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On the Distribution of the Maximum of Random Variables

On the Distribution of the Maximum of Random Variables,10.1214/aoms/1177692632,The Annals of Mathematical Statistics,Janos Galambos

On the Distribution of the Maximum of Random Variables   (Citations: 7)
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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.
Journal: The Annals of Mathematical Statistics , vol. 43, no. 1972, pp. 516-521, 1972
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