Dynamic Cumulative Residual Entropy Generating Function and its properties

TL;DR

This paper introduces the dynamic cumulative residual entropy generating function (DCREGF), explores its properties, characterizes distributions, and develops a test for decreasing DCREGF, contributing to lifetime distribution analysis.

Contribution

It proposes the DCREGF, establishes its unique determination of distributions, and develops a statistical test for decreasing DCREGF, advancing lifetime distribution modeling.

Findings

DCREGF uniquely determines distributions.

A new class of life distributions based on decreasing DCREGF is introduced.

A test for decreasing DCREGF is developed and its performance analyzed.

Abstract

In this work, we study the properties of cumulative residual entropy generating function. We then introduce dynamic cumulative residual entropy generating function (DCREGF). It is shown that the DCREGF determines the distribution uniquely. We study some characterization results using the relationship between DCREGF and hazard rate and mean residual life function. A new class of life distribution based on decreasing DCREGF is introduced. Finally we develop a test for decreasing DCREGF and study its performance.