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On the limit behavior of extreme order statistics

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Abstract

Anderson and Sethuraman described a class of distributions on positive integers for which the sample maximum and other extreme order statistics are asymptotically concentrated on k values. We prove a similar result for general distributions. Bibliography: 4 titles.

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References

  1. B. V. Gnedenko, “Sur la distribution limite du terme maximum d’une série aléatoire,” Ann. Math., 44, 423–453 (1943).

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  2. C. Anderson, “Extreme value theory for a class of discrete distributions with applications to some stochastic processes,” J. Appl. Probab., 7, 99–113 (1970).

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  3. J. Athreya and S. Sethuraman, “On the asymptotics of discrete order statistics,” Statist. Probab. Lett., 54, 243–249 (2001).

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  4. S. Sethuraman, “A clustering law for some discrete order statistics,” J. Appl. Probab., 40, 226–241 (2003).

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    A. I. Martikainen

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  1. A. I. Martikainen
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 106–109.

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Martikainen, A.I. On the limit behavior of extreme order statistics. J Math Sci 137, 4546–4548 (2006). https://doi.org/10.1007/s10958-006-0248-x

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  • DOI: https://doi.org/10.1007/s10958-006-0248-x

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