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Representations and limit theorems for extreme value distributions

Published online by Cambridge University Press:  14 July 2016

Peter Hall
Peter Hall*
Affiliation:
University of Melbourne
*
∗Now at The Australian National University, Canberra.
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Abstract

Let Xn1 ≦ Xn2 ≦ ··· ≦ Xnn denote the order statistics from a sample of n independent, identically distributed random variables, and suppose that the variables Xnn, Xn, n–1, ···, when suitably normalized, have a non-trivial limiting joint distribution ξ1, ξ2, ···, as n → ∞. It is well known that the limiting distribution must be one of just three types. We provide a canonical representation of the stochastic process {ξn, n ≧ 1} in terms of exponential variables, and use this representation to obtain limit theorems for ξ n as n →∞.

Keywords

EXTREME VALUE DISTRIBUTIONSEXTREMAL PROCESSESREPRESENTATIONSLIMIT THEOREMS
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 639 - 644
Copyright
Copyright © Applied Probability Trust 1978 

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