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Asymptotic Distributions of Extremes

  • M. R. Leadbetter
  • Georg Lindgren
  • Holger Rootzén
Part of the Springer Series in Statistics book series (SSS)

Abstract

This chapter is primarily concerned with the central result of classical extreme value theory—the Extremal Types Theorem—which specifies the possible forms for the limiting distribution of maxima in sequences of i.i.d. random variables. In the derivation, the possible limiting distributions are identified with a class having a certain stability property—the so-called max-stable distributions. It is further shown that this class consists precisely of the three families known (loosely) as the three extreme value distributions.

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Copyright information

© Springer-Verlag New York Inc. 1983

Authors and Affiliations

  • M. R. Leadbetter
    • 1
  • Georg Lindgren
    • 2
  • Holger Rootzén
    • 3
  1. 1.Department of StatisticsThe University of North CarolinaChapel HillUSA
  2. 2.Department of Mathematical StatisticsUniversity of LundLundSweden
  3. 3.Institute of Mathematical StatisticsUniversity of CopenhagenCopenhagen øDenmark

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