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
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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