Distribution of the Largest Observed Uncensored and the LargestObserved Survival Times

We calculate finite sample and asymptotic distributions for the largest censored and uncensored survival times, from a sample of survival data generated according to an iid censoring model. A key structural result obtained is that, conditional on the value of the largest uncensored survival time, and knowing the number of censored observations exceeding this time, the sample partitions into two independent subsequences, each subsequence having the distribution of an iid sample of censored survival times, of reduced size, from truncated random variables. We apply extreme value methods to deriving asymptotic distributions for some statistics.