On Weighted Entropy Generating Function

TL;DR

This paper explores properties of the weighted entropy generating function (WEGF), introduces a related residual version, and develops new life distribution classes, estimation methods, and a goodness-of-fit test with real-data applications.

Contribution

It introduces the weighted residual entropy generating function (WREGF), establishes its properties, and develops new distribution classes and non-parametric estimation techniques.

Findings

WREGF properties linked to hazard rate and mean residual life.

New life distribution classes derived from WREGF.

Effective non-parametric Pareto I distribution test demonstrated.

Abstract

In this paper, we study the properties of the weighted entropy generating function (WEGF). We also introduce the weighted residual entropy generating function (WREGF) and establish some characterization results based on its connections with the hazard rate and the mean residual life function. Furthermore, we propose two new classes of life distributions derived from WREGF. We also study the non-parametric estimation of WREGF. A non-parametric test for the Pareto type I distribution is developed based on entropy characterization. To evaluate the performance of the test statistics, we conduct an extensive Monte Carlo simulation study. Finally, we apply the proposed method to two real-life datasets.