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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.

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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:70:y:2004:i:1:p:109-117
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. M. Sreehari & S. Ravi, 2010. "On extremes of mixtures of distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(1), pages 117-123, January.
    2. An, Yonghong, 2017. "Identification of first-price auctions with non-equilibrium beliefs: A measurement error approach," Journal of Econometrics, Elsevier, vol. 200(2), pages 326-343.

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