2005-02-18 20:54:39 +01:00
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function ldens = lpdfig1(x,s,nu)
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2008-01-11 16:49:59 +01:00
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% function ldens = lpdfig1(x,s,nu)
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% log INVERSE GAMMA (type 1)
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2005-02-18 20:54:39 +01:00
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% X ~ IG1(s,nu)
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% 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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2008-01-11 16:49:59 +01:00
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%
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% INPUTS
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% x: density evatuated at x
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% s: shape parameter
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% nu: scale parameter
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% OUTPUTS
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% ldens: the log INVERSE GAMMA density function (type 1)
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%
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% SPECIAL REQUIREMENTS
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2005-02-18 20:54:39 +01:00
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% See L. Bauwens, M. Lubrano and J-F. Richard [1999, appendix A] for more
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% details.
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2008-01-11 16:49:59 +01:00
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%
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% part of DYNARE, copyright Dynare Team (2004-2008)
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% Gnu Public License.
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2005-02-18 20:54:39 +01:00
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ldens = log(2) - gammaln(nu/2) - (nu/2).*log(2/s) - (nu+1)*log(x) - .5*s./(x.^2);
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