Information Distances and Divergences for the Generalized Normal Distribution

Abstract

The study of relative measures of information between two distributions that characterizes an Input/Output System is important for the investigation of the informational ability and behaviour of that system. The most important measures of information distance and divergence are brie?y presented and grouped. In Statistical Geometry, and for the study of statistical manifolds, relative measures of information are needed that are also distance metrics. The Hellinger distance metric is studied, providing a compact measure of informational proximity between of two distributions. Certain formulations of the Hellinger distance between two generalized normal distributions are given and discussed. Some results for the Bhattacharyya distance are also given. Moreover, the symmetricity of the Kullback-Leibler divergence between a generalized normal and a t -distribution, is examined for this key measure of information divergence.