65 lines
2.3 KiB
Matlab
65 lines
2.3 KiB
Matlab
function [ldens,Dldens,D2ldens] = lpdfig1(x,s,nu)
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% Evaluates the logged INVERSE-GAMMA-1 PDF at x.
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%
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% X ~ IG1(s,nu) if X = sqrt(Y) where Y ~ IG2(s,nu) and Y = inv(Z) with Z ~ G(nu/2,2/s) (Gamma distribution)
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%
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% See L. Bauwens, M. Lubrano and J-F. Richard [1999, appendix A] for more details.
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%
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%
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% INPUTS
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% x [double] m*n matrix of locations,
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% s [double] m*n matrix or scalar, First INVERSE-GAMMA-1 distribution parameters,
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% nu [double] m*n matrix or scalar, Second INVERSE-GAMMA-1 distribution parameters.
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%
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% OUTPUTS
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% ldens [double] m*n matrix of logged INVERSE-GAMMA-1 densities evaluated at x.
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% Dldens [double] m*n matrix of first derivatives of logged INVERSE-GAMMA-1 densities.
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% D2ldens [double] m*n matrix of second derivatives of logged matrix of logged INVERSE-GAMMA-1 densities.
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%
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% SPECIAL REQUIREMENTS
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% none
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% Copyright © 2004-2021 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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ldens = -Inf( size(x) ) ;
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idx = find( x>0 ) ;
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if length(s)==1
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ldens(idx) = log(2) - gammaln(.5*nu) - .5*nu*(log(2)-log(s)) - (nu+1)*log(x(idx)) - .5*s./(x(idx).*x(idx)) ;
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else
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ldens(idx) = log(2) - gammaln(.5*nu(idx)) - .5*nu(idx).*(log(2)-log(s(idx))) - (nu(idx)+1).*log(x(idx)) - .5*s(idx)./(x(idx).*x(idx)) ;
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end
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if nargout >1
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Dldens = ldens ;
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if length(s)==1
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Dldens(idx) = - (nu+1)./(x(idx)) + s./(x(idx).^3) ;
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else
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Dldens(idx) = - (nu(idx)+1)./(x(idx)) + s(idx)./(x(idx).^3) ;
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end
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end
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if nargout == 3
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D2ldens = ldens ;
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if length(s)==1
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D2ldens(idx) = (nu+1)./(x(idx).^2) - 3*s(idx)./(x(idx).^4) ;
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else
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D2ldens(idx) = (nu(idx)+1)./(x(idx).^2) - 3*s(idx)./(x(idx).^4) ;
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end
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end
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