Entropy generating function for past lifetime and its properties

TL;DR

This paper introduces a new past entropy-generating function, explores its properties, and demonstrates its ability to uniquely determine distributions and characterize lifetime models, enhancing uncertainty measurement in lifetime analysis.

Contribution

The paper proposes a novel past entropy-generating function and investigates its properties, providing new tools for lifetime distribution analysis and model characterization.

Findings

The past entropy-generating function uniquely determines the distribution.

Characterizations of lifetime models using the past entropy-generating function.

Properties of the new entropy measure are systematically studied.

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.