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On the rate of convergence of normal extremes

  • Peter Hall (a1)

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.

Corresponding author
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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Abramowtiz M. and Stegun I. A. (1964) Handbook of Mathematical Functions. National Bureau of Standards, Washington, D.C.
Cramér H. (1946) Mathematical Methods of Statistics. Princeton University Press, Princeton, N.J.
David H. A. (1970) Order Statistics. Wiley, New York.
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, 180190.
Gnedenko B. V. (1943) Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. 44, 423453.
Zolotarev V. M. (1967) A generalization of the Lindeberg-Feller theorem. Theory Prob. Appl. 12, 608618.
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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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