# Random Wishart matrix

### Description

Generate a draw from a Wishart distribution.

### Usage

1 |

### Arguments

`df` |
degrees of freedom. It has to be integer. |

`p` |
dimension of the matrix to simulate. |

`Sigma` |
the matrix parameter Sigma of the Wishart distribution. |

`SqrtSigma` |
a |

### Details

The Wishart is a distribution on the set of nonnegative definite symmetric matrices. Its density is

*
p(W) = c|W|^((n-p-1)/2) / |Sigma|^(n/2) exp(-tr(Sigma^(-1)W)/2)*

where *n* is the degrees of freedom parameter `df`

and
*c* is a normalizing constant.
The mean of the Wishart distribution is *n Sigma* and the
variance of an entry is

*
Var(W[i,j]) = n (Sigma[i,j]^2 + Sigma[i,i] Sigma[j,j])*

The matrix parameter, which should be a positive definite symmetric matrix, can be specified via either the argument Sigma or SqrtSigma. If Sigma is specified, then SqrtSigma is ignored. No checks are made for symmetry and positive definiteness of Sigma.

### Value

The function returns one draw from the Wishart distribution with
`df`

degrees of freedom and matrix parameter `Sigma`

or
`crossprod(SqrtSigma)`

### Warning

The function only works for an integer number of degrees of freedom.

### Note

From a suggestion by B.Venables, posted on S-news

### Author(s)

Giovanni Petris GPetris@uark.edu

### References

Press (1982). Applied multivariate analysis.

### Examples

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