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On the rate of convergence of normal extremes

  • Peter Hall (a1)
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.

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Corresponding author
Present address: Department of Statistics, S.G.S., The Australian National University, P.O. Box 4, Canberra, A.C.T. 2600, Australia.
References
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Gnedenko B. V. (1943) Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. 44, 423453.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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