## The Annals of Mathematical Statistics

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

### One-Sided Confidence Contours for Probability Distribution Functions

Z. W. Birnbaum and Fred H. Tingey

#### 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 $X_1, X_2, \cdots, X_n$. 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.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177729550

**Digital Object Identifier**

doi:10.1214/aoms/1177729550

**Mathematical Reviews number (MathSciNet)**

MR44081

**Zentralblatt MATH identifier**

0044.14601

**JSTOR**

links.jstor.org

#### Citation

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. https://projecteuclid.org/euclid.aoms/1177729550