Notation | |||
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Parameters |
shape parameter (real) | ||
Support | positive-definite real matrix | ||
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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 identified; the density depends on these two parameters through the product .