A random vector \(\bold{X} = (X_1,\dots,X_p)^T\) has a multivariate t distribution,
with a \(\bold{\mu}\) mean vector, covariance matrix \(\bold{\Sigma}\), and \(0 \leq \eta
< 1/2\) shape parameter, if its density function is given by
$$
f(\bold{x}) = K_p(\eta)|\bold{\Sigma}|^{-1/2}\left\{1 + c(\eta)(\bold{x} - \bold{\mu})^T
\bold{\Sigma}^{-1} (\bold{x} - \bold{\mu})\right\}^{-\frac{1}{2\eta}(1 + \eta p)}.
$$
where
$$
K_p(\eta) = \left(\frac{c(\eta)}{\pi}\right)^{p/2}\frac{\Gamma(\frac{1}{2\eta}(1 + \eta p))}
{\Gamma(\frac{1}{2\eta})},
$$
with \(c(\eta)=\eta/(1 - 2\eta)\). This parameterization of the multivariate t distribution
is introduced mainly because \(\bold{\mu}\) and \(\bold{\Sigma}\) correspond to the mean vector
and covariance matrix, respectively.
The function rmt is an interface to C routines, which make calls to subroutines from LAPACK.
The matrix decomposition is internally done using the Cholesky decomposition. If Sigma is not
non-negative definite then there will be a warning message.
This parameterization of the multivariate-t includes the normal distribution as a particular
case when eta = 0.