Results on a Generalized Fractional Cumulative Entropy

Farid Foroghi, Saeid Tahmasebi, Mahmoud Afshari and Francesco Buono ()
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Farid Foroghi: Persian Gulf University
Saeid Tahmasebi: Persian Gulf University
Mahmoud Afshari: Persian Gulf University
Francesco Buono: Universitá degli Studi di Napoli Federico II

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 5, 138-163

Abstract: 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.

Keywords: Cumulative entropy; Evaluation of MRI scans; Fractional entropy; Financial stock; Inverse Mittag-Leffler function; Logistic map equations; Studying chaos; 60E15; 62B10; 94A17 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13171-023-00316-8

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