The Annals of Mathematical Statistics

An Extension of the Kolmogorov Distribution

Jerome Blackman

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Abstract

Let $x_1, x_2, \cdots, x_n, x'_1, x'_2, \cdots, x'_{nk}$ be independent random variables with a common continuous distribution $F(x)$. Let $x_1, x_2, \cdots, x_n$ have the empiric distribution $F_n(x)$ and $x'_1, x'_2, \cdots, x'_{kn}$ have the empiric distribution $G_{nk}(x)$. The exact values of $P(-y < F_n(s) - G_{nk}(s) < x$ for all $s$) and $P(-y < F(s) - F_n(s) < x$ for all $s$) are obtained, as well as the first two terms of the asymptotic series for large $n$.

Article information

Source
Ann. Math. Statist., Volume 27, Number 2 (1956), 513-520.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177728274

Digital Object Identifier
doi:10.1214/aoms/1177728274

Mathematical Reviews number (MathSciNet)
MR82751

Zentralblatt MATH identifier
0116.10703

JSTOR
links.jstor.org

Citation

Blackman, Jerome. An Extension of the Kolmogorov Distribution. Ann. Math. Statist. 27 (1956), no. 2, 513--520. doi:10.1214/aoms/1177728274. https://projecteuclid.org/euclid.aoms/1177728274


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Corrections

  • See Correction: Jerome Blackman. Correction to "An Extension of the Kolmogorov Distribution". Ann. Math. Statist., Vol. 29, Iss. 1 (1958), 318--322.