Inverse matrix gamma distribution

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.

Inverse matrix gamma

shape parameter
scale parameter

scale (positive-definite real matrix)
Support positive-definite real matrix

This reduces to the inverse Wishart distribution with degrees of freedom when .

See also


  1. Iranmanesha, Anis; Arashib, M.; Tabatabaeya, S. M. M. (2010). "On Conditional Applications of Matrix Variate Normal Distribution". Iranian Journal of Mathematical Sciences and Informatics. 5 (2): 33–43.
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