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Scaled Sibuya distribution and discrete self-decomposability

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  • Christoph, Gerd
  • Schreiber, Karina

Abstract

The Sibuya distribution plays an important role in considering several discrete self-decomposable distributions. Here we will consider several properties of the Sibuya distribution. The main results will concern the discrete self-decomposability and infinite divisibility of the scaled Sibuya distribution in dependence of the scale parameter.

Suggested Citation

  • Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    • Handle: RePEc:eee:stapro:v:48:y:2000:i:2:p:181-187
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    References listed on IDEAS

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    1. Christoph, Gerd & Schreiber, Karina, 1998. "Discrete stable random variables," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 243-247, March.
    2. Bondesson, Lennart & Kristiansen, Gundorph K. & Steutel, Fred W., 1996. "Infinite divisibility of random variables and their integer parts," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 271-278, July.
    3. Pakes, Anthony G., 1995. "Characterization of discrete laws via mixed sums and Markov branching processes," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 285-300, February.
    4. R. Pillai, 1990. "On Mittag-Leffler functions and related distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 157-161, March.
    5. 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. Nadjib Bouzar & K. Jayakumar, 2008. "Time series with discrete semistable marginals," Statistical Papers, Springer, vol. 49(4), pages 619-635, October.
    2. Nadjib Bouzar, 2008. "The semi-Sibuya distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 459-464, June.
    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. Thierry E. Huillet, 2022. "Chance Mechanisms Involving Sibuya Distribution and its Relatives," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 722-764, November.
    5. Peter Kern & Svenja Lage, 2023. "On Self-Similar Bernstein Functions and Corresponding Generalized Fractional Derivatives," Journal of Theoretical Probability, Springer, vol. 36(1), pages 348-371, March.
    6. 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.
    7. 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.
    8. Rodrigues, Josemar & Balakrishnan, N. & Cordeiro, Gauss M. & de Castro, Mário, 2011. "A unified view on lifetime distributions arising from selection mechanisms," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3311-3319, December.
    9. Nadjib Bouzar, 2024. "On the Convolution of Scaled Sibuya Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 699-720, August.
    10. Nadjib Bouzar, 2008. "Semi-self-decomposable distributions on Z +," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 901-917, December.
    11. N. Bouzar & S. Satheesh, 2008. "Comments on a-decomposability," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 243-252.

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