Entropy generating function for past lifetime and its properties

Abstract: The past entropy is considered as an uncertainty measure for the past lifetime distribution. Generating function approach to entropy become popular in recent time as it generate several well-known entropy measures. In this paper, we introduce the past entropy-generating function. We study certain properties of this measure. It is shown that the past entropy-generating function uniquely determines the distribution. Further, we present characterizations for some lifetime models using the relationship between reliability concepts and the past entropy-generating function.