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Research Article Open access CC BY 4.0

Hellinger Distance Between Generalized Normal Distributions

C. P. Kitsos, T. L. Toulias

Journal of Advances in Mathematics and Computer Science · pp. 1–16 · Published 16 Mar 2017

10.9734/BJMCS/2017/32229

Abstract

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.

Generalized γ-order normal distribution kullback-Leibler divergence hellinger distance relative risk.

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