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On Cumulative Tsallis Entropy and Its Dynamic Past Version

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  • Mohamed Said Mohamed

    (Ain Shams University)

Abstract

Cumulative Tsallis entropy and its residual have developed by many others, and they proposed alternative (second) forms of them. In this article, we illustrate the differences and the relation between the proposed model and its alternative form. Furthermore, we study some properties and features for the concept of cumulative Tsallis entropy and its residual. In addition, we propose a dynamic past form of cumulative Tsallis entropy and obtain some of its properties.

Suggested Citation

  • Mohamed Said Mohamed, 2020. "On Cumulative Tsallis Entropy and Its Dynamic Past Version," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1903-1917, December.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:4:d:10.1007_s13226-020-0503-8
    DOI: 10.1007/s13226-020-0503-8
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    References listed on IDEAS

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    1. Calì, Camilla & Longobardi, Maria & Ahmadi, Jafar, 2017. "Some properties of cumulative Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 1012-1021.
    2. J. Navarro & Y. Aguila & J. Ruiz, 2001. "Characterizations through reliability measures from weighted distributions," Statistical Papers, Springer, vol. 42(3), pages 395-402, July.
    3. Vikas Kumar, 2017. "Characterization results based on dynamic Tsallis cumulative residual entropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8343-8354, September.
    4. V. Zardasht & S. Parsi & M. Mousazadeh, 2015. "On empirical cumulative residual entropy and a goodness-of-fit test for exponentiality," Statistical Papers, Springer, vol. 56(3), pages 677-688, August.
    5. G. Rajesh & S. M. Sunoj, 2019. "Some properties of cumulative Tsallis entropy of order $$\alpha $$ α," Statistical Papers, Springer, vol. 60(3), pages 933-943, June.
    6. Madan Mohan Sati & Nitin Gupta, 2015. "Some Characterization Results on Dynamic Cumulative Residual Tsallis Entropy," Journal of Probability and Statistics, Hindawi, vol. 2015, pages 1-8, October.
    7. Murali Rao, 2005. "More on a New Concept of Entropy and Information," Journal of Theoretical Probability, Springer, vol. 18(4), pages 967-981, October.
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