In statistics, the inverse matrix gamma distribution is a generalization of the inverse gamma distribution to positive-definite matrices.[1] It is a more general version of the inverse Wishart distribution, and is used similarly, e.g. as the conjugate prior of the covariance matrix of a multivariate normal distribution or matrix normal distribution. The compound distribution resulting from compounding a matrix normal with an inverse matrix gamma prior over the covariance matrix is a generalized matrix t-distribution.
This reduces to the inverse Wishart distribution with
\nu
\beta=2,\alpha=
| \nu | |
| 2 |