A simple estimator of the bivariate distribution function for censored gap times

Let (T1,T2) be gap times corresponding to two consecutive events, which are observed subject to random right-censoring. In this paper a simple estimator of the bivariate distribution function of (T1,T2) is proposed. We investigate the conditions under which the introduced estimator is consistent. Applications to the estimation of the marginal distributions of the gap times and to correlation analysis are included. We explore the behaviour of the proposed methods through simulations.