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Inverse-Wishart distribution
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Inverse-Wishart distribution : ウィキペディア英語版
Inverse-Wishart distribution
}}\Gamma_p(\frac)} \left|\mathbf\right|^}e^\operatorname(\mathbf^)}
*\Gamma_p is the multivariate gamma function
*\mathrm is the trace function
|
cdf =|
mean = \fracFor \nu > p + 1|
median =|
mode = \frac|
variance =see below|
skewness =|
kurtosis =|
entropy =|
mgf =|
char =|
}}
In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite matrices. In Bayesian statistics it is used as the conjugate prior for the covariance matrix of a
multivariate normal distribution.
We say \mathbf follows an inverse Wishart distribution, denoted as \mathbf\sim \mathcal^(,\nu), if its inverse \mathbf^ has a Wishart distribution \mathcal(^, \nu) . Important identities have been derived for Inverse-Wishart distribution.〔
==Density==
The probability density function of the inverse Wishart is:
:
\frac}}}\Gamma_p(\frac)} \left|\mathbf\right|^}e^\operatorname(\mathbf^)}

where \mathbf and are p\times p positive definite matrices, and Γ''p''(·) is the multivariate gamma function.

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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