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On the asymptotics of discrete order statistics

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  • Athreya, J. S.
  • Sethuraman, S.

Abstract

Let X1,X2,...,Xn be a sequence of independent, identically distributed positive integer random variables. We study the asymptotics of the likelihood that the sample maximum is achieved k times and in its spacing relative to the second highest value. Earlier and other results are discussed in context. Also, some investigation is made when the sample is Markovian. Different results emerge in this case.

Suggested Citation

  • Athreya, J. S. & Sethuraman, S., 2001. "On the asymptotics of discrete order statistics," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 243-249, October.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:3:p:243-249
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    References listed on IDEAS

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    1. Baryshnikov, Yuliy & Eisenberg, Bennett & Stengle, Gilbert, 1995. "A necessary and sufficient condition for the existence of the limiting probability of a tie for first place," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 203-209, May.
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    Cited by:

    1. Arvydas Astrauskas, 2023. "Some Bounds for the Expectations of Functions on Order Statistics and Their Applications," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1116-1147, June.

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