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Asymptotic distribution of normalized maximum under finite mixture models

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  • AL-Hussaini, Essam K.
  • El-Adll, Magdy E.
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    Abstract

    In this paper, we study the asymptotic distribution of the generally normalized maximum under finite mixture models. In one of the two theorems presented, we obtain a necessary and sufficient condition for this weak convergence, as well as the limit forms. The second theorem gives sufficient conditions for this convergence when the components of the mixture have different general normalizations. Examples are given to illustrate the applications of the two theorems.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-4DB4WG6-1/2/59580f1235906207f3c14141a0e636d8
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 70 (2004)
    Issue (Month): 1 (October)
    Pages: 109-117

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    Handle: RePEc:eee:stapro:v:70:y:2004:i:1:p:109-117

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    Related research

    Keywords: Mixture distributions Weak convergence l-max stable laws p-max stable laws General normalization Domains of attraction;

    References

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    1. Christoph, Gerd & Falk, Michael, 1996. "A note on domains of attraction of p-max stable laws," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 279-284, July.
    2. H.M. Barakat & E.M. Nigm & M.E. El-Adll, 2004. "Asymptotic properties of random extremes under general normalization from nonidentical distributions," Metrika, Springer, vol. 59(3), pages 275-287, 06.
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    Cited by:
    1. M. Sreehari & S. Ravi, 2010. "On extremes of mixtures of distributions," Metrika, Springer, vol. 71(1), pages 117-123, January.

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