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A note on the paper of Khmaladze et al

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  • Balakrishnan, N.
  • Stepanov, A.
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    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].

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-4CGM47J-2/2/8dc0714577c09f953a2d7e1c4845b29e
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 68 (2004)
    Issue (Month): 4 (July)
    Pages: 415-419

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    Handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:415-419

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    Related research

    Keywords: Near-maximum observations Barndorff-Nielsen's lemma Strong law;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    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. 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.
    3. Li, Yun, 1999. "A note on the number of records near the maximum," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 153-158, June.
    4. 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.
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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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