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 

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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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