Evaluating the Uncertainty in Mean Residual Times: Estimators Based on Residence Times from Discrete Time Processes

TL;DR

This paper introduces computationally inexpensive estimators for quantifying uncertainty in mean residual times derived from discrete time processes, validated through numerical experiments and an application to molecular dynamics simulations.

Contribution

The paper presents novel estimators for uncertainty in mean residual times that are easy to compute and highly accurate, applicable to various simulation data.

Findings

Estimators perform well across different probability distributions.

Application to molecular dynamics demonstrates practical utility.

Estimators are computationally inexpensive and accurate.

Abstract

In this work, we propose estimators for the uncertainty in mean residual times that require, for their evaluation, statistically independent individual residence times obtained from a discrete time 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.