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December, 1951 One-Sided Confidence Contours for Probability Distribution Functions
Z. W. Birnbaum, Fred H. Tingey
Ann. Math. Statist. 22(4): 592-596 (December, 1951). DOI: 10.1214/aoms/1177729550


Let $F(x)$ be the continuous distribution function of a random variable $X,$ and $F_n(x)$ the empirical distribution function determined by a sample $X_1, X_2, \cdots, X_n$. It is well known that the probability $P_n(\epsilon)$ of $F(x)$ being everywhere majorized by $F_n(x) + \epsilon$ is independent of $F(x)$. The present paper contains the derivation of an explicit expression for $P_n(\epsilon)$, and a tabulation of the 10%, 5%, 1%, and 0.1% points of $P_n(\epsilon)$ for $n =$ 5, 8, 10, 20, 40, 50. For $n =$ 50 these values agree closely with those obtained from an asymptotic expression due to N. Smirnov.


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Z. W. Birnbaum. Fred H. Tingey. "One-Sided Confidence Contours for Probability Distribution Functions." Ann. Math. Statist. 22 (4) 592 - 596, December, 1951.


Published: December, 1951
First available in Project Euclid: 28 April 2007

zbMATH: 0044.14601
MathSciNet: MR44081
Digital Object Identifier: 10.1214/aoms/1177729550

Rights: Copyright © 1951 Institute of Mathematical Statistics

Vol.22 • No. 4 • December, 1951
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