Identifiability and censored data

It is well known that, without the assumption of independence between two nonnegative random variables X and Y, the survival function of X is not identifiable on the basis of the joint distribution function of Z = min(X, Y) and (delta)= I(Z = Y). In this paper, we provide a simple condition in the form of conditional distribution of Y given X. We show that our condition is equivalent to the constant-sum condition proposed by Williams & Lagakos (1977). As a result the survival function of X can be identified from the joint distribution of Z and (delta) and the Kaplan–Meier estimator with Greenwoodʹs formula for its variance remains valid. Examples which satisfy the condition are given.