Some Results on Dynamic Discrimination Measures of Order (alpha, beta)

Abstract

In this paper we propose two measures of discrimination of order (α, β) for residual and past lifetimes. Lower and upper bounds of the proposed measures are derived. Some bounds are obtained by considering weighted distributions and subsequently, examples are presented. Finally, characterization results of the proportional hazards and proportional reversed hazards models are given.

Generalized Residual Entropy and Upper Record Values

“…For some results and applications on weighted distributions, one may refer to Di Crescenzo and Longobardi [22], Gupta and Kirmani [23], Kayal [9], Maya and Sunoj [24], Navarro et al [25], and Patil [26]. In the present section, we obtain some comparison results based on the generalized residual entropy between a random variable and its weighted version.…”

“…Based on the generalized entropy measures given in (1) and (2), several authors obtained various results in the literature. In this direction, we refer to Kayal [8][9][10][11], Kayal and Vellaisamy [12], Kumar and Taneja [13], and Sati and Gupta [14]. In this paper, we study some properties and characterizations of the generalized residual entropy given by (2) based on the upper record values.…”