Hellinger Distance Between Generalized Normal Distributions

A relative measure of informational distance between two distributions is introduced in this paper. For this purpose the Hellinger distance is used as it obeys to the definition of a distance metric and, thus, provides a measure of informational “proximity” between of two distributions. Certain formulations of the Hellinger distance between two generalized Normal distributions are given and discussed. Motivated by the notion of Relative Risk we introduce a relative distance measure between two continuous distributions in order to obtain a measure of informational “proximity” from one distribution to another. The Relative Risk idea from logistic regression is then extended, in an information theoretic context, using an exponentiated form of Hellinger distance.