Extensions of fractional cumulative residual entropy with applications

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.