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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)
*\Gamma_p is the multivariate gamma function.|
cdf =|
mean =|
median =|
mode =|
variance =|
skewness =|
kurtosis =|
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mgf =|
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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 \beta=2, \alpha=\frac.
== 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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