Weighted Cumulative Residual Mathai-Haubold Entropy

TL;DR

This paper introduces a new entropy measure called weighted cumulative residual Mathai-Haubold entropy, explores its properties, and applies it to lifetime distributions and goodness-of-fit testing.

Contribution

It develops the entropy measure, derives bounds and expressions, and proposes a new goodness-of-fit test for the Rayleigh distribution.

Findings

Derived bounds and explicit expressions for lifetime distributions.

Formulated two new classes of life distributions.

Evaluated the goodness-of-fit test through Monte Carlo simulations.

Abstract

In this paper, we introduce the weighted cumulative residual Mathai--Haubold entropy and establish its fundamental properties. A dynamic version is developed, and its behavior under linear transformations is studied. Bounds and explicit expressions for some lifetime distributions are derived. Characterization results based on the associated measure are obtained and two new classes of life distributions are formulated. A goodness-of-fit test for the Rayleigh distribution is proposed and its performance is evaluated through a Monte Carlo simulation study. Applications to real data sets demonstrate the practical applicability of the proposed methodology