Stochastic Properties of Fractional Generalized Cumulative Residual Entropy and Its Extensions

Ghadah Alomani; Mohamed Kayid

doi:10.3390/e24081041

Stochastic Properties of Fractional Generalized Cumulative Residual Entropy and Its Extensions

Entropy (Basel). 2022 Jul 28;24(8):1041. doi: 10.3390/e24081041.

Authors

Ghadah Alomani¹, Mohamed Kayid²

Affiliations

¹ Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.
² Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.

Abstract

The fractional generalized cumulative residual entropy (FGCRE) has been introduced recently as a novel uncertainty measure which can be compared with the fractional Shannon entropy. Various properties of the FGCRE have been studied in the literature. In this paper, further results for this measure are obtained. The results include new representations of the FGCRE and a derivation of some bounds for it. We conduct a number of stochastic comparisons using this measure and detect the connections it has with some well-known stochastic orders and other reliability measures. We also show that the FGCRE is the Bayesian risk of a mean residual lifetime (MRL) under a suitable prior distribution function. A normalized version of the FGCRE is considered and its properties and connections with the Lorenz curve ordering are studied. The dynamic version of the measure is considered in the context of the residual lifetime and appropriate aging paths.

Keywords: FGCRE; generalized cumulative residual entropy; mean residual lifetime; stochastic orders.

Grants and funding

Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R226), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.