Results on a Generalized Fractional Cumulative Entropy, By Mahmoud Afshari

Research

Title	Results on a Generalized Fractional Cumulative Entropy
Type	Article
Keywords	Cumulative entropy, Evaluation of MRI scans, Fractional entropy, Financial stock, Inverse Mittag-Leffler function, Logistic map equations, Studying chaos.
Journal	Sankhya A
DOI	https://doi.org/10.1007/s13171-023-00316-8
Researchers	farid foroghi (First researcher) , Saeid Tahmasebi (Second researcher) , Mahmoud Afshari (Third researcher) , Francesco Buono (Fourth researcher)

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.