The Cumulative Residual Mathai--Haubold Entropy and its Non-parametric Inference

TL;DR

This paper introduces the cumulative residual Mathai--Haubold entropy and its dynamic version, proposing non-parametric estimators and demonstrating their effectiveness through simulations and real-world data analysis.

Contribution

It develops new entropy measures based on the Mathai--Haubold distribution and proposes kernel-based non-parametric estimators with practical applications.

Findings

Estimators perform well in simulations

DCRMHE effectively characterizes distribution functions

Applied to real failure time datasets

Abstract

We introduce the cumulative residual Mathai--Haubold entropy (CRMHE) and investigate its properties. We then propose a dynamic counterpart, the dynamic cumulative residual Mathai--Haubold entropy (DCRMHE), and establish its uniqueness in characterizing the distribution function. Non-parametric estimators for the CRMHE and DCRMHE are developed based on the kernel density estimation of the survival function. The efficacy of the estimators is assessed through a comprehensive Monte Carlo simulation study. The relevance of the proposed DCRMHE estimator is illustrated using two real-world datasets: on the failure times of 70 aircraft windshields and failure times of 40 randomly selected mechanical switches.