Unbiased estimation of P (X>Y) for two-parameter exponential populations using order statistics

摘要

The problem considered is that of unbiased estimation of P [X>Y] (=θ) for two independent random variables X and Y each following a two-parameter exponential distribution. We give necessary and sufficient conditions for the existence of an unbiased estimator of θ based on arbitrary sets of order statistics obtained from independent random samples from the two populations and suggest unbiased estimators in some situations where unbiased estimators exist.