A Short-Cut Method for Estimation in Renewal Processes

This article proposes a simple, noniterative estimator of the lifetime distribution from stationary renewal processes data, which is a variation of the Kaplan-Meier estimator. The method is compared with the nonparametric maximum likelihood estimator using real and simulated data, and the results show that as long as the censoring level is not too high the two estimates are remarkably close. A heuristic asymptotic argument is given to support the simulation results and to justify the rationale behind the estimator. The estimator's connection with the Kaplan–Meier estimator is exploited to suggest a variance estimate and associated confidence interval, which, through a simulation study, are found to be conservative.