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On statistical properties of Jizba–Arimitsu hybrid entropy

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  • Çankaya, Mehmet Niyazi
  • Korbel, Jan

Abstract

Jizba–Arimitsu entropy (also called hybrid entropy) combines axiomatics of Rényi 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 Rényi and Tsallis entropy. This motivates us to introduce average hybrid entropy, which can be understood as an average between Tsallis and Rényi entropy.

Suggested Citation

  • Çankaya, Mehmet Niyazi & Korbel, Jan, 2017. "On statistical properties of Jizba–Arimitsu hybrid entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 475(C), pages 1-10.
    • Handle: RePEc:eee:phsmap:v:475:y:2017:i:c:p:1-10
    DOI: 10.1016/j.physa.2017.02.009
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    Cited by:

    1. Mehmet Niyazi Çankaya & Abdullah Yalçınkaya & Ömer Altındaǧ & Olcay Arslan, 2019. "On the robustness of an epsilon skew extension for Burr III distribution on the real line," Computational Statistics, Springer, vol. 34(3), pages 1247-1273, September.

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