On Weighted Kullback–Leibler Divergence for Doubly Truncated Random Variables

Abstract

In this communication, we study doubly truncated weighted Kullback–Leibler divergence (KLD) between two nonnegative random variables. The proposed measure is a generalization of the dynamic weighted KLD introduced by Yasaei Sekeh et al. (2013). In reliability theory and survival analysis, it plays a significant role to study several aspects of a system when lifetimes fall in a time interval. It is showed that under some conditions, the proposed measure determines the distribution function uniquely. Further, characterization theorems for various lifetime distributions are proved. The effect of the monotone transformation on the proposed measure is studied. Some inequalities and bounds in terms of useful measures are obtained and finally, few applications are provided.