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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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    1. Aly, E. E. A. A. & Bouzar, N., 1994. "On Some Integer-Valued Autoregressive Moving Average Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 132-151, July.
    2. Nadjib Bouzar & K. Jayakumar, 2008. "Time series with discrete semistable marginals," Statistical Papers, Springer, vol. 49(4), pages 619-635, October.
    3. Christoph, Gerd & Schreiber, Karina, 1998. "Discrete stable random variables," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 243-247, March.
    4. Press, S. J., 1972. "Multivariate stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 2(4), pages 444-462, December.
    5. 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.
    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. Nadjib Bouzar, 2004. "Discrete semi-stable distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(3), pages 497-510, September.
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    Cited by:

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