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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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References

Feller, W. (1966) An Introduction to Probability Theory and its Applications , Vol. II, John Wiley and Sons, New York.Google Scholar
Fisher, R. A. and Tippett, L. H. C. (1928) Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proc. Camb. Phil. Soc. 24, 180–190.Google Scholar
Fréchet, M. (1927) Sur la loi de probabilité de l'écart maximum. Ann. Soc. Polonaise Math. (Cracow) 6, 93–116.Google Scholar
Gnedenko, B. V. (1943) Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. 44, 423–453.Google Scholar
Gnedenko, B. V. and Kolmogorov, A. N. (1968) Limit Distributions for Sums of Independent Random Variables. Addison-Wesley, Reading, Massachusetts.Google Scholar
Gumbel, E. J. (1958) Statistics of Extremes. Columbia University Press, New York.Google Scholar
von Mises, R. (1936) La distribution de la plus grande de n valeurs. Rev. Math. de l'Union Interbalkanique (Athens) 1, 1–20.Google Scholar