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Generalized cumulative residual entropy and record values

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  • Georgios Psarrakos
  • Jorge Navarro

Abstract

The Shannon entropy of a random variable has become a very useful tool in Probability Theory. In this paper we extend the concept of cumulative residual entropy introduced by Rao et al. (in IEEE Trans Inf Theory 50:1220–1228, 2004 ). The new concept called generalized cumulative residual entropy (GCRE) is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. We also consider a dynamic GCRE obtained using the residual lifetime. For these concepts we obtain some characterization results, stochastic ordering and aging classes properties and some relationships with other entropy concepts. Copyright Springer-Verlag 2013

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  • Georgios Psarrakos & Jorge Navarro, 2013. "Generalized cumulative residual entropy and record values," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 623-640, July.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:5:p:623-640
    DOI: 10.1007/s00184-012-0408-6
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    References listed on IDEAS

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    1. Felix Belzunce & Jorge Navarro & José M. Ruiz & Yolanda del Aguila, 2004. "Some results on residual entropy function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(2), pages 147-161, May.
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    Cited by:

    1. Jafar Ahmadi, 2021. "Characterization of continuous symmetric distributions using information measures of records," Statistical Papers, Springer, vol. 62(6), pages 2603-2626, December.
    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. Sordo, Miguel A. & Castaño-Martínez, Antonia & Pigueiras, Gema, 2016. "A family of premium principles based on mixtures of TVaRs," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 397-405.
    4. Xia Han & Ruodu Wang & Xun Yu Zhou, 2022. "Choquet regularization for reinforcement learning," Papers 2208.08497, arXiv.org.
    5. Psarrakos, Georgios & Toomaj, Abdolsaeed & Vliora, Polyxeni, 2024. "A family of variability measures based on the cumulative residual entropy and distortion functions," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 212-222.
    6. Baishuai Zuo & Chuancun Yin, 2024. "Worst-cases of distortion riskmetrics and weighted entropy with partial information," Papers 2405.19075, arXiv.org.
    7. Abdolsaeed Toomaj & Antonio Di Crescenzo, 2020. "Connections between Weighted Generalized Cumulative Residual Entropy and Variance," Mathematics, MDPI, vol. 8(7), pages 1-27, July.
    8. Georgios Psarrakos, 2016. "An Operator Property of the Distribution of a Nonhomogeneous Poisson Process with Applications," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1197-1215, December.
    9. Majid Asadi & Somayeh Zarezadeh, 2020. "A unified approach to constructing correlation coefficients between random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 657-676, August.
    10. Georgios Psarrakos & Antonio Di Crescenzo, 2018. "A residual inaccuracy measure based on the relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 37-59, January.
    11. Tahmasebi, Saeid & Eskandarzadeh, Maryam, 2017. "Generalized cumulative entropy based on kth lower record values," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 164-172.
    12. Hu, Taizhong & Chen, Ouxiang, 2020. "On a family of coherent measures of variability," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 173-182.
    13. 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.
    14. 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.
    15. Amit Ghosh & Chanchal Kundu, 2019. "Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures," Statistical Papers, Springer, vol. 60(6), pages 2225-2252, December.
    16. 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.
    17. Mao, Xuegeng & Shang, Pengjian & Wang, Jianing & Yin, Yi, 2020. "Fractional cumulative residual Kullback-Leibler information based on Tsallis entropy," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    18. Sun, Hongfang & Chen, Yu & Hu, Taizhong, 2022. "Statistical inference for tail-based cumulative residual entropy," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 66-95.
    19. Maryam Eskandarzadeh & Antonio Di Crescenzo & Saeid Tahmasebi, 2019. "Cumulative Measure of Inaccuracy and Mutual Information in k -th Lower Record Values," Mathematics, MDPI, vol. 7(2), pages 1-19, February.
    20. 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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