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

Famous quotes containing the words probability and/or function:

    “Only in Britain could it be thought a defect to be “too clever by half.” The probability is that too many people are too stupid by three-quarters.”
    —John Major (b. 1943)

    “The function of literature, through all its mutations, has been to make us aware of the particularity of selves, and the high authority of the self in its quarrel with its society and its culture. Literature is in that sense subversive.”
    —Lionel Trilling (1905–1975)