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Probability Theory and Related Fields

, Volume 78, Issue 1, pp 39–50 | Cite as

On the asymptotic joint distribution of an unbounded number of sample extremes

  • Ishay Weissman
Article

Summary

Convergence of the sample maximum to a nondegenerate random variable, as the sample sizen→∞, implies the convergence in distribution of thek largest sample extremes to ak-dimensional random vectorM k , for all fixedk. If we letk=k(n)→∞,k/n→0, then a question arises in a natural way: how fast cank grow so that asymptotic probability statements are unaffected when sample extremes are replaced byM k . We answer this question for two classes of events-the class of all Lebesgue sets inR k and the class of events of the form\(\left( {x \in R^k :\sum\limits_1^k {x_i } \leqq a} \right)\).

Keywords

Stochastic Process Probability Theory Mathematical Biology Probability Statement Joint Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Ishay Weissman
    • 1
  1. 1.Israel Institute of Technology, Faculty of Industrial Engineering and ManagementTechnionTechnion City, HaifaIsrael

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