Nonparametric estimation of a lifetime distribution when censoring times are missing

We consider datasets for which lifetimes associated with the units in a population are observed if they occur within certain time intervals but for which lengths of the time intervals, or censoring times of unfailed units, are missing. We consider nonparametric estimation of the lifetime distribution for the population from such data; a maximum likelihood estimator and a simple moment estimator are obtained. An example involving automobile warranty data is discussed at some length.