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Results on a Generalized Fractional Cumulative Entropy

Author

Listed:
  • Farid Foroghi

    (Persian Gulf University)

  • Saeid Tahmasebi

    (Persian Gulf University)

  • Mahmoud Afshari

    (Persian Gulf University)

  • Francesco Buono

    (Universitá degli Studi di Napoli Federico II)

Abstract

Recently, a modification of fractional entropy based on the inverse Mittag-Leffler function (MLF) was proposed by Zhang and Shang (2021). In this paper, we present an extension of the fractional cumulative entropy (FCE) and obtain some further results about this measure. We study new equivalent expressions, bounds, stochastic ordering, and properties of dynamic generalized FCE. By using the empirical approach, we give an estimator of this measure and study large sample properties of it. In addition, the validity of this new measure is supported by numerical simulations on logistic map equations. Finally, an application of this measure is proposed in the evaluation of MRI scans for brain cancer.

Suggested Citation

  • Farid Foroghi & Saeid Tahmasebi & Mahmoud Afshari & Francesco Buono, 2024. "Results on a Generalized Fractional Cumulative Entropy," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 138-163, February.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00316-8
    DOI: 10.1007/s13171-023-00316-8
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    References listed on IDEAS

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    1. Shaun Wang, 1998. "An Actuarial Index of the Right-Tail Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(2), pages 88-101.
    2. Murali Rao, 2005. "More on a New Concept of Entropy and Information," Journal of Theoretical Probability, Springer, vol. 18(4), pages 967-981, October.
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