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The limit behaviour of the maximum of random variables with applications to outlier-resistance

Published online by Cambridge University Press:  14 July 2016

Rudolf Mathar
Rudolf Mathar*
Affiliation:
Technical University, Aachen
*
∗Postal address: Institute of Statistics, Technical University Aachen, Wüllnerstr. 3, D-5100 Aachen, West Germany.
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Abstract

We consider degenerate limit laws for the sequence {Xn, n}n(N of successive maxima of identically distributed random variables. It turns out that the concentration of Xn, n for large n can be determined in terms of a tail ratio of the underlying distribution function F. Applications to the outlier-behaviour of probability distributions are given.

Keywords

DEGENERATE LIMIT LAWSTAIL-BEHAVIOURMAXIMALLY DEPENDENT
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 3 , September 1984 , pp. 646 - 650
Copyright
Copyright © Applied Probability Trust 1984 

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References

Anderson, C. W. (1970) Extreme value theory for a class of discrete distributions with applications to some stochastic processes. J. Appl. Prob. 7, 99–113.Google Scholar
Galambos, J. (1978) The Asymptotic Theory of Extreme Order Statistics. Wiley, New York.Google Scholar
Gather, U. and Mathar, R. (1984) Analysing the outlier-behaviour of non-continuous distribution functions. J. Indian Statist. Assoc. Google Scholar
Gnedenko, B. (1943) Sur la distribution limite du terme maximum d'une, série aléatoire. Ann. Math. 44, 423–453.Google Scholar
Green, R. F. (1976) Outlier-prone and outlier-resistant distributions. J. Amer. Statist. Assoc. 71, 502–505.Google Scholar
Lai, T. L. and Robbins, H. (1978) A class of dependent random variables and their maxima. Z. Wahrscheinlichkeitsth. 42, 89–111.Google Scholar