Exact Expressions for Kullback-Leibler Divergence for Multivariate and Matrix-Variate Distributions.

The Kullback-Leibler divergence is a measure of the divergence between two probability distributions, often used in statistics and information theory. However, exact expressions for it are not known for multivariate or matrix-variate distributions apart from a few cases. In this paper, exact expressions for the Kullback-Leibler divergence are derived for over twenty multivariate and matrix-variate distributions. The expressions involve various special functions.