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On the rate of convergence of normal extremes

Published online by Cambridge University Press:  14 July 2016

Peter Hall
Peter Hall*
Affiliation:
University of Melbourne
*
∗Present address: Department of Statistics, S.G.S., The Australian National University, P.O. Box 4, Canberra, A.C.T. 2600, Australia.
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Abstract

Let Yn denote the largest of n independent N(0, 1) variables. It is shown that if the constants an and bn are chosen in an optimal way then the rate of convergence of (Yn – bn)/an to the extreme value distribution exp(–e–x), as measured by the supremum metric or the Lévy metric, is proportional to 1/log n.

Keywords

NORMAL DISTRIBUTIONEXTREME VALUEEXTREME VALUE DISTRIBUTIONRATE OF CONVERGENCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 433 - 439
Copyright
Copyright © Applied Probability Trust 1979 

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References

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