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October, 1967 Sample Sequences of Maxima
James Pickands III
Ann. Math. Statist. 38(5): 1570-1574 (October, 1967). DOI: 10.1214/aoms/1177698711


Let $X_1, X_2, \cdots, X_n, \cdots$ be a sequence of independent, identically distributed random variables with common distribution function $F$. Let $Z_n = \max \{X_1, X_2, \cdots X_n\}$. Conditions for the stability and relative stability of such sequences with the various modes of convergence have been given by Geffroy [3], and Barndorff-Nielsen [1]. The principal result of this paper is Theorem 2.1, which is an analogue for maxima of the law of the iterated logarithm for sums (Loeve [6] pages 260-1). In Section 3, it is indicated that the theorem is satisfied by a wide class of distributions, and specific forms are given for the normal and exponential distributions.


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James Pickands III. "Sample Sequences of Maxima." Ann. Math. Statist. 38 (5) 1570 - 1574, October, 1967.


Published: October, 1967
First available in Project Euclid: 27 April 2007

zbMATH: 0171.16904
MathSciNet: MR215346
Digital Object Identifier: 10.1214/aoms/1177698711

Rights: Copyright © 1967 Institute of Mathematical Statistics

Vol.38 • No. 5 • October, 1967
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