Matrix gamma
Notation
Parameters

shape parameter (real)
scale parameter

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

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]

This reduces to the Wishart distribution with

Notice that in this parametrization, the parameters and are not identifiable; the density depends on these two parameters through the product .

See also

Notes

  1. ^ a b 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.

References