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A note on the paper of Khmaladze et al


  • Balakrishnan, N.
  • Stepanov, A.


Let X1,...,Xn be a sequence of i.i.d. random variables from some continuous distribution function F. Let Zn(a) be the number of observations of the sample that appeared after the maximum Mn was already registered and belong to the random interval (Mn-a,Mn] (a>0). In this note, we prove a strong limit law for Zn(a) which extends the corresponding result of Khmaladze et al. [Statist. Probab. Lett. 35 (1997) 49].

Suggested Citation

  • Balakrishnan, N. & Stepanov, A., 2004. "A note on the paper of Khmaladze et al," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 415-419, July.
  • Handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:415-419

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    References listed on IDEAS

    1. Khmaladze, E. & Nadareishvili, M. & Nikabadze, A., 1997. "Asymptotic behaviour of a number of repeated records," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 49-58, August.
    2. Pakes, Anthony G. & Li, Yun, 1998. "Limit laws for the number of near maxima via the Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 395-401, November.
    3. Qi, Yongcheng, 1997. "A note on the number of maxima in a discrete sample," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 373-377, May.
    4. Li, Yun, 1999. "A note on the number of records near the maximum," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 153-158, June.
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    Cited by:

    1. Bairamov, I. & Stepanov, A., 2010. "Numbers of near-maxima for the bivariate case," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 196-205, February.
    2. Stepanov, A., 2011. "Limit theorems for runs based on 'small spacings'," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 54-61, January.


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