Expressions for Rényi and Shannon entropies for multivariate distributions

Abstract

Exact forms of Rényi and Shannon entropies are determined for several multivariate distributions, including multivariate t, multivariate Cauchy, multivariate Pearson type VII, multivariate Pearson type II, multivariate symmetric Kotz type, multivariate logistic, multivariate Burr, multivariate Pareto type I, multivariate Pareto type II, multivariate Pareto type III, multivariate Pareto type IV, Dirichlet, inverted Dirichlet, multivariate Liouville, multivariate exponential, multivariate Weinman exponential, multivariate ordered Weinman exponential, bivariate gamma exponential, bivariate conditionally specified exponential, multivariate Weibull and multivariate log-normal. Monotonicity properties of Rényi and Shannon entropies for these distributions are also studied. We believe that the results presented here will serve as an important reference for scientists and engineers in many areas.