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Integer valued stable random variables

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  • Klebanov, Lev B.
  • Slámová, Lenka

Abstract

The aim of this paper is to define the notion of stability for random variables on Z. A definition of discrete stable distributions is introduced and we study properties of such distributions. The generating functions are given, as well as the probabilities of lattice distribution. We show how these distributions converge to classical stable distributions and thus can be considered as a discrete approximation of their absolutely continuous counterparts.

Suggested Citation

  • Klebanov, Lev B. & Slámová, Lenka, 2013. "Integer valued stable random variables," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1513-1519.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:6:p:1513-1519
    DOI: 10.1016/j.spl.2013.02.016
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    References listed on IDEAS

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    5. Press, S. J., 1972. "Multivariate stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 2(4), pages 444-462, December.
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    7. 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.
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    Cited by:

    1. Lucio Barabesi & Luca Pratelli, 2014. "Discussion of “On simulation and properties of the stable law” by L. Devroye and L. James," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 345-351, August.
    2. Michael Grabchak, 2022. "Discrete Tempered Stable Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1877-1890, September.
    3. Krutto Annika & Haugdahl Nøst Therese & Thoresen Magne, 2024. "A heavy-tailed model for analyzing miRNA-seq raw read counts," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 23(1), pages 1-30.

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