represents a Wishart distribution with scale matrix Σ and degrees of freedom parameter m.


  • To use WishartDistribution, you first need to load the Multivariate Statistics Package using Needs["MultivariateStatistics`"].
  • The probability density for a symmetric positive definite matrix in a Wishart distribution is proportional to .
  • The scale matrix Σ can be any symmetric positive definite matrix. The parameter m can be any number such that m>Length[Σ].
  • For integer m, the Wishart distribution gives the distribution of covariance matrices of multinormal samples.
  • WishartDistribution can be used with such functions as Mean, PDF, and RandomReal.


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Basic Examples  (3)

The mean of a Wishart distribution:

The variance:

Probability density function:

Scope  (3)

Generate a set of pseudorandom matrices that follow a Wishart distribution:

Possible Issues  (2)

WishartDistribution is not defined when Σ is not symmetric and positive definite:

WishartDistribution is not defined when m<Length[Σ]:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: