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A note on the paper of Khmaladze et al

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  • Balakrishnan, N.
  • Stepanov, A.

Abstract

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

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    1. Li, Yun, 1999. "A note on the number of records near the maximum," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 153-158, June.
    2. 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.
    3. 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.
    4. 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.
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    Cited by:

    1. Yun Li & Quanxi Shao, 2007. "Slow convergence of the number of near-maxima for Burr XII distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(1), pages 89-104, July.
    2. Serkan Eryılmaz & Alexei Stepanov, 2008. "Runs in an ordered sequence of random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 299-313, April.
    3. 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.
    4. 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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