Inverse matrix gamma distribution
Notation  

Parameters 
shape parameter (real) 
Support  positivedefinite real matrix 

In statistics, the inverse matrix gamma distribution is a generalization of the inverse gamma distribution to positivedefinite 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 tdistribution.
This reduces to the inverse Wishart distribution with .
See also
 inverse Wishart distribution.
 matrix gamma distribution.
 matrix normal distribution.
 matrix tdistribution.
 Wishart distribution.
References
 ↑ Iranmanesha, Anis, M. Arashib and S. M. M. Tabatabaeya (2010). "On Conditional Applications of Matrix Variate Normal Distribution". Iranian Journal of Mathematical Sciences and Informatics, 5:2, pp. 33–43.
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