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Abstract
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Recently, Zhan and Shang (2021) proposed a modification of fractional
entropy and proved some properties based on the inverse
Mittag-Leffler function (MLF). In this article, we introduce extensions
of fractional cumulative residual entropy (FCRE). Our results contain
bivariate version of extended FCRE, linear transformation, bounds,
stochastic ordering, and some properties of its dynamic version. We
also study on the fractional cumulative residual mutual information
and the conditional extended FCRE. Finally, we propose an estimator
of extended FCRE using empirical approach. We establish a central
limit theorem for the empirical extended FCRE under the exponential
distribution. Additionally, the validity of this new measure is supported
by numerical simulations on logistic map.
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