Further Results Involving Residual and Past Extropy with their Applications

TL;DR

This paper investigates the properties of residual and past extropy, introduces estimators for these measures, and applies the findings to order statistics, coherent systems, and record values with both simulated and real data.

Contribution

It provides new insights into the monotonicity and characterization of residual and past extropy, along with non-parametric estimators and their practical applications.

Findings

Monotonicity properties of residual and past extropy established

New non-parametric estimators introduced and evaluated

Applications demonstrated on simulated and real data sets

Abstract

In this paper we focus on the study of the monotonicity properties of the residual and the past extropy as well as on some characterization problems. We then apply the derived results to analyze further stochastic aspects of order statistics, coherent systems, and record values. Using various examples, we illustrate the applicability and significance of the results obtained. In addition, non-parametric estimators for the residual and past extropy measures are introduced. The performance of the acquired estimators has been illustrated using simulated data sets and also real data sets.