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Journal of Applied Mathematics and Computing

, Volume 20, Issue 1–2, pp 225–238 | Cite as

On the restricted convergence of generalized extreme order statistics

  • M. A. El-Shandidy
Article
  • 41 Downloads

Abstract

Generalized order statistics (gos) introduced by Kamps [8] as a unified approach to several models of order random variables (rv’s), e.g., (ordinary) order statistics (oos), records, sequential order statistics (sos). In a wide subclass of gos, included oos and sos, the possible limit distribution functions (df’s) of the maximum gos are obtained in Nasri-Roudsari [10]. In this paper, for this subclass, as the df of the suitably normalized extreme gos converges on an interval [c, d] to one of possible limit df’s of the extreme gos, the continuation of this (weak) convergence on the whole real line to this limit df is proved.

AMS Mathematics Subject Classification

60F05 62F15 62E20 62G30 

Key words and phrases

Week convergence generalized order statistics generalized extremes continuation of the convergence 

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Copyright information

© Korean Society for Computational & Applied Mathematics and Korean SIGCAM 2006

Authors and Affiliations

  • M. A. El-Shandidy
    • 1
  1. 1.Department of MathematicsAlexandria UniversityAlexandriaEgypt

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