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Waiting time representation of discrete distributions

Author

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  • Kozubowski, Tomasz J.
  • Młynarczyk, Dorota
  • Panorska, Anna K.

Abstract

We discuss a representation of any probability distribution on the set of non-negative integers as a waiting time distribution in a sequence of independent Bernoulli trials. Several associated results are derived and illustrated by examples. Multivariate extensions are briefly treated as well.

Suggested Citation

  • Kozubowski, Tomasz J. & Młynarczyk, Dorota & Panorska, Anna K., 2025. "Waiting time representation of discrete distributions," Statistics & Probability Letters, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:stapro:v:216:y:2025:i:c:s016771522400244x
    DOI: 10.1016/j.spl.2024.110275
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    References listed on IDEAS

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    1. Tomasz J. Kozubowski & Krzysztof Podgórski, 2018. "A generalized Sibuya distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 855-887, August.
    2. K. & Davis Antony Mundassery, 2007. "On bivariate geometric distribution," Statistica, Department of Statistics, University of Bologna, vol. 67(4), pages 389-404.
    3. Masaaki Sibuya, 2014. "Prediction in Ewens–Pitman sampling formula and random samples from number partitions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 833-864, October.
    4. Roy, D., 1993. "Reliability Measures in the Discrete Bivariate Set-Up and Related Characterization Results for a Bivariate Geometric Distribution," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 362-373, August.
    5. Lovison, Gianfranco, 2006. "A matrix-valued Bernoulli distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1573-1585, August.
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