|Parameters||scale (positive-definite real matrix)|
|Support||positive-definite real matrix|
In statistics, a matrix gamma distribution is a generalization of the gamma distribution to positive-definite matrices. It is a more general version of the Wishart distribution, and is used similarly, e.g. as the conjugate prior of the precision matrix of a multivariate normal distribution and matrix normal distribution. The compound distribution resulting from compounding a matrix normal with a matrix gamma prior over the precision matrix is a generalized matrix t-distribution.
This reduces to the Wishart distribution with
Notice that in this parametrization, the parameters and are not identified; the density depends on these two parameters through the product .