Non-parametric estimation of cumulative (residual) extropy

TL;DR

This paper introduces non-parametric estimators for cumulative and residual extropy, explores their properties, and applies them to real data, advancing uncertainty quantification methods in reliability analysis.

Contribution

It provides new simple estimators for cumulative residual extropy, studies their asymptotic behavior, and extends them to right-censored data, linking extropy measures with reliability concepts.

Findings

Estimators perform well in simulations.

Application to real data demonstrates practical utility.

New relationships between extropy measures and reliability are established.

Abstract

Extropy and its properties are explored to quantify the uncertainty. In this paper, we obtain alternative expressions for cumulative residual extropy and negative cumulative extropy. We obtain simple estimators of cumulative (residual) extropy. Asymptotic properties of the proposed estimators are studied. We also present new estimators of cumulative (residual) extropy when the data is right censored. The finite sample performance of the estimators is evaluated through Monte Carlo simulation studies. We use the proposed estimators to analyse different real data sets. Finally, we obtain the relationship between different dynamic and weighted extropy measures and reliability concepts, which leads to several open problems associated with these measures.