Data collected from many independent identically distributed renewal processes, each of which is observed for an arbitrary period of time, is usually affected by censoring coupled with length biased sampling. In this paper we derive an algorithm that produces the nonparametric maximum likelihood estimator (i.e., the analog of the single-sample empirical distribution function) of the common lifetime distribution, based on such data.
"Nonparametric Estimation in Renewal Processes." Ann. Statist. 10 (3) 772 - 785, September, 1982. https://doi.org/10.1214/aos/1176345870