134 lines
2.8 KiB
Matlab
134 lines
2.8 KiB
Matlab
function [a, b] = beta_specification(mu, sigma2, lb, ub, name)
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% Returns the hyperparameters of the beta distribution given the expectation and variance.
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%
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% INPUTS
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% - mu [double] Expectation of the Gamma random variable.
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% - sigma2 [double] Variance of the Gamma random variable.
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% - lb [double] Lower bound of the domain (default is zero).
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% - ub [double] Upper bound of the domain (default is one).
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%
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% OUTPUTS
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% - a [double] First hyperparameter of the Beta density.
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% - b [double] Second hyperparameter of the Beta density.
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% Copyright © 2015-2023 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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if nargin<3
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lb = 0;
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ub = 1;
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end
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if nargin<4
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ub = 1;
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end
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if nargin>4 && ~isempty(name)
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name1 = sprintf('of %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 Beta distribution (%f)!'], mu, name1, lb)
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end
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if mu>ub
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error('The prior expectation (%f) %scannot be greater than the upper bound of the Beta distribution (%f)!', mu, name1, ub)
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end
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len = ub-lb;
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mu = (mu-lb)/len;
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sigma2 = sigma2/(len*len);
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if sigma2>(1-mu)*mu
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error('Beta prior%s. Given the declared prior expectation, prior lower and upper bounds, the prior std. has to be smaller than %f.',name2,sqrt((1-mu)*mu))
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end
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a = (1-mu)*mu*mu/sigma2-mu;
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b = a*(1/mu-1);
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return % --*-- Unit tests --*--
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%@test:1
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try
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[a, b] = beta_specification(.5, .05);
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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(0.5-a/(a+b))<1e-12;
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t(3) = abs(0.05-a*b/((a+b)^2*(a+b+1)))<1e-12;
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end
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T = all(t);
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%@eof:1
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%@test:2
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try
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[a, b] = beta_specification(0.5, .05, 1, 2);
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t(1) = false;
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catch
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t(1) = true;
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end
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T = all(t);
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%@eof:2
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%@test:3
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try
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[a, b] = beta_specification(2.5, .05, 1, 2);
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t(1) = false;
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catch
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t(1) = true;
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end
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T = all(t);
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%@eof:3
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%@test:4
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try
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[a, b] = beta_specification(.4, .6*.4+1e-4);
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t(1) = false;
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catch
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t(1) = true;
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end
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T = all(t);
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%@eof:4
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%@test:5
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try
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[a, b] = beta_specification(.4, .6*.4+1e-6);
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t(1) = false;
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catch
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t(1) = true;
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end
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try
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[a, b] = beta_specification(.4, .6*.4-1e-6);
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t(2) = true;
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catch
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t(2) = false;
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end
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T = all(t);
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%@eof:5 |