Nonparametric Upper Confidence Bounds for Pr{Y < X} and Confidence Limits for Pr{Y<X} WhenXandYare Normal
- 1 September 1964
- journal article
- research article
- Published by Taylor & Francis in Journal of the American Statistical Association
- Vol. 59 (307) , 906-924
- https://doi.org/10.1080/01621459.1964.10480739
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.Keywords
This publication has 4 references indexed in Scilit:
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- A Distribution-Free Upper Confidence Bound for $\Pr \{Y < X\}$, Based on Independent Samples of $X$ and $Y$The Annals of Mathematical Statistics, 1958
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