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From: Kevin Murphy on 4 Nov 2009 14:21

You can just write your own function to compute it - see below.
Note that the mvtpdf function in the stats toolbox
first converts Sigma to a correlation matrix,
which is nonstandard (as far as I know).
Thus these two methods only
give the same results if Sigma has 1 on all the diagonals.

HTH
Kevin

function logp = mvtLogpdf(X, mu, Sigma, nu)
% Multivariate student T distribution, log pdf
% X(i,:) is i'th case
[N d] = size(X);
M = repmat(mu(:)', N, 1); % replicate the mean across rows
X = X-M;
mahal = sum((X*inv(Sigma)).*X,2); %#ok
logc = gammaln(nu/2 + d/2) - gammaln(nu/2) - 0.5*logdet(Sigma) ...
- (d/2)*log(nu) - (d/2)*log(pi);
logp = logc -(nu+d)/2*log1p(mahal/nu);

if 0
% this check only works if Sigma is a correlation matrix
logp2 = log(mvtpdf(X, Sigma, nu));
assert(approxeq(logp, logp2))
end




Peter Perkins <Peter.PerkinsRemoveThis(a)mathworks.com> wrote in message <go8tt0$rma$1(a)fred.mathworks.com>...
> per wrote:
>
> > can you please say more about the transformation? i'm not sure i am
> > following. what kind of transformation of the data would make it so i
> > don't have to give the location (mu) parameter, but just the
> > covariance matrix/correlation matrix (parameter C)?
>
> No transformation will do that; you will always have to specify the degrees of freedom parameter as well.
>
> All you need to do to use MVT as a location/scale family is, separately for each column of your data, subtract the corresponding mean and divide by the corresponding scale factor. It sounds like you have the Statistics Toolbox. Take a look in stats/private/addtls.m; that code the handles the univariate t-location-scale distribution for the Distribution Fitting Tool is in there. Look at tlspdf and tlscdf. You need to do the same thing coordinate-wise.
>
> Hope this helps.
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