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Quantile based Tsallis entropy in residual lifetime

Author

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  • Khammar, A.H.
  • Jahanshahi, S.M.A.

Abstract

Tsallis entropy is a generalization of type α of the Shannon entropy, that is a nonadditive entropy unlike the Shannon entropy. Shannon entropy may be negative for some distributions, but Tsallis entropy can always be made nonnegative by choosing appropriate value of α. In this paper, we derive the quantile form of this nonadditive’s entropy function in the residual lifetime, namely the residual quantile Tsallis entropy (RQTE) and get the bounds for it, depending on the Renyi’s residual quantile entropy. Also, we obtain relationship between RQTE and concept of proportional hazards model in the quantile setup. Based on the new measure, we propose a stochastic order and aging classes, and study its properties. Finally, we prove characterizations theorems for some well known lifetime distributions. It is shown that RQTE uniquely determines the parent distribution unlike the residual Tsallis entropy.

Suggested Citation

  • Khammar, A.H. & Jahanshahi, S.M.A., 2018. "Quantile based Tsallis entropy in residual lifetime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 994-1006.
    • Handle: RePEc:eee:phsmap:v:492:y:2018:i:c:p:994-1006
    DOI: 10.1016/j.physa.2017.11.030
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    Citations

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    Cited by:

    1. Kayal, Suchandan, 2018. "Quantile-based cumulative inaccuracy measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 329-344.
    2. Aswathy S. Krishnan & S. M. Sunoj & P. G. Sankaran, 2019. "Quantile-based reliability aspects of cumulative Tsallis entropy in past lifetime," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 17-38, January.
    3. Xiaozhuan Gao & Yong Deng, 2019. "The generalization negation of probability distribution and its application in target recognition based on sensor fusion," International Journal of Distributed Sensor Networks, , vol. 15(5), pages 15501477198, May.

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