logt_lpdf.m

function y = logt_lpdf(x,v,mu,sigma)
%LOGT_LPDF Log probability density function (lpdf) for log Student's T
%
%   distribution Y = LOGT_LPDF(X,V,MU,SIGMA) returns the lpdf of
%   log Student's T distribution with degrees of freedom, V, mean, MU
%   and standard deviation, SIGMA, at the values in X.
%   
%   The size of Y is the common size of the input arguments. A scalar input  
%   functions as a constant matrix of the same size as the other inputs.     
%
%   Default values for MU and SIGMA are 0 and 1 respectively.
%
%   References:
%      [1]  E. Kreyszig, "Introductory Mathematical Statistics",
%      John Wiley, New York, 1970, Section 10.3, pages 144-146.
%
% Copyright (c) 1998-2004 Aki Vehtari

% This software is distributed under the GNU General Public 
% License (version 3 or later); please refer to the file 
% License.txt, included with the software, for details.

if nargin < 4, 
  sigma = 1;
end

if nargin < 3;
  mu = 0;
end

if nargin < 2, 
  error('Requires at least two input arguments.'); 
end

term = gammaln((v + 1) / 2) - gammaln(v/2) -log(x.*sqrt(v*pi));
y = bsxfun(@minus,term,log(sigma .* (1 + (((log(x)-mu)./sigma) .^ 2) ./ v) .^ ((v+1)/2)));