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Convergence rates for the ultimate and pentultimate approximations in extreme-value theory

Published online by Cambridge University Press:  01 July 2016

Jonathan P. Cohen
Jonathan P. Cohen*
Affiliation:
Imperial College, London
*
∗Present address: Department of Theoretical Statistics, University of Minnesota, 270 Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, U.S.A.
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Abstract

Let F be a distribution in the domain of attraction of the type I extreme-value distribution Λ(x). In this paper we derive uniform rates of convergence of Fn to Λfor a large class of distributions F. We also generalise the penultimate approximation of Fisher and Tippett (1928) and show that for many F a type II or type III extreme-value distribution gives a better approximation than the limiting type I distribution.

Keywords

EXTREME-VALUE DISTRIBUTIONRATE OF CONVERGENCE
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 4 , December 1982 , pp. 833 - 854
Copyright
Copyright © Applied Probability Trust 1982 

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