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On the asymptotic joint distribution of an unbounded number of sample extremes
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  • Published: March 1988

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

  • Ishay Weissman1 

Probability Theory and Related Fields volume 78, pages 39–50 (1988)Cite this article

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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\(\left( {x \in R^k :\sum\limits_1^k {x_i } \leqq a} \right)\).

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Authors and Affiliations

  1. Israel Institute of Technology, Faculty of Industrial Engineering and Management, Technion, 32000, Technion City, Haifa, Israel

    Ishay Weissman

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  1. Ishay Weissman
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Cite this article

Weissman, I. On the asymptotic joint distribution of an unbounded number of sample extremes. Probab. Th. Rel. Fields 78, 39–50 (1988). https://doi.org/10.1007/BF00718033

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  • Received: 09 December 1985

  • Revised: 09 December 1987

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF00718033

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Probability Statement
  • Joint Distribution
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