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A discrete truncated Zipf distribution

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Listed:
  • Kwame Boamah‐Addo
  • Tomasz J. Kozubowski
  • Anna K. Panorska

Abstract

We provide a comprehensive account of fundamental properties of a truncated discrete Zipf distribution, complementing the results available in the literature. In particular, we obtain results on existence and uniqueness of maximum likelihood parameter estimators and propose new testing methodology for the shape parameter. We also include data examples illustrating applicability of this stochastic model.

Suggested Citation

  • Kwame Boamah‐Addo & Tomasz J. Kozubowski & Anna K. Panorska, 2023. "A discrete truncated Zipf distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 156-187, May.
    • Handle: RePEc:bla:stanee:v:77:y:2023:i:2:p:156-187
    DOI: 10.1111/stan.12280
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    References listed on IDEAS

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    1. Rousseau, Ronald, 2007. "The influence of missing publications on the Hirsch index," Journal of Informetrics, Elsevier, vol. 1(1), pages 2-7.
    2. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    3. Leo Egghe & Ronald Rousseau, 2006. "An informetric model for the Hirsch-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 121-129, October.
    4. C. Kapadia & R. Thomasson, 1975. "On estimating the parameter of a truncated geometric distribution by the method of moments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 269-272, December.
    5. Aban, Inmaculada B. & Meerschaert, Mark M. & Panorska, Anna K., 2006. "Parameter Estimation for the Truncated Pareto Distribution," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 270-277, March.
    6. L. Crosato & P. Ganugi, 2007. "Statistical regularity of firm size distribution: the Pareto IV and truncated Yule for Italian SCI manufacturing," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(1), pages 85-115, June.
    7. Laudagé, Christian & Desmettre, Sascha & Wenzel, Jörg, 2019. "Severity modeling of extreme insurance claims for tariffication," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 77-92.
    8. Zornig, Peter & Altmann, Gabriel, 1995. "Unified representation of Zipf distributions," Computational Statistics & Data Analysis, Elsevier, vol. 19(4), pages 461-473, April.
    9. Charles K. Amponsah & Tomasz J. Kozubowski & Anna K. Panorska, 2021. "A general stochastic model for bivariate episodes driven by a gamma sequence," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-31, December.
    10. H. Bauke, 2007. "Parameter estimation for power-law distributions by maximum likelihood methods," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 58(2), pages 167-173, July.
    11. Blank, Aharon & Solomon, Sorin, 2000. "Power laws in cities population, financial markets and internet sites (scaling in systems with a variable number of components)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 279-288.
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