Evaluating the uncertainty in mean residual times: Estimators based on residence times from discrete time processes

Abstract

In this work, we propose estimators for the variance of mean residual times, which rely on individual residence times. The latter are assumed to be described by independent and identically distributed random variables, generated by a discrete-time stochastic process. We examine their performance through numerical experiments involving well-known probability distributions, and an application example using molecular dynamics simulation results, from an aqueous NaCl solution, is provided. These computationally inexpensive estimators, capable of achieving very accurate outcomes, serve as useful tools for assessing and reporting uncertainties in mean residual times across a wide range of simulations.