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Some Results on Quantile Version of R é $\acute {e}$ nyi Entropy of Order Statistics

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  • Vikas Kumar

    (UIET, M. D. University)

  • Nirdesh Singh

    (Deenbandhu Chhotu Ram University of Science and Technology Murthal)

Abstract

In this article, we introduce the quantile version of R é $\acute {e}$ nyi entropy and R é $\acute {e}$ nyi information measure of order statistics and study their properties. Also article deals with R é $\acute {e}$ nyi quantile entropy of order statistics for the residual lifetime and inactivity time. The generalized Pareto and finite range distributions, which are commonly used in the reliability modeling have been characterized in terms of the proposed quantile entropy measures with extreme order statistics.

Suggested Citation

  • Vikas Kumar & Nirdesh Singh, 2023. "Some Results on Quantile Version of R é $\acute {e}$ nyi Entropy of Order Statistics," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 248-273, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-020-00241-0
    DOI: 10.1007/s13171-020-00241-0
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    References listed on IDEAS

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    1. Sunoj, S.M. & Sankaran, P.G. & Nanda, Asok K., 2013. "Quantile based entropy function in past lifetime," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 366-372.
    2. Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S., 2005. "Dynamic generalized information measures," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 85-98, January.
    3. Sankaran, P.G. & Sunoj, S.M. & Nair, N. Unnikrishnan, 2016. "Kullback–Leibler divergence: A quantile approach," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 72-79.
    4. Thapliyal, Richa & Taneja, H.C. & Kumar, Vikas, 2015. "Characterization results based on non-additive entropy of order statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 297-303.
    5. Asok Nanda & Prasanta Paul, 2006. "Some Properties of Past Entropy and their Applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(1), pages 47-61, August.
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