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Quantile-based cumulative entropies

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  • P. G. Sankaran
  • S. M. Sunoj

Abstract

It is well known that Shannon’s entropy plays an important role in the measurement of uncertainty of probability distributions. However, in certain situations Shannon entropy is not appropriate to measure the uncertainty and therefore an alternative measure has been introduced called cumulative residual entropy, based on the survival function (sf) F‾(x)=P(X>x)$\bar{F}(x) = P(X > x)$ instead of the probability density function (pdf) f(x) used in Shannon’s entropy. In the present paper, we introduce and study quantile versions of the cumulative entropy functions in the residual and past lifetimes. Unlike the cumulative entropies based on sf, the quantile-based cumulative entropy measures uniquely determine the underlying probability distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:2:p:805-814
    DOI: 10.1080/03610926.2015.1006779
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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. Klein, Ingo, 2017. "(Generalized) maximum cumulative direct, paired, and residual Φ entropy principle," FAU Discussion Papers in Economics 25/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    3. 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.
    4. 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.

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