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function [a, b] = gamma_specification(mu, sigma2, lb, name) % --*-- Unitary tests --*--
% Returns the hyperparameters of the gamma distribution given the expectation and variance.
%
% INPUTS
% - mu [double] Expectation of the Gamma random variable.
% - sigma2 [double] Variance of the Gamma random variable.
% - lb [double] Lower bound of the domain (default is zero).
% - name [string] Name of the parameter (or random variable).
%
% OUTPUTS
% - a [double] First hyperparameter of the Gamma density (shape).
% - b [double] Second hyperparameter of the Gamma density (scale).
% Copyright (C) 2015-2017 Dynare Team
%
% This file is part of Dynare.
%
% Dynare 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.
%
% Dynare 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 Dynare. If not, see <http://www.gnu.org/licenses/>.
if nargin<3
lb = 0;
end
if nargin>3 && ~isempty(name)
name1 = sprintf('for %s ', name);
name2 = sprintf(' (for %s)', name);
else
name1 = '';
name2 = '';
end
if mu<lb
error('The prior expectation (%f) %scannot be smaller than the lower bound of the Gamma distribution (%f)!', mu, name1, lb)
end
if isinf(sigma2)
error('The variance of the Gamma distribution has to be finite%s!', name2)
end
mu = mu-lb;
b = sigma2/mu;
a = mu/b;
%@test:1
%$ try
%$ [a, b] = gamma_specification(.5, 1);
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ if t(1)
%$ t(2) = abs(0.5-a*b)<1e-12;
%$ t(3) = abs(1.0-a*b*b)<1e-12;
%$ end
%$ T = all(t);
%@eof:1
%@test:2
%$ try
%$ [a, b] = gamma_specification(2, 1);
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ if t(1)
%$ t(2) = abs(2.0-a*b)<1e-12;
%$ t(3) = abs(1.0-a*b*b)<1e-12;
%$ end
%$ T = all(t);
%@eof:2
%@test:3
%$ try
%$ [a, b] = gamma_specification(2, 1, 3);
%$ t(1) = false;
%$ catch
%$ t(1) = true;
%$ end
%$
%$ T = all(t);
%@eof:3
%@test:4
%$ try
%$ [a, b] = gamma_specification(2, Inf, 3);
%$ t(1) = false;
%$ catch
%$ t(1) = true;
%$ end
%$
%$ T = all(t);
%@eof:4
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