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May, 1984 Limit Laws for the Maximum of Weighted and Shifted I.I.D. Random Variables
D. J. Daley, Peter Hall
Ann. Probab. 12(2): 571-587 (May, 1984). DOI: 10.1214/aop/1176993306


Gnedenko's (1943) study of the class $\mathscr{G}$ of limit laws for the sequence of maxima $M_n \equiv \max\{X_0, \cdots, X_{n - 1}\}$ of independent identically distributed random variables $X_0, X_1, \cdots$ is extended to limit laws for weighted sequences $\{w_n(\gamma)X_n\}$ (the simplest case $\{\gamma^nX_n\}$ has geometric weights $(0 \leq \gamma < 1))$ and translated sequences $\{X_n - v_n(\delta)\}$ (the simplest case is $\{X_n - n\delta\} (\delta > 0))$. Limit laws for these simplest cases belong to the family $\mathscr{G}$ characterized by Gnedenko; with more general weights or translates, limit laws outside $\mathscr{G}$ may arise.


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D. J. Daley. Peter Hall. "Limit Laws for the Maximum of Weighted and Shifted I.I.D. Random Variables." Ann. Probab. 12 (2) 571 - 587, May, 1984.


Published: May, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0538.60024
MathSciNet: MR735854
Digital Object Identifier: 10.1214/aop/1176993306

Primary: 60F05
Secondary: 62G30

Keywords: domain of attraction , extreme value distribution , Extreme value theory , Maxima , regular variation , shifted sequence , weighted sequence

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 2 • May, 1984
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