Matrix gamma distribution

In statistics, a matrix gamma distribution is a generalization of the gamma distribution to positive-definite matrices.[1] 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.[1]

Matrix gamma

shape parameter (real)
scale parameter

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

This reduces to the Wishart distribution with

See also


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


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