Inverse matrix gamma distribution

In statistics, the inverse matrix gamma distribution is a generalization of the inverse gamma distribution to positive-definite matrices. 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.Template:Citation needed

This reduces to the inverse Wishart distribution with $\nu$ degrees of freedom when $\beta =2,\alpha =\frac{\nu }{2}$.

See also

• inverse Wishart distribution.
• matrix gamma distribution.
• matrix normal distribution.
• matrix t-distribution.
• Wishart distribution.

References

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