Estimation of rate and mean functions from truncated recurrent event data

This article investigates data on recurrent events that arise from sources such as warranty claims, where the observation period for a unit is unknown until it experiences at least one event. This creates a type of truncation in the data. We consider nonparametric estimation of means and rates of the event occurrences with such ''zero-truncated'' data and examine the case where the population size and the distribution of observation times across units are at least approximately known. We study the behaviors of the proposed estimators by simulation. We examine some car warranty data by applying the methodology developed here and considering the underlying assumptions.