Unbiased variance estimation in estimating P (X > Y) for one and two parameter exponential populations

摘要

In this paper we consider the problem of unbiased estimation of the variance of the uniformly minimum variance unbiased estimator (UMVUE) of P (X > Y) for two independent random variables X and Y each following a one or two parameter exponential distribution with unknown parameters. In each case we give a necessary and sufficient condition for the existence of an unbiased variance estimator based on random samples from the two populations and obtain the UMVUE of the variance in situations where unbiased estimators exist.