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Asymptotic properties of random extremes under general normalization from nonidentical distributions


  • H.M. Barakat


  • E.M. Nigm
  • M.E. El-Adll


In this paper we study the weak convergence of the generally normalized extremes (extremes under nonlinear monotone normalization) of random number of independent (nonidentically distributed) random variables. When the random sample size is assumed to converge in probability and the interrelation between the basic variables and their random size is not restricted, the limit forms as well as the sufficient conditions of convergence are derived. Moreover, when the random sample size is assumed to converge weakly and independent of the basic variables, the necessary and sufficient conditions for the convergence are derived. Copyright Springer-Verlag 2004

Suggested Citation

  • H.M. Barakat & E.M. Nigm & M.E. El-Adll, 2004. "Asymptotic properties of random extremes under general normalization from nonidentical distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(3), pages 275-287, June.
  • Handle: RePEc:spr:metrik:v:59:y:2004:i:3:p:275-287
    DOI: 10.1007/s001840300284

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    Cited by:

    1. AL-Hussaini, Essam K. & El-Adll, Magdy E., 2004. "Asymptotic distribution of normalized maximum under finite mixture models," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 109-117, October.
    2. E. Nigm, 2006. "Bootstrapping extremes of random variables under power normalization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 257-269, June.


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