Matrix gamma distribution

In statistics, a matrix gamma distribution is a generalization of the gamma distribution to positive-definite matrices. It is effectively a different parametrization 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.

A matrix gamma distributions is identical to a Wishart distribution with ${\displaystyle \beta {\boldsymbol {\Sigma }}=2V,\alpha ={\frac {n}{2}}.}$

Notice that the parameters ${\displaystyle \beta }$and ${\displaystyle {\boldsymbol {\Sigma }}}$are not identified; the density depends on these two parameters through the product ${\displaystyle \beta {\boldsymbol {\Sigma }}}$.

• inverse matrix gamma distribution.
• matrix normal distribution.
• matrix t-distribution.
• Wishart distribution.

• Gupta, A. K.; Nagar, D. K. (1999) Matrix Variate Distributions, Chapman and Hall/CRCISBN 978-1584880462