143 lines
3.8 KiB
Matlab
143 lines
3.8 KiB
Matlab
function [shape, scale] = weibull_specification(mu, sigma2, lb, name) % --*-- Unitary tests --*--
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% Returns the hyperparameters of the Weibull distribution given the expectation and variance.
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%
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% INPUTS
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%
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%
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% OUTPUTS
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%
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%
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% Copyright (C) 2015-2017 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 <http://www.gnu.org/licenses/>.
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if nargin<3
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lb = 0;
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end
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if nargin>3 && ~isempty(name)
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name1 = sprintf('for %s ', name);
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name2 = sprintf(' (for %s)', name);
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else
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name1 = '';
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name2 = '';
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end
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if mu<lb
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error('The prior expectation (%f) %scannot be smaller than the lower bound of the Weibull distribution (%f)!', mu, name1, lb)
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end
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if isinf(sigma2)
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error('The variance of the Gamma distribution has to be finite%s!', name2)
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end
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scale = NaN;
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shape = NaN;
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mu = mu-lb;
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mu2 = mu*mu;
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eqn = @(k) gammaln(1+2./k) - 2*gammaln(1+1./k) - log(1+sigma2/mu2);
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eqn2 = @(k) eqn(k).*eqn(k);
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kstar = fminbnd(eqn2, 1e-9, 100);
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[shape, fval, exitflag] = fzero(eqn, kstar);
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if exitflag<1
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shape = NaN;
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return
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end
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scale = mu/gamma(1+1/shape);
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%@test:1
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%$ debug = false;
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%$ scales = 1:.01:5;
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%$ shapes = .5:.01:2;
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%$ n_scales = length(scales);
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%$ n_shapes = length(shapes);
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%$ mu = NaN(n_scales, n_shapes);
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%$ s2 = NaN(n_scales, n_shapes);
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%$ for i=1:n_shapes
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%$ g1 = gamma(1+1/shapes(i));
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%$ g2 = gamma(1+2/shapes(i));
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%$ g3 = g1*g1;
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%$ for j=1:n_scales
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%$ mu(j, i) = scales(j)*g1;
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%$ s2(j, i) = scales(j)*scales(j)*(g2-g3);
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%$ end
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%$ end
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%$ if debug
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%$ success = [];
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%$ failed1 = [];
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%$ failed1_ = [];
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%$ failed2 = [];
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%$ end
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%$ try
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%$ for i=1:n_shapes
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%$ for j=1:n_scales
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%$ if debug
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%$ disp(sprintf('... mu=%s and s2=%s', num2str(mu(j,i)),num2str(s2(j,i))))
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%$ end
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%$ if ~isnan(mu(j,i)) && ~isnan(s2(j,i)) && ~isinf(mu(j,i)) && ~isinf(s2(j,i))
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%$ [shape, scale] = weibull_specification(mu(j,i), s2(j,i));
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%$ if isnan(scale)
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%$ t = false;
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%$ else
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%$ if abs(scales(j)-scale)<1e-9 && abs(shapes(i)-shape)<1e-9
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%$ t = true;
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%$ else
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%$ t = false;
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%$ end
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%$ end
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%$ if ~t && debug
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%$ failed1 = [failed1; mu(j,i) s2(j,i)];
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%$ failed1_ = [failed1_; shapes(i) scales(j)];
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%$ error('UnitTest','Cannot compute scale and shape hyperparameters for mu=%s and s2=%s', num2str(mu(j,i)), num2str(s2(j,i)))
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%$ end
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%$ if debug
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%$ success = [success; mu(j,i) s2(j,i)];
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%$ end
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%$ else
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%$ failed2 = [failed2; shapes(i) scales(j)];
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%$ continue % Pass this test
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%$ end
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%$ end
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%$ end
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%$ catch
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%$ t = false;
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%$ end
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%$
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%$ if debug
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%$ figure(1)
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%$ plot(success(:,1),success(:,2),'ok');
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%$ if ~isempty(failed1)
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%$ hold on
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%$ plot(failed1(:,1),failed1(:,2),'or');
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%$ hold off
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%$ figure(2)
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%$ plot(failed1_(:,1),failed1_(:,2),'or')
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%$ end
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%$ if ~isempty(failed2)
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%$ figure(2)
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%$ plot(failed2(:,1),failed2(:,2),'or');
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%$ end
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%$ end
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%$ T = all(t);
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%@eof:1
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