lpdfig1

 log INVERSE GAMMA (type 1)

 X ~ IG1(s,nu)
 X = sqrt(Y) where Y ~ IG2(s,nu) and Y = inv(Z) with Z ~ G(nu/2,2/s) (Gamma distribution) 
 
 See L. Bauwens, M. Lubrano and J-F. Richard [1999, appendix A] for more
 details.

 stephane.adjemian@cepremap.cnrs.fr [01/16/2004]

0001 function ldens = lpdfig1(x,s,nu)
0002 % log INVERSE GAMMA (type 1)
0003 %
0004 % X ~ IG1(s,nu)
0005 % X = sqrt(Y) where Y ~ IG2(s,nu) and Y = inv(Z) with Z ~ G(nu/2,2/s) (Gamma distribution)
0006 %
0007 % See L. Bauwens, M. Lubrano and J-F. Richard [1999, appendix A] for more
0008 % details.
0009 %
0010 % stephane.adjemian@cepremap.cnrs.fr [01/16/2004]
0011 
0012 ldens = log(2) - gammaln(nu/2) - (nu/2).*log(2/s) - (nu+1)*log(x) - .5*s./(x.^2);