One-Sided Confidence Contours for Probability Distribution Functions

  • Birnbaum Z
  • Tingey F
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Abstract

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 {$X_1}, X_2, {\textbackslash}cdots, X_n$. It is well known that the probability {$P_n({\textbackslash}epsilon)$} of {$F(x)$} being everywhere majorized by {$F_n(x)} + {\textbackslash}epsilon$ is independent of {$F(x)$.} The present paper contains the derivation of an explicit expression for {$P_n({\textbackslash}epsilon)$}, and a tabulation of the 10%, 5%, 1%, and 0.1% points of {$P_n({\textbackslash}epsilon)$} 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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APA

Birnbaum, Z. W., & Tingey, F. H. (1951). One-Sided Confidence Contours for Probability Distribution Functions. The Annals of Mathematical Statistics, 22(4), 592–596. https://doi.org/10.1214/aoms/1177729550

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