WishartMatrixDistribution

represents a Wishart matrix distribution with ν degrees of freedom and covariance matrix Σ.

Details • WishartMatrixDistribution is the distribution of the sample covariance from ν independent realizations of a multivariate Gaussian distribution with covariance matrix Σ when the degrees of freedom parameter ν is an integer.
• WishartMatrixDistribution is also known as WishartLaguerre ensemble.
• The probability density for a symmetric matrix in a Wishart matrix distribution is proportional to , where is the size of matrix Σ.
• The covariance matrix can be any positive definite symmetric matrix of dimensions and ν can be any real number greater than .
• WishartMatrixDistribution can be used with such functions as MatrixPropertyDistribution, EstimatedDistribution, and RandomVariate.

Examples

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Basic Examples(3)

Generate a pseudorandom matrix:

 In:= Out= Check that it is symmetric and positive definite:

 In:= Out= Sample eigenvalues of a Wishart random matrix using MatrixPropertyDistribution:

 In:= Estimate joint distribution of eigenvalues:

 In:= Out= Mean and variance:

 In:= Out//MatrixForm= In:= Out//MatrixForm= Properties & Relations(4)

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