Some distributional results through past entropy

Measure of uncertainty in past lifetime distribution plays an important role in the context of Information Theory, Forensic Science and other related fields. In this paper we provide characterizations of quite a few continuous and discrete distributions based on certain functional relationships among past entropy, reversed hazard rate and expected inactivity time. Based on past entropy, a conditional measure of uncertainty has been defined, which has helped in defining a new stochastic order and an ageing class. The properties of the stochastic order and those of the ageing class are also studied here.