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Weighted fractional generalized cumulative past entropy and its properties

Author

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  • Suchandan Kayal

    (National Institute of Technology Rourkela)

  • N. Balakrishnan

    (McMaster University)

Abstract

In this paper, we introduce weighted fractional generalized cumulative past entropy of a nonnegative absolutely continuous random variable. Various properties of the proposed weighted fractional measure are studied, including some bounds and stochastic orders. A connection between the proposed measure and the left-sided Riemann-Liouville fractional integral is established. Further, the proposed measure is studied for the proportional reversed hazard rate model. Next, a nonparametric estimator of the weighted fractional generalized cumulative past entropy is proposed based on empirical distribution function. Various examples with a real-life data set are considered for illustrative purpose. A validation of the proposed measure is provided using the logistic map and some applications are also discussed. Weighted fractional generalized cumulative paired entropy is proposed and some of its properties are explored. Finally, large-sample properties of the proposed empirical estimator are studied.

Suggested Citation

  • Suchandan Kayal & N. Balakrishnan, 2023. "Weighted fractional generalized cumulative past entropy and its properties," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-23, June.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10035-0
    DOI: 10.1007/s11009-023-10035-0
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    References listed on IDEAS

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    1. Kharazmi, Omid & Balakrishnan, Narayanaswamy, 2021. "Jensen-information generating function and its connections to some well-known information measures," Statistics & Probability Letters, Elsevier, vol. 170(C).
    2. Fausto Ferrari, 2018. "Weyl and Marchaud Derivatives: A Forgotten History," Mathematics, MDPI, vol. 6(1), pages 1-25, January.
    3. Farsam Misagh, 2016. "On Shift-Dependent Cumulative Entropy Measures," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-8, June.
    4. M. Mirali & S. Baratpour & V. Fakoor, 2017. "On weighted cumulative residual entropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(6), pages 2857-2869, March.
    5. Suchismita Das, 2017. "On weighted generalized entropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(12), pages 5707-5727, June.
    6. M. Mirali & S. Baratpour, 2017. "Dynamic version of weighted cumulative residual entropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(22), pages 11047-11059, November.
    7. 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.
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    Cited by:

    1. Contreras-Reyes, Javier E. & Kharazmi, Omid, 2023. "Belief Fisher–Shannon information plane: Properties, extensions, and applications to time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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