rwishart(df, p = nrow(SqrtSigma), Sigma, SqrtSigma = diag(p))
Arguments
df
degrees of freedom. It has to be integer.
p
dimension of the matrix to simulate.
Sigma
the matrix parameter Sigma of the Wishart distribution.
SqrtSigma
a square root of the matrix parameter Sigma of the
Wishart distribution. Sigma must be equal to crossprod(SqrtSigma).
Value
The function returns one draw from the Wishart distribution with
df degrees of freedom and matrix parameter Sigma or
crossprod(SqrtSigma)
Warning
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.