Dynamic cumulative residual entropy generating function and its properties

Abstract

In this work, we study the properties of the cumulative residual entropy generating function (CREGF). We also discuss the non parametric estimation of CREGF. We 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, hazard rate, and mean residual life function. A new class of life distributions based on decreasing DCREGF is introduced. Finally, we develop a test for decreasing DCREGF and study its performance.