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On the expectation of the maximum of IID geometric random variables

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  • Eisenberg, Bennett

Abstract

A study of the expected value of the maximum of independent, identically distributed (IID) geometric random variables is presented based on the Fourier analysis of the distribution of the fractional part of the maximum of corresponding IID exponential random variables.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:78:y:2008:i:2:p:135-143
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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. Brands, J. J. A. M. & Steutel, F. W. & Wilms, R. J. G., 1994. "On the number of maxima in a discrete sample," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 209-217, June.
    3. Jeske, Daniel R. & Blessinger, Todd, 2004. "Tunable Approximations for the Mean and Variance of the Maximum of Heterogeneous Geometrically Distributed Random Variables," The American Statistician, American Statistical Association, vol. 58, pages 322-327, November.
    4. Olofsson, Peter, 1999. "A Poisson approximation with applications to the number of maxima in a discrete sample," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 23-27, August.
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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. Fontes, Luiz Renato & Schinazi, Rinaldo B., 2019. "Implosion of a pure death process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1171-1174.
    3. Thierry E. Huillet, 2019. "Partitioning Problems Arising From Independent Shifted-Geometric and Exponential Samples With Unequal Intensities," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(6), pages 1-31, November.

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