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Asymptotics of Maxima of Discrete Random Variables

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Abstract

If X1, X2,..., Xn are independent and identically distributed discrete random variables and Mn=max (X1,..., Xn) we examine the limiting behavior of (Mn−b(n))/a(n) as n → ∞. It is well known that for discrete distributions such as Poisson and geometric the limiting distribution is not non-degenerate. However, by tuning the parameters of the discrete distribution to vary as n → ∞, it is possible to obtain non-degenerate limits for (Mn−b(n))/a(n). We consider four families of discrete distributions and show how this can be done.

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Authors and Affiliations

  1. Department of Mathematics, University of South Florida, Tampa, Florida, 33620, USA

    Saralees Nadarajah

  2. Department of Informatics and Mathematics, Airforce Academy “G. Benkovski”, Pleven, Bulgaria

    Kosto Mitov

Authors
  1. Saralees Nadarajah
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  2. Kosto Mitov
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Nadarajah, S., Mitov, K. Asymptotics of Maxima of Discrete Random Variables. Extremes 5, 287–294 (2002). https://doi.org/10.1023/A:1024081112501

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  • DOI: https://doi.org/10.1023/A:1024081112501

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