Approximate Identifiability, Moments and Censored Data

It is well known that the joint distribution of a pair of random variables ( X,Y ) is not identifiable on the basis of the joint distribution of the function (min ( X,Y ), 1 X < Y ]). This paper introduces the concept of approximate identifiability and studies its relevance to the function (min ( X,Y ), Y ). It shows that the distribution of ( X,Y ) is approximately identifiable on the basis of the distribution of (min ( X,Y ), Y ). The identification is explicitly executed by a method of moments. The method is applied to the analysis of censored distributions arising in the theory of clinical trials and is compared to the standard method of Kaplan and Meier.