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June, 1956 An Extension of the Kolmogorov Distribution
Jerome Blackman
Ann. Math. Statist. 27(2): 513-520 (June, 1956). DOI: 10.1214/aoms/1177728274


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 $n$.


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Jerome Blackman. "An Extension of the Kolmogorov Distribution." Ann. Math. Statist. 27 (2) 513 - 520, June, 1956.


Published: June, 1956
First available in Project Euclid: 28 April 2007

zbMATH: 0116.10703
MathSciNet: MR82751
Digital Object Identifier: 10.1214/aoms/1177728274

Rights: Copyright © 1956 Institute of Mathematical Statistics

Vol.27 • No. 2 • June, 1956
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