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.

[citation needed] This reduces to the inverse Wishart distribution with

degrees of freedom when

β = 2 , α =

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