On differential Renyi's–Tsallis divergence measure and its applications

Abstract

In this article, we introduce the differential Renyi's–Tsallis divergence as a measure of difference between two probability distributions which implies that the proposed divergence measure is a positive constant time the sum of Renyi's and Tsallis differential divergences and also generalized the differential Kullback–Leibler divergence measure. The properties of the proposed measure are presented. Then some bounds for this divergence measure are obtained, and a new divergence measure for any distribution belonging to the exponential families is defined. Also, we present the differential Renyi's–Tsallis divergence between the order statistics. Finally, this new divergence measure is applied to the proportional reversed hazards model and testing exponentiality. We construct a goodness-of-fit test for the exponential distribution based on the estimator of the differential Renyi's–Tsallis divergence measure.

Keywords:

• Renyi's–Tsallis divergence
• exponential family
• order statistic
• proportional reversed hazards model
• testing exponentiality

Mathematics Subject Classification:

• 62B10

Acknowledgments

The authors are grateful to anonymous referees and the associate editor for providing some useful comments on an earlier version of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).