ABSTRACT
The differential entropy of the reversed residual life, called as past entropy is a useful measure in different contexts. We give the definition of past entropy and explain its properties in Sections 3.1 and 3.2. The new contribution of the section is the conditions under which the reversed hazard rate can be constant and the corresponding results in past entropy. The relationship the past entropy has with reversed hazard rate lead to characterization of a large class of distributions. Section 3.3 contains results on quantile functions and classes of life distributions thereof. We then discuss the role of order statistics and their entropies. Stochastic orders based on distribution as well as quantile functions are presented weighted and interval entropies are treated in the next two sections. We conclude the Chapter by studying the concept of past extropy by considering almost all similar aspects we have considered in the case of past entropy.
