The Annals of Mathematical Statistics

One-Sided Confidence Contours for Probability Distribution Functions

Z. W. Birnbaum and Fred H. Tingey

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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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Ann. Math. Statist., Volume 22, Number 4 (1951), 592-596.

First available in Project Euclid: 28 April 2007

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Birnbaum, Z. W.; Tingey, Fred H. One-Sided Confidence Contours for Probability Distribution Functions. Ann. Math. Statist. 22 (1951), no. 4, 592--596. doi:10.1214/aoms/1177729550.

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