MultivariateStatistics`
MultivariateStatistics`

# WishartDistribution

WishartDistribution[Σ,m]

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

# Details and Options

• 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.

# Examples

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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:

Wolfram Research (2007), WishartDistribution, Wolfram Language function, https://reference.wolfram.com/language/MultivariateStatistics/ref/WishartDistribution.html.

#### Text

Wolfram Research (2007), WishartDistribution, Wolfram Language function, https://reference.wolfram.com/language/MultivariateStatistics/ref/WishartDistribution.html.

#### CMS

Wolfram Language. 2007. "WishartDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/MultivariateStatistics/ref/WishartDistribution.html.

#### APA

Wolfram Language. (2007). WishartDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/MultivariateStatistics/ref/WishartDistribution.html

#### BibTeX

@misc{reference.wolfram_2024_wishartdistribution, author="Wolfram Research", title="{WishartDistribution}", year="2007", howpublished="\url{https://reference.wolfram.com/language/MultivariateStatistics/ref/WishartDistribution.html}", note=[Accessed: 23-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_wishartdistribution, organization={Wolfram Research}, title={WishartDistribution}, year={2007}, url={https://reference.wolfram.com/language/MultivariateStatistics/ref/WishartDistribution.html}, note=[Accessed: 23-July-2024 ]}