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Discrete stable random variables

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  • Christoph, Gerd
  • Schreiber, Karina

Abstract

In Steutel and van Ham (1979) a discrete analogue of stable random variables was introduced. In the present note we consider some explicit and asymptotic formulae for the probabilities of discrete stable random variables and give rates for the convergence of sequences of certain discrete stable random variables to a stable one.

Suggested Citation

  • Christoph, Gerd & Schreiber, Karina, 1998. "Discrete stable random variables," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 243-247, March.
    • Handle: RePEc:eee:stapro:v:37:y:1998:i:3:p:243-247
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    References listed on IDEAS

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    1. Devroye, Luc, 1993. "A triptych of discrete distributions related to the stable law," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 349-351, December.
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    Cited by:

    1. Di Noia, Antonio & Marcheselli, Marzia & Pisani, Caterina & Pratelli, Luca, 2023. "Censoring heavy-tail count distributions for parameter estimation with an application to stable distributions," Statistics & Probability Letters, Elsevier, vol. 202(C).
    2. Klebanov, Lev B. & Slámová, Lenka, 2013. "Integer valued stable random variables," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1513-1519.
    3. 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.
    4. Buddana Amrutha & Kozubowski Tomasz J., 2014. "Discrete Pareto Distributions," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 143-156, December.
    5. Vladimir V. Vinogradov & Richard B. Paris, 2017. "On Poisson–Tweedie mixtures," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-23, December.
    6. Rémillard Bruno & Theodorescu Radu, 2000. "Inference Based On The Empirical Probability Generating Function For Mixtures Of Poisson Distributions," Statistics & Risk Modeling, De Gruyter, vol. 18(4), pages 349-366, April.
    7. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    8. Zhu, Rong & Joe, Harry, 2009. "Modelling heavy-tailed count data using a generalised Poisson-inverse Gaussian family," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1695-1703, August.
    9. Kukla, Jonas & Möhle, Martin, 2018. "On the block counting process and the fixation line of the Bolthausen–Sznitman coalescent," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 939-962.
    10. Michael Grabchak, 2022. "Discrete Tempered Stable Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1877-1890, September.

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