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April, 1972 On the Distribution of the Maximum of Random Variables
Janos Galambos
Ann. Math. Statist. 43(2): 516-521 (April, 1972). DOI: 10.1214/aoms/1177692632


For a wide class of (dependent) random variables $X_1, X_2, \cdots, X_n$, a limit law is proved for the maximum, with suitable normalization, of $X_1, X_2, \cdots, X_n$. The results are more general in two aspects than the ones obtained earlier by several authors, namely, the stationary of the $X$'s is not assumed and secondly, the assumptions on the dependence of the $X$'s are weaker than those occurring in previous papers. A generalization of the method of inclusion and exclusion is one of the main tools.


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Janos Galambos. "On the Distribution of the Maximum of Random Variables." Ann. Math. Statist. 43 (2) 516 - 521, April, 1972.


Published: April, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0238.62060
MathSciNet: MR298730
Digital Object Identifier: 10.1214/aoms/1177692632

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 2 • April, 1972
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