Английская Википедия:Inverse matrix gamma distribution

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Шаблон:Probability distribution{\beta^{p\alpha}\Gamma_p(\alpha)} |\mathbf{X}|^{-\alpha-(p+1)/2}\exp\left(-\frac{1}{\beta}{\rm tr}\left(\boldsymbol\Psi\mathbf{X}^{-1}\right)\right)</math>

• <math>\Gamma_p</math> is the multivariate gamma function.|

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In statistics, the inverse matrix gamma distribution is a generalization of the inverse gamma distribution to positive-definite matrices. 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 t-distribution.Шаблон:Citation needed

This reduces to the inverse Wishart distribution with <math>\nu</math> degrees of freedom when <math>\beta=2, \alpha=\frac{\nu}{2}</math>.

See also

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

References

Шаблон:Matrix-stub