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A quantile-based study of cumulative residual Tsallis entropy measures

Author

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  • Sunoj, S.M.
  • Krishnan, Aswathy S.
  • Sankaran, P.G.

Abstract

In the present paper we introduce a quantile-based cumulative residual Tsallis entropy (CRTE) and quantile-based CRTE for order statistics. Unlike the cumulative residual Tsallis entropy measures in the distribution function approach due to Sati and Gupta (2015) and Rajesh and Sunoj (2016) respectively, the corresponding quantile versions possess some unique properties. In many applied works there do not have any tractable distribution functions while the quantile function exists and in such cases the proposed measures become more useful in measuring uncertainty of random variables. We obtain some characterizations for distributions based on the quantile versions of CRTE and derive certain bounds. We also study various properties of quantile-based CRTE for order statistics.

Suggested Citation

  • Sunoj, S.M. & Krishnan, Aswathy S. & Sankaran, P.G., 2018. "A quantile-based study of cumulative residual Tsallis entropy measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 410-421.
    • Handle: RePEc:eee:phsmap:v:494:y:2018:i:c:p:410-421
    DOI: 10.1016/j.physa.2017.12.058
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    References listed on IDEAS

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    1. Taruya, Atsushi & Sakagami, Masa-aki, 2003. "Gravothermal catastrophe and Tsallis’ generalized entropy of self-gravitating systems. (II). Thermodynamic properties of stellar polytrope," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(3), pages 387-413.
    2. Sunoj, S.M. & Sankaran, P.G., 2012. "Quantile based entropy function," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1049-1053.
    3. Preda, Vasile & Dedu, Silvia & Gheorghe, Carmen, 2015. "New classes of Lorenz curves by maximizing Tsallis entropy under mean and Gini equality and inequality constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 925-932.
    4. Fashandi, M. & Ahmadi, Jafar, 2012. "Characterizations of symmetric distributions based on Rényi entropy," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 798-804.
    5. Nanda, Asok K. & Sankaran, P.G. & Sunoj, S.M., 2014. "Rényi’s residual entropy: A quantile approach," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 114-121.
    6. Arimitsu, Toshihico & Arimitsu, Naoko, 2002. "PDF of velocity fluctuation in turbulence by a statistics based on generalized entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 218-226.
    7. P. G. Sankaran & S. M. Sunoj, 2017. "Quantile-based cumulative entropies," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(2), pages 805-814, January.
    8. Tong, S. & Bezerianos, A. & Paul, J. & Zhu, Y. & Thakor, N., 2002. "Nonextensive entropy measure of EEG following brain injury from cardiac arrest," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(3), pages 619-628.
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    Cited by:

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    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. Psarrakos, Georgios & Sordo, Miguel A., 2019. "On a family of risk measures based on proportional hazards models and tail probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 232-240.

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