Non parametric estimation of residual-past entropy, mean residual-past lifetime, residual-past inaccuracy measure and asymptotic limits

TL;DR

This paper investigates the asymptotic properties of residual-past entropy, mean residual-past lifetime, and inaccuracy measures in discrete distributions, providing theoretical insights validated through simulations.

Contribution

It introduces non-parametric methods for estimating these measures and establishes their asymptotic behavior, including convergence rates and normality.

Findings

Asymptotic normality of estimators proven

Almost sure convergence rates established

Simulation results confirm theoretical findings

Abstract

In the present work, we provide the asymptotic behavior of the residual-past entropy, of the mean residual-past lifetime distribution and of the residual-past inaccuracy measure. We are interested in these measures of uncertainty in the discrete case. Almost sure rates of convergence and asymptotic normality results are established. Our theoretical results are validated by simulations