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Descents following maximal values in samples of geometric random variables

Author

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  • Archibald, Margaret
  • Blecher, Aubrey
  • Brennan, Charlotte
  • Knopfmacher, Arnold

Abstract

We consider samples of geometric random variables and find the average size of the descent after the first and last maximal values. These are asymptotically but not exactly equal, with the descent after the last maximum being slightly larger than that after the first. Thereafter we calculate the probability that the descent after the last maximum is equal to, greater than, or less than the descent after the first maximum. Finally we compute asymptotic expansions for these probabilities.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:97:y:2015:i:c:p:229-240
    DOI: 10.1016/j.spl.2014.11.023
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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 & Knopfmacher, Arnold, 2009. "The average position of the dth maximum in a sample of geometric random variables," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 864-872, April.
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    Cited by:

    1. Yakubovich, Yu., 2015. "On descents after maximal values in samples of discrete random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 203-208.
    2. 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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