On statistical properties of Jizba–Arimitsu hybrid entropy

WOS: 000396960200001 Jizba-Arimitsu entropy (also called hybrid entropy) combines axiomatics of Renyi and Tsallis entropy. It has many common properties with them, on the other hand, some aspects as e.g., MaxEnt distributions, are different. In this paper, we discuss statistical properties of hybrid entropy. We define hybrid entropy for continuous distributions and its relation to discrete entropy. Additionally, definition of hybrid divergence and its connection to Fisher metric is also presented. Interestingly, Fisher metric connected to hybrid entropy differs from corresponding Fisher metrics of Renyi and Tsallis entropy. This motivates us to introduce average hybrid entropy, which can be understood as an average between Tsallis and Renyi entropy. (C) 2017 Elsevier B.V. All rights reserved. Czech Science FoundationGrant Agency of the Czech Republic [17-33812L] We acknowledge helpful conversations with Petr Jizba. We are grateful to the referee for his/her constructive comments. J. K. was supported by the Czech Science Foundation, grant No. 17-33812L.