IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v84y2022i2d10.1007_s13571-022-00282-5.html
   My bibliography  Save this article

Chance Mechanisms Involving Sibuya Distribution and its Relatives

Author

Listed:
  • Thierry E. Huillet

    (CY Cergy Paris Université)

Abstract

The two-parameters generalized Sibuya discrete distributions capture the essence of random phenomena presenting large probability mass near the lower bound of its support balanced with heavy-tails in their deep upper bound. They are heavy-tailed as a result of the reinforcement mechanism that produced them, related to the modern notion of preferential attachment. We describe stochastic mechanisms (chiefly Markov chains) leading to the emergence of such distributions, starting with the particular case of the one-parameter Simon distribution appearing in the context of word frequencies occurring in a textbook. We exhibit some of the remarkable statistical properties of the generalized Sibuya distributions. A second related two-parameters Sibuya family is investigated in the same spirit: the class of scaled Sibuya distributions.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sankhb:v:84:y:2022:i:2:d:10.1007_s13571-022-00282-5
    DOI: 10.1007/s13571-022-00282-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-022-00282-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s13571-022-00282-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pillai, R. N. & Jayakumar, K., 1995. "Discrete Mittag-Leffler distributions," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 271-274, May.
    2. 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.
    3. Holger Dette & James Allen Fill & Jim Pitman & William J. Studden, 1997. "Wall and Siegmund Duality Relations for Birth and Death Chains with Reflecting Barrier," Journal of Theoretical Probability, Springer, vol. 10(2), pages 349-374, April.
    4. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    5. Thierry E. Huillet, 2020. "On New Mechanisms Leading to Heavy-Tailed Distributions Related to the Ones Of Yule-Simon," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 321-344, March.
    6. Devroye, Luc, 1993. "A triptych of discrete distributions related to the stable law," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 349-351, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Thierry E. Huillet, 2020. "On New Mechanisms Leading to Heavy-Tailed Distributions Related to the Ones Of Yule-Simon," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 321-344, March.
    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. 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.
    5. Buddana Amrutha & Kozubowski Tomasz J., 2014. "Discrete Pareto Distributions," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 143-156, December.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Masanao Aoki, 2006. "Thermodynamic Limits of Macroeconomic or Financial Models: One-and Two-Parameter Poisson-Dirichlet Models (Forthcoming in "Journal of Economic Dynamics and Control", 2007. )," CARF F-Series CARF-F-083, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    12. Nadjib Bouzar & K. Jayakumar, 2008. "Time series with discrete semistable marginals," Statistical Papers, Springer, vol. 49(4), pages 619-635, October.
    13. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    14. Sapatinas, Theofanis, 1995. "Characterizations of probability distributions based on discrete p-monotonicity," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 339-344, September.
    15. Emad-Eldin Aly & Nadjib Bouzar, 2000. "On Geometric Infinite Divisibility and Stability," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 790-799, December.
    16. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
    17. Subrata Chakraborty & S. H. Ong, 2017. "Mittag - Leffler function distribution - a new generalization of hyper-Poisson distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-17, December.
    18. Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
    19. Michael Grabchak, 2022. "Discrete Tempered Stable Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1877-1890, September.
    20. Masanao Aoki & Hiroshi Yoshikawa, 2012. "Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 7(1), pages 1-22, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankhb:v:84:y:2022:i:2:d:10.1007_s13571-022-00282-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.