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Partial attraction of maxima

Published online by Cambridge University Press:  14 July 2016

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

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.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1976 

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