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Characterizations based on generalized cumulative residual entropy functions

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  • Jorge Navarro
  • Georgios Psarrakos

Abstract

The Shannon entropy and the cumulative residual entropy (CRE) of a random variable are useful tools in probability theory. Recently, a new concept called generalized cumulative residual entropy (GCRE) of order n was introduced and studied. It is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. In this paper, we show that, under some assumptions, the GCRE function of a fixed order n uniquely determines the distribution function. Some characterizations of particular probability models are obtained from this general result.

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  • Jorge Navarro & Georgios Psarrakos, 2017. "Characterizations based on generalized cumulative residual entropy functions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1247-1260, February.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:3:p:1247-1260
    DOI: 10.1080/03610926.2015.1014111
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    Cited by:

    1. Suchandan Kayal, 2018. "On Weighted Generalized Cumulative Residual Entropy of Order n," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 487-503, June.
    2. Tahmasebi Saeid & Parsa Hojat, 2019. "Notes on Cumulative Entropy as a Risk Measure," Stochastics and Quality Control, De Gruyter, vol. 34(1), pages 1-7, June.
    3. 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.
    4. Antonio Di Crescenzo & Suchandan Kayal & Abdolsaeed Toomaj, 2019. "A past inaccuracy measure based on the reversed relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(5), pages 607-631, July.

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