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Keywords
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Cumulative entropy, Evaluation of MRI scans, Fractional
entropy, Financial stock, Inverse Mittag-Leffler function, Logistic map equations, Studying chaos.
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Abstract
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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.
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