MatrixTDistribution

MatrixTDistribution[Σrow,Σcol,ν]

represents zero mean matrix distribution with row covariance matrix Σrow, column covariance matrix Σcol, and degrees of freedom parameter ν.

MatrixTDistribution[μ,Σrow,Σcol,ν]

represents matrix distribution with mean matrix μ.

Details • The probability density for a matrix of dimensions in a matrix distribution is proportional to with an identity matrix of length .
• MatrixTDistribution[Σrow,Σcol,ν] is the distribution of MatrixNormalDistribution[Σ,Σcol] with sampled from InverseWishartMatrixDistribution[ν+n-1,Σrow].
• MatrixTDistribution[μ,c Σrow,c-1 Σcol,ν] has the same distribution as MatrixTDistribution[μ,Σrow,Σcol,ν] for any positive real constant c.
• The covariance matrices Σrow and Σcol can be any symmetric positive definite matrices of real numbers of dimensions {n,n} and {m,m}, respectively. The degrees of freedom parameter ν can be any positive number, and the mean matrix μ can be any matrix of real numbers of dimensions {n,m}.
• MatrixTDistribution can be used with such functions as MatrixPropertyDistribution, EstimatedDistribution, and RandomVariate.

Examples

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Basic Examples(2)

Sample from matrix distribution:

 In:= In:= Out= Mean and variance:

 In:= Out//MatrixForm= In:= Out//MatrixForm= Possible Issues(1)

Introduced in 2015
(10.3)
|
Updated in 2017
(11.1)