36 lines
1.5 KiB
Matlab
36 lines
1.5 KiB
Matlab
function density = multivariate_student_pdf(X,Mean,Sigma_upper_chol,df)
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% Evaluates the density of a multivariate student, with expectation Mean,
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% variance Sigma_upper_chol'*Sigma_upper_chol and degrees of freedom df, at X.
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%
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% INPUTS
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%
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% X [double] 1*n vector
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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 (the "covariance matrix").
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% df [integer] degrees of freedom.
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%
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% OUTPUTS
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% density [double] density.
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%
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% SPECIAL REQUIREMENTS
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% Copyright © 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 <https://www.gnu.org/licenses/>.
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nn = length(X);
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t1 = gamma( .5*(nn+df) ) / ( gamma( .5*nn ) * (df*pi)^(.5*nn) ) ;
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t2 = t1 / prod(diag(Sigma_upper_chol)) ;
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density = t2 / ( 1 + (X-Mean)*(Sigma_upper_chol\(transpose(Sigma_upper_chol)\transpose(X-Mean)))/df )^(.5*(nn+df)); |