Abstract
Abstract Birnbaum and McCarty give a distribution-free upper confidence bound on Pr{Y < X} when X and Y are independent and have continuous cumulative distribution functions. In this paper the restriction to a continuous distribution function is removed. The same problem is then considered where X and Y have a joint bivariate normal distribution function. The distribution of the estimator of Pr{Y < X} is non-central t. Upper confidence limits on Pr{Y < X} are examined for sample sizes n = 10(10)100 in two cases—where X and Y are independent and where observations are taken in pairs and X and Y may be dependent.
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