Extensions of fractional cumulative residual entropy with applications, By Mahmoud Afshari

Research

Title	Extensions of fractional cumulative residual entropy with applications
Type	Article
Keywords	Fractional cumulative residual entropy; fractional entropy; inverse Mittag- Leffler function; logistic map
Journal	COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
DOI	https://doi.org/10.1080/03610926.2022.2044493
Researchers	farid foroghi (First researcher) , Saeid Tahmasebi (Second researcher) , Mahmoud Afshari (Third researcher) , Fazlollah Lak (Fourth researcher)

Abstract

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.