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| matrix gamma distribution ： ウィキペディア英語版 |
matrix gamma distribution
|\mathbf|^ \exp\left(\left(-\frac\boldsymbol\Sigma^\mathbf\right)\right)
* is the multivariate gamma function.|
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In statistics, a matrix gamma distribution is a generalization of the gamma distribution to positive-definite matrices.〔Iranmanesh, Anis, M. Arashib and S. M. M. Tabatabaey (2010). ("On Conditional Applications of Matrix Variate Normal Distribution" ). ''Iranian Journal of Mathematical Sciences and Informatics'', 5:2, pp. 33–43.〕 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.〔
This reduces to the Wishart distribution with
== See also ==
* inverse matrix gamma distribution.
* matrix normal distribution.
* matrix t-distribution.
* Wishart distribution.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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