45 lines
1.9 KiB
Matlab
45 lines
1.9 KiB
Matlab
function draw = rand_multivariate_student(Mean,Sigma_upper_chol,df)
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% function draw = rand_multivariate_student(Mean,Sigma_upper_chol,df)
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% Pseudo random draws from a multivariate student distribution,
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% with expectation Mean, variance Sigma*df/(df-2) and degrees of freedom df>0.
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%
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% INPUTS
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%
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% Mean [double] 1*n vector, expectation of the multivariate random variable.
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% Sigma_upper_chol [double] n*n matrix, upper triangular Cholesky decomposition of Sigma
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% (the covariance matrix up to a factor df/(df-2)).
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% df [integer] degrees of freedom.
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%
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% OUTPUTS
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% draw [double] 1*n vector drawn from a multivariate normal distribution with expectation Mean and
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% covariance Sigma.
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%
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%
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% NOTE See Zellner (appendix B.2, 1971) for a definition.
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% Computes the t-distributed random numbers from
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% X = \mu + Y\sqrt{\frac{\nu}{U}}
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% where
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% Y~N(0,Sigma) with Sigma=Sigma_upper_chol'*Sigma_upper_chol
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% U~\Chi^2_{\nu}
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% The latter is constructed as the sum of \nu standard normals.
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% Copyright (C) 2003-2017 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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n = length(Mean);
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draw = Mean + randn(1,n) * Sigma_upper_chol * sqrt(df/sum(randn(df,1).^2));
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