Wishart Distribution - Probability Density Function

Probability Density Function

The Wishart distribution can be characterized by its probability density function, as follows.

Let be a p × p symmetric matrix of random variables that is positive definite. Let V be a (fixed) positive definite matrix of size p × p.

Then, if n ≥ p, has a Wishart distribution with n degrees of freedom if it has a probability density function given by

where Γp(·) is the multivariate gamma function defined as

\Gamma_p(n/2)= \pi^{p(p-1)/4}\Pi_{j=1}^p \Gamma\left.

In fact the above definition can be extended to any real n > p − 1. If n ≤ p − 2, then the Wishart no longer has a density—instead it represents a singular distribution.

Read more about this topic:  Wishart Distribution

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