On the Asymptotic Behavior of Sums of Order Statistics from a Distribution with a Slowly Varying Upper Tail

  • Erich Haeusler
  • David M. Mason
Part of the Progress in Probability book series (PRPR, volume 23)


Let (X n)n≥1 be a sequence of independent non-negative random variables from a common distribution function F with a regiilarly varying upper tail. A number of results are presented on the stability, asymptotic distribution and law of the iterated logarithm for trimmed sums formed by deleting a number of the upper extreme values from the partial sum X 1 +...+X n at each stage n. The methods of proof are entirely based on quantile function techniques. This paper should provide the reader with a good introduction to some of the possibilities and the scope of this methodology.


Asymptotic Distribution Empirical Process Iterate Logarithm Empirical Distribution Function Common Distribution Function 
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

© Birkhäuser Boston 1991

Authors and Affiliations

  • Erich Haeusler
    • 1
  • David M. Mason
    • 2
  1. 1.Mathematical InstituteUniversity of MunichMunich 2West Germany
  2. 2.Department of Mathematics SciencesUniversity of DelawareNewarkUSA

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