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Geometric random variables: Descents following maxima

Author

Listed:
  • Archibald, Margaret
  • Blecher, Aubrey
  • Brennan, Charlotte
  • Knopfmacher, Arnold
  • Prodinger, Helmut

Abstract

We study descents from maximal elements in samples of geometric random variables and consider two different averages for this statistic. We then compare the asymptotics of these averages as the number of parts in the samples tends to infinity, and also find an asymptotic expression for the mean of the greatest descent after a maximum value in such a sample.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:124:y:2017:i:c:p:140-147
    DOI: 10.1016/j.spl.2017.01.017
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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. Yakubovich, Yu., 2015. "On descents after maximal values in samples of discrete random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 203-208.
    3. 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.
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