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On descents after maximal values in samples of discrete random variables

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  • Yakubovich, Yu.

Abstract

We show that the expected value of the descent after the first maximum in a sample of i.i.d. discrete random variables, as the sample size grows, behaves asymptotically up to vanishing terms as the expectation of the maximal value minus the expectation of a sampled random variable, provided the latter is finite. We also show that the expected value after the last maximum exhibits the same behaviour, although it is in general slightly bigger in mean.

Suggested Citation

  • Yakubovich, Yu., 2015. "On descents after maximal values in samples of discrete random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 203-208.
    • Handle: RePEc:eee:stapro:v:105:y:2015:i:c:p:203-208
    DOI: 10.1016/j.spl.2015.06.020
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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.
    2. Archibald, Margaret & Blecher, Aubrey & Brennan, Charlotte & Knopfmacher, Arnold, 2015. "Descents following maximal values in samples of geometric random variables," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 229-240.
    3. Eisenberg, Bennett, 2008. "On the expectation of the maximum of IID geometric random variables," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 135-143, February.
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    Cited by:

    1. Archibald, Margaret & Blecher, Aubrey & Brennan, Charlotte & Knopfmacher, Arnold & Prodinger, Helmut, 2017. "Geometric random variables: Descents following maxima," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 140-147.

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