IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v86y2024i1d10.1007_s13171-023-00316-8.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-023-00316-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-023-00316-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. López-Díaz, Miguel & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "On the Lp-metric between a probability distribution and its distortion," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 257-264.
    3. Wentao Hu & Cuixia Chen & Yufeng Shi & Ze Chen, 2022. "A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 831-874, June.
    4. Mohamed Said Mohamed, 2020. "On Cumulative Tsallis Entropy and Its Dynamic Past Version," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1903-1917, December.
    5. Kaluszka, Marek, 2001. "Optimal reinsurance under mean-variance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 61-67, February.
    6. Marco Capaldo & Antonio Di Crescenzo & Alessandra Meoli, 2024. "Cumulative information generating function and generalized Gini functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(7), pages 775-803, October.
    7. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    8. Psarrakos, Georgios & Vliora, Polyxeni, 2021. "Sensitivity analysis and tail variability for the Wang’s actuarial index," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 147-152.
    9. Landsman, Zinoviy & Sherris, Michael, 2001. "Risk measures and insurance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 103-115, August.
    10. Belzunce, Félix & Pinar, José F. & Ruiz, José M. & Sordo, Miguel A., 2012. "Comparison of risks based on the expected proportional shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 292-302.
    11. Sordo, Miguel A., 2008. "Characterizations of classes of risk measures by dispersive orders," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1028-1034, June.
    12. M. Hashempour & M. Mohammadi & S. M. A. Jahanshahi & A. H. Khammar, 2024. "Modified Cumulative Extropies of Doubly Truncated Random Variables," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 558-585, November.
    13. Morteza Mohammadi & Majid Hashempour, 2024. "On weighted version of dynamic cumulative residual inaccuracy measure based on extropy," Statistical Papers, Springer, vol. 65(7), pages 4599-4629, September.
    14. Hu, Taizhong & Chen, Ouxiang, 2020. "On a family of coherent measures of variability," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 173-182.
    15. Gajek, Leslaw & Zagrodny, Dariusz, 2004. "Optimal reinsurance under general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 227-240, April.
    16. Francesca Greselin & Ričardas Zitikis, 2018. "From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective," Econometrics, MDPI, vol. 6(1), pages 1-20, January.
    17. Tzougas, George & Karlis, Dimitris, 2020. "An EM algorithm for fitting a new class of mixed exponential regression models with varying dispersion," LSE Research Online Documents on Economics 104027, London School of Economics and Political Science, LSE Library.
    18. Vanderlei da Costa Bueno & Narayanaswamy Balakrishnan, 2025. "A Conditioned Kullback-Leibler Divergence Measure through Compensator Processes and its Relationship to Cumulative Residual Inaccuracy Measure with Applications," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-25, June.
    19. Wei, Wang & Yatracos, Yannis, 2004. "A stop-loss risk index," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 241-250, April.
    20. Matthias Fischer & Thorsten Moser & Marius Pfeuffer, 2018. "A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations," Risks, MDPI, vol. 6(4), pages 1-28, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00316-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.