A note on the sampling distribution of the maximum likelihood estimators in a competing exponential risks model

In this paper we consider a model for competing risks where the underlying failure times are exponential. The moments of the maximum likelihood estimators, based on Type 1 censoring, are derived, extending some results on the pure death process in Beyer, Keiding and Simonsen (1976). The small-sample behaviour is compared with the standard asymptotic results and some numerical results are included.