Entropy inequalities for classes of probability distributions II. The multivariate case

Abstract

In this paper we continue our investigation of entropy comparisons with emphasis on multivariate distributions. For multiparameter cases of the multinomial and negative multinomial distributions we consider various higher-order forms of multivariate convexity. For the multinormal, Wishart, and t-distributions we define a partial ordering on the set of covariance matrices and determine monotonicity of the entropy functional. We further indicate some entropy inequalities for different sampling schemes. Because of the complex nature of multivariate partial ordering relations several problems remain open.