lpdfig2

 Evaluates the logged INVERSE-GAMMA-2 PDF at x.

 X ~ IG2(s,nu) if X = inv(Z) where Z ~ G(nu/2,2/s) (Gamma distribution) 

 See L. Bauwens, M. Lubrano and J-F. Richard [1999, appendix A] for more details.


 INPUTS     
    x     [double]  m*n matrix of locations,
    s     [double]  m*n matrix or scalar, First INVERSE-GAMMA-2 distribution parameters, 
    nu    [double]  m*n matrix or scalar, Second INVERSE-GAMMA-2 distribution parameters. 

 OUTPUTS
    ldens [double]  m*n matrix of logged INVERSE-GAMMA-2 densities evaluated at x.

 SPECIAL REQUIREMENTS
    none

0001 function [ldens,Dldens,D2ldens] = lpdfig2(x,s,nu)
0002 % Evaluates the logged INVERSE-GAMMA-2 PDF at x.
0003 %
0004 % X ~ IG2(s,nu) if X = inv(Z) where Z ~ G(nu/2,2/s) (Gamma distribution)
0005 %
0006 % See L. Bauwens, M. Lubrano and J-F. Richard [1999, appendix A] for more details.
0007 %
0008 %
0009 % INPUTS
0010 %    x     [double]  m*n matrix of locations,
0011 %    s     [double]  m*n matrix or scalar, First INVERSE-GAMMA-2 distribution parameters,
0012 %    nu    [double]  m*n matrix or scalar, Second INVERSE-GAMMA-2 distribution parameters.
0013 %
0014 % OUTPUTS
0015 %    ldens [double]  m*n matrix of logged INVERSE-GAMMA-2 densities evaluated at x.
0016 %
0017 % SPECIAL REQUIREMENTS
0018 %    none
0019 
0020 % Copyright (C) 2004-2009 Dynare Team
0021 %
0022 % This file is part of Dynare.
0023 %
0024 % Dynare is free software: you can redistribute it and/or modify
0025 % it under the terms of the GNU General Public License as published by
0026 % the Free Software Foundation, either version 3 of the License, or
0027 % (at your option) any later version.
0028 %
0029 % Dynare is distributed in the hope that it will be useful,
0030 % but WITHOUT ANY WARRANTY; without even the implied warranty of
0031 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0032 % GNU General Public License for more details.
0033 %
0034 % You should have received a copy of the GNU General Public License
0035 % along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
0036 
0037 ldens = -Inf( size(x) ) ;
0038 idx = find( x>0 ) ;    
0039 
0040 if length(s)==1
0041     ldens(idx) = -gammaln(.5*nu) - (.5*nu)*(log(2)-log(s)) - .5*(nu+2)*log(x(idx)) -.5*s./x(idx);
0042 else
0043     ldens(idx) = -gammaln(.5*nu(idx)) - (.5*nu(idx)).*(log(2)-log(s(idx))) - .5*(nu(idx)+2).*log(x(idx)) -.5*s(idx)./x(idx);
0044 end
0045 
0046 if nargout >1 
0047     if length(s)==1
0048         Dldens(idx) = - .5*(nu+2)./(x(idx)) + .5*s./x(idx).^2;
0049     else
0050         Dldens(idx) = - .5*(nu(idx)+2)./(x(idx)) + .5*s(idx)./x(idx).^2;
0051     end
0052 end
0053 
0054 if nargout == 3 
0055     if length(s)==1
0056         D2ldens(idx) = .5*(nu+2)./(x(idx)).^2 - s./x(idx).^3;
0057     else
0058         D2ldens(idx) = .5*(nu(idx)+2)./(x(idx)).^2 - s(idx)./x(idx).^3;
0059     end
0060 end