The function only works for an integer number
of degrees of freedom.
Details
The Wishart is a distribution on the set of nonnegative definite
symmetric matrices. Its density is
$$p(W) = \frac{c |W|^{(n-p-1)/2}}{|\Sigma|^{n/2}}
\exp\left\{-\frac{1}{2}\mathrm{tr}(\Sigma^{-1}W)\right\}$$
where \(n\) is the degrees of freedom parameter df and
\(c\) is a normalizing constant.
The mean of the Wishart distribution is \(n\Sigma\) and the
variance of an entry is
$$\mathrm{Var}(W_{ij}) = n (\Sigma_{ij}^2 +
\Sigma_{ii}\Sigma_{jj})$$
The matrix parameter, which should be a positive definite symmetric
matrix, can be specified via either the argument Sigma or
SqrtSigma. If Sigma is specified, then SqrtSigma is ignored. No checks
are made for symmetry and positive definiteness of Sigma.