test:2
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if ~isoctave && ~user_has_matlab_license('statistics_toolbox')
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method = struct('small', 'Johnk', 'large', 'Knuth');
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n = 1000000;
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m = 100;
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a = 0.1;
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b = 1.0;
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try
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mu = 0;
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s2 = 0;
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levels = .01:.01:10;
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ecdf = zeros(length(levels),1);
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for i = 1:m
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x = gamrnd(ones(n, 1)*a, ones(n,1)*b, method);
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mu = mu + mean(x);
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s2 = s2 + var(x);
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for j=1:length(levels)
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ecdf(j) = ecdf(j)+sum(x<levels(j))/n;
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end
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end
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mu = mu/m;
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s2 = s2/m;
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ecdf = ecdf/m;
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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t(2) = abs(mu-a*b)<1e-3;
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t(3) = abs(s2-a*b^2)<1e-3;
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t(4) = max(abs(ecdf-gamcdf(transpose(levels), a, b)))<1e-3;
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end
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T = all(t);
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else
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t = true(4, 1);
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T = true;
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end
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%@eof:2
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%@test:3
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if ~isoctave && ~user_has_matlab_license('statistics_toolbox')
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method = struct('small', 'Berman', 'large', 'Knuth');
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n = 1000000;
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m = 100;
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a = 0.1;
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b = 1.0;
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try
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mu = 0;
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s2 = 0;
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levels = .01:.01:10;
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ecdf = zeros(length(levels),1);
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for i = 1:m
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x = gamrnd(ones(n, 1)*a, ones(n,1)*b, method);
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mu = mu + mean(x);
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s2 = s2 + var(x);
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for j=1:length(levels)
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ecdf(j) = ecdf(j)+sum(x<levels(j))/n;
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end
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end
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mu = mu/m;
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s2 = s2/m;
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ecdf = ecdf/m;
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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t(2) = abs(mu-a*b)<1e-3;
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t(3) = abs(s2-a*b^2)<1e-3;
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t(4) = max(abs(ecdf-gamcdf(transpose(levels), a, b)))<1e-3;
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end
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T = all(t);
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else
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t = true(4, 1);
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T = true;
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end
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%@eof:3
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%@test:4
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if ~isoctave && ~user_has_matlab_license('statistics_toolbox')
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method = struct('small', 'Ahrens-Dieter', 'large', 'Knuth');
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n = 1000000;
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m = 100;
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a = 0.1;
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b = 1.0;
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try
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mu = 0;
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s2 = 0;
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levels = .01:.01:10;
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ecdf = zeros(length(levels),1);
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for i = 1:m
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x = gamrnd(ones(n, 1)*a, ones(n,1)*b, method);
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mu = mu + mean(x);
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s2 = s2 + var(x);
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for j=1:length(levels)
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ecdf(j) = ecdf(j)+sum(x<levels(j))/n;
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end
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end
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mu = mu/m;
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s2 = s2/m;
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ecdf = ecdf/m;
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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t(2) = abs(mu-a*b)<1e-3;
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t(3) = abs(s2-a*b^2)<1e-3;
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t(4) = max(abs(ecdf-gamcdf(transpose(levels), a, b)))<1e-3;
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end
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T = all(t);
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else
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t = true(4, 1);
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T = true;
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end
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%@eof:4
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%@test:5
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if ~isoctave && ~user_has_matlab_license('statistics_toolbox')
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method = struct('small', 'Best', 'large', 'Knuth');
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n = 1000000;
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m = 100;
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a = 0.1;
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b = 1.0;
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try
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mu = 0;
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s2 = 0;
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levels = .01:.01:10;
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ecdf = zeros(length(levels),1);
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for i = 1:m
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x = gamrnd(ones(n, 1)*a, ones(n,1)*b, method);
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mu = mu + mean(x);
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s2 = s2 + var(x);
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for j=1:length(levels)
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ecdf(j) = ecdf(j)+sum(x<levels(j))/n;
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end
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end
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mu = mu/m;
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s2 = s2/m;
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ecdf = ecdf/m;
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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t(2) = abs(mu-a*b)<1e-3;
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t(3) = abs(s2-a*b^2)<1e-3;
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t(4) = max(abs(ecdf-gamcdf(transpose(levels), a, b)))<1e-3;
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end
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T = all(t);
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else
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t = true(4, 1);
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T = true;
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end
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%@eof:5
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%@test:6
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if ~isoctave && ~user_has_matlab_license('statistics_toolbox')
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method = struct('small', 'Weibull-rejection', 'large', 'Knuth');
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n = 1000000;
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m = 100;
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a = 1.5;
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b = 1.0;
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try
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mu = 0;
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s2 = 0;
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levels = .01:.01:15;
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ecdf = zeros(length(levels),1);
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for i = 1:m
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x = gamrnd(ones(n, 1)*a, ones(n,1)*b, method);
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mu = mu + mean(x);
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s2 = s2 + var(x);
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for j=1:length(levels)
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ecdf(j) = ecdf(j)+sum(x<levels(j))/n;
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end
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end
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mu = mu/m;
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s2 = s2/m;
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ecdf = ecdf/m;
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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t(2) = abs(mu-a*b)<1e-3;
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t(3) = abs(s2-a*b^2)<1e-3;
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t(4) = max(abs(ecdf-gamcdf(transpose(levels), a, b)))<1e-3;
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end
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T = all(t);
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else
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t = true(4, 1);
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T = true;
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end
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%@eof:6
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%@test:7
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if ~isoctave && ~user_has_matlab_license('statistics_toolbox')
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method = struct('small', 'Weibull-rejection', 'large', 'Cheng');
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n = 1000000;
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m = 100;
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a = 1.5;
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b = 1.0;
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try
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mu = 0;
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s2 = 0;
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levels = .01:.01:15;
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ecdf = zeros(length(levels),1);
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for i = 1:m
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x = gamrnd(ones(n, 1)*a, ones(n,1)*b, method);
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mu = mu + mean(x);
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s2 = s2 + var(x);
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for j=1:length(levels)
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ecdf(j) = ecdf(j)+sum(x<levels(j))/n;
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end
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end
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mu = mu/m;
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s2 = s2/m;
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ecdf = ecdf/m;
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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t(2) = abs(mu-a*b)<1e-3;
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t(3) = abs(s2-a*b^2)<1e-3;
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t(4) = max(abs(ecdf-gamcdf(transpose(levels), a, b)))<1e-3;
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end
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T = all(t);
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else
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t = true(4, 1);
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T = true;
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end
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%@eof:7
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%@test:8
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if ~isoctave && ~user_has_matlab_license('statistics_toolbox')
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method = struct('small', 'Weibull-rejection', 'large', 'Best');
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n = 1000000;
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m = 100;
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a = 1.5;
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b = 1.0;
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try
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mu = 0;
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s2 = 0;
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levels = .01:.01:15;
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ecdf = zeros(length(levels),1);
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for i = 1:m
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x = gamrnd(ones(n, 1)*a, ones(n,1)*b, method);
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mu = mu + mean(x);
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s2 = s2 + var(x);
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for j=1:length(levels)
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ecdf(j) = ecdf(j)+sum(x<levels(j))/n;
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end
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end
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mu = mu/m;
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s2 = s2/m;
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ecdf = ecdf/m;
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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t(2) = abs(mu-a*b)<1e-3;
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t(3) = abs(s2-a*b^2)<1e-3;
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t(4) = max(abs(ecdf-gamcdf(transpose(levels), a, b)))<1e-3;
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end
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T = all(t);
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else
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t = true(4, 1);
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T = true;
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end
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%@eof:8
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