• Source: Matrix gamma distribution

In statistics, a matrix gamma distribution is a generalization of the gamma distribution to positive-definite matrices. It is effectively a different parametrization 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.
A matrix gamma distributions is identical to a Wishart distribution with



β

Σ

=
2
V
,
α
=


n
2


.


{\displaystyle \beta {\boldsymbol {\Sigma }}=2V,\alpha ={\frac {n}{2}}.}


Notice that the parameters



β


{\displaystyle \beta }

and




Σ



{\displaystyle {\boldsymbol {\Sigma }}}

are not identified; the density depends on these two parameters through the product



β

Σ



{\displaystyle \beta {\boldsymbol {\Sigma }}}

.




See also


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




Notes






References


Gupta, A. K.; Nagar, D. K. (1999) Matrix Variate Distributions, Chapman and Hall/CRC ISBN 978-1584880462

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