# InverseWishartMatrixDistribution

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

# Examples

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## Basic Examples(3)

Generate a pseudorandom matrix:

Check that it is positive definite:

Sample eigenvalues of an inverse Wishart random matrix using MatrixPropertyDistribution:

Mean and variance:

## Scope(6)

Generate a single pseudorandom matrix:

Generate a set of pseudorandom matrices:

Sample at extended precision:

Compute statistical properties numerically:

Numerically approximate expectation of the largest matrix eigenvalue :

Distribution parameters estimation:

Estimate the distribution parameters from sample data:

Compare LogLikelihood for both distributions:

Skewness:

## Properties & Relations(3)

, where and are independent Gaussian vector and Wishart matrix follows HotellingTSquareDistribution:

Use MatrixPropertyDistribution to sample expressions :

Any diagonal element of inverse Wishart random matrix follows scaled inverse χ2 distribution:

Diagonal elements are not independent:

For any nonzero vector and inverse Wishart matrix with scale matrix , is χ2 distributed:

Wolfram Research (2015), InverseWishartMatrixDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseWishartMatrixDistribution.html (updated 2017).

#### Text

Wolfram Research (2015), InverseWishartMatrixDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseWishartMatrixDistribution.html (updated 2017).

#### CMS

Wolfram Language. 2015. "InverseWishartMatrixDistribution." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/InverseWishartMatrixDistribution.html.

#### APA

Wolfram Language. (2015). InverseWishartMatrixDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseWishartMatrixDistribution.html

#### BibTeX

@misc{reference.wolfram_2023_inversewishartmatrixdistribution, author="Wolfram Research", title="{InverseWishartMatrixDistribution}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/InverseWishartMatrixDistribution.html}", note=[Accessed: 27-September-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_inversewishartmatrixdistribution, organization={Wolfram Research}, title={InverseWishartMatrixDistribution}, year={2017}, url={https://reference.wolfram.com/language/ref/InverseWishartMatrixDistribution.html}, note=[Accessed: 27-September-2023 ]}