“Inverse matrix gamma distribution”的意思、由来-开放百科全书

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Inverse matrix gamma distribution

释义

See also
References

{{Probability distribution|

  name       =Inverse matrix gamma|  type       =density|  pdf_image  =|  cdf_image  =|  notation   =|  parameters =  shape parameter (real)

scale parameter

scale (positive-definite real matrix)

  support    = positive-definite real  matrix|  pdf        =

is the multivariate gamma function.|

  cdf        =|  mean       =|  median     =|  mode       =|  variance   =|  skewness   =|  kurtosis   =|  entropy    =|  mgf        =|  char       =|

}}

In statistics, the inverse matrix gamma distribution is a generalization of the inverse gamma distribution to positive-definite matrices.^[1] 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.{{citation needed|date=May 2012}}

This reduces to the inverse Wishart distribution with degrees of freedom when .

References

1. ^{{cite journal |last=Iranmanesha |first=Anis |first2=M. |last2=Arashib |first3=S. M. M. |last3=Tabatabaeya |year=2010 |title=On Conditional Applications of Matrix Variate Normal Distribution |journal=Iranian Journal of Mathematical Sciences and Informatics |volume=5 |issue=2 |pages=33–43 |doi= |url=https://www.sid.ir/En/Journal/ViewPaper.aspx?ID=220524 }}

3 : Random matrices|Continuous distributions|Multivariate continuous distributions

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References