On estimation of bivariate survival function from random censored data

At present there are several approaches to estimate survival functions of vectors of lifetimes. However, some of these estimators are either inconsistent or not fully defined in the range of joint survival functions. Therefore they are not applicable in practice. In this paper three types of estimates of exponential-hazard, product-limit and relative-risk power structures for the bivariate survival function are considered when the number of summands in empirical estimates is replaced with a sequence of Poisson random variables. It is shown that proposed estimates are asymptotically equivalent.