# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# InverseWishartMatrixDistribution

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

## DetailsDetails

• The probability density for a symmetric matrix in an inverse Wishart matrix distribution is proportional to , where is the size of matrix Σ.
• For a matrix distributed as , the inverse is distributed as WishartMatrixDistribution[ν,Σ-1].
• The covariance matrix can be any positive definite symmetric matrix of dimensions and ν can be any real number greater than .
• InverseWishartMatrixDistribution can be used with such functions as MatrixPropertyDistribution and RandomVariate.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

Generate a pseudorandom matrix:

 In[1]:=
 Out[1]=

Check that it is positive definite:

 In[2]:=
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Sample eigenvalues of an inverse Wishart random matrix using MatrixPropertyDistribution:

 In[1]:=
 In[2]:=
 Out[2]=

## See AlsoSee Also

Introduced in 2015
(10.3)