Information Distances and Divergences for the Generalized Normal Distribution

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 briefly
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.