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Partial attraction of maxima

Published online by Cambridge University Press:  14 July 2016

Richard F. Green
Richard F. Green*
Affiliation:
University of California, Riverside
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Abstract

There exist three classes of probability laws that are stable for maxima. A number of well-known distributions lie in the domains of attraction of these laws. This fact is sometimes exploited by fitting the distribution of maxima with one of the stable laws. Such a procedure may well be misguided, however, since distributions exist which produce maxima having any desired distribution and not just a stable type. In this paper partial attraction of maxima is defined and it is shown that all distributions have a non-empty domain of partial attraction of maxima. In fact, there exists a distribution that lies simultaneously in the domain of partial attraction of maxima of all distributions.

Keywords

STABLE LAWSDOMAIN OF ATTRACTIONPARTIAL ATTRACTIONPARTIAL ATTRACTION OF MAXIMA
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 159 - 163
Copyright
Copyright © Applied Probability Trust 1976 

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