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A class of discrete distributions induced by stable laws

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  • Soltani, A.R.
  • Shirvani, A.
  • Alqallaf, F.

Abstract

A new class of discrete probability distributions with infinite second moments is introduced and studied. The class is induced by stable laws, and contains the discrete stable distributions. Members of this class appear to be suitable substitutes for the Poisson distributions, as underlying statistical distributions for certain erratic phenomena. A case study on blackhole data is provided.

Suggested Citation

  • Soltani, A.R. & Shirvani, A. & Alqallaf, F., 2009. "A class of discrete distributions induced by stable laws," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1608-1614, July.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:14:p:1608-1614
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    References listed on IDEAS

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    1. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    2. 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.
    3. 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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    1. Soltani, A.R. & Tafakori, L., 2013. "A class of continuous kernels and Cauchy type heavy tail distributions," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1018-1027.
    2. A. Shirvani & A. Soltani, 2013. "A characterization for truncated cauchy random variables with nonzero skewness parameter," Computational Statistics, Springer, vol. 28(3), pages 1011-1016, June.
    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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