British Journal of Mathematics & Computer Science 21(2): 1-16, 2017, Article no.BJMCS.32229 ISSN: 2231-0851 SCIENCEDOMAIN international www.sciencedomain.org Hellinger Distance Between Generalized Normal Distributions C. P. Kitsos 1 and T. L. Toulias 2 ∗ 1 Department of Informatics, Technological Educational Institute of Athens, Athens, Greece. 2 Avenue Charbo 20, Schaerbeek 1030, Brussels, Belgium. Authors’ contributions This work was carried out in collaboration between both authors. Author CPK provided the generalized normal distribution and the information relative risk framework. Author TLT performed all the mathematical computations. Both authors read and approved the final manuscript. Article Information DOI: 10.9734/BJMCS/2017/32229 Editor(s): (1) Andrej V. Plotnikov, Department of Applied and Calculus Mathematics and CAD, Odessa State Academy of Civil Engineering and Architecture, Ukraine. Reviewers: (1) John Tumaku, Ho Technical University, Ghana. (2) Anjali Munde, Amity University, India. Complete Peer review History: http://www.sciencedomain.org/review-history/18235 Received: 15 th February 2017 Accepted: 9 th March 2017 Review Article Published: 16 th March 2017 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. Keywords: Generalized γ-order normal distribution; kullback-Leibler divergence; hellinger distance; relative risk. 2010 Mathematics Subject Classification: 94A17, 97K50. *Corresponding author: E-mail: th.toulias@gmail.com;