WishartMatrixDistribution

WishartMatrixDistribution[ν,Σ]

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:

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Check that it is symmetric and positive definite:

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Sample eigenvalues of a Wishart random matrix using MatrixPropertyDistribution:

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Estimate joint distribution of eigenvalues:

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Mean and variance:

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Scope  (6)

Applications  (2)

Properties & Relations  (4)

See Also

InverseWishartMatrixDistribution  MatrixNormalDistribution  MarchenkoPasturDistribution  TracyWidomDistribution  ChiSquareDistribution

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