Open Access
February, 1965 Some Renyi Type Limit Theorems for Empirical Distribution Functions
Miklos Csorgo
Ann. Math. Statist. 36(1): 322-326 (February, 1965). DOI: 10.1214/aoms/1177700296


Let $F_n(x)$ denote the empirical distribution function of a random sample of size $n$ drawn from a population having continuous distribution function $F(x)$. In Section 3 the limiting distribution of the supremum of the random variables $\{F_n(x) - F(x)\}/F_n(x), |F_n(x) - F(x)|/F_n(x), \{F_n(x) - F(x)\}/(1 - F(x)), |F_n(x) - F(x)|/(1 - F(x)), \{F_n(x) - F(x)\}/(1 - F_n(x)), |F_n(x) - F(x))|/(1 - F_n(x))$ is derived where sup is taken over suitable ranges of $x$ respectively. Relevant tests and some combinations of them are also discussed briefly in Section 3.


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Miklos Csorgo. "Some Renyi Type Limit Theorems for Empirical Distribution Functions." Ann. Math. Statist. 36 (1) 322 - 326, February, 1965.


Published: February, 1965
First available in Project Euclid: 27 April 2007

zbMATH: 0127.10603
MathSciNet: MR179893
Digital Object Identifier: 10.1214/aoms/1177700296

Rights: Copyright © 1965 Institute of Mathematical Statistics

Vol.36 • No. 1 • February, 1965
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