On Comparing Estimators of Pr{Y < X} in the Exponential Case

Let X and Y be s-independent exponentially distributed random variables with mean ß and ¿ respectively. This work povides simple approximations for s-bias and mean square error of the maximum likelihood estimator of Pr{Y < X} for two cases: 1) both ¿ and ß are unknown; 2) only ß is unknown. When ¿ is known, the mean square error is compared with that of the minimum variance s-unbiased estimator and a preference relationship between them is established using the mean square error criterion.