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The Zipf–Poisson-stopped-sum distribution with an application for modeling the degree sequence of social networks

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  • Duarte-López, Ariel
  • Pérez-Casany, Marta
  • Valero, Jordi

Abstract

Under the Zipf Distribution, the frequency of a value is a power function of its size. Thus, when plotting frequencies versus size in log–log scale of data following that distribution, one obtains a straight line. The Zipf has been assumed to be appropriate for modeling highly skewed data from many different areas. Nevertheless, for many real data sets, the linearity is observed only in the tail; thus, the Zipf is fitted only for values larger than a given threshold and, consequently, there is a loss of information. The Zipf–Poisson-stopped-sum distribution is introduced as a more flexible alternative. It is proven that in log–log scale allows for top-concavity, maintaining the linearity in the tail. Consequently, the distribution fits properly many data sets in their entire range. To prove the suitability of our model 16 network degree sequences describing the interaction between members of a given platform have been fitted. The results have been compared with the fits obtained through other bi-parametric distributions.

Suggested Citation

  • Duarte-López, Ariel & Pérez-Casany, Marta & Valero, Jordi, 2020. "The Zipf–Poisson-stopped-sum distribution with an application for modeling the degree sequence of social networks," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:csdana:v:143:y:2020:i:c:s0167947319301938
    DOI: 10.1016/j.csda.2019.106838
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    References listed on IDEAS

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    1. Ramon Ferrer‐i‐Cancho & Michael S. Vitevitch, 2018. "The origins of Zipf's meaning‐frequency law," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 69(11), pages 1369-1379, November.
    2. Meng, Shengwang & Gao, Guangyuan, 2018. "Compound Poisson Claims Reserving Models: Extensions And Inference," ASTIN Bulletin, Cambridge University Press, vol. 48(3), pages 1137-1156, September.
    3. Zornig, Peter & Altmann, Gabriel, 1995. "Unified representation of Zipf distributions," Computational Statistics & Data Analysis, Elsevier, vol. 19(4), pages 461-473, April.
    4. Sundt, Bjørn & Jewell, William S., 1981. "Further Results on Recursive Evaluation of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 27-39, June.
    5. Wan Jing Low & Paul Wilson & Mike Thelwall, 2016. "Stopped sum models and proposed variants for citation data," Scientometrics, Springer;Akadémiai Kiadó, vol. 107(2), pages 369-384, May.
    6. Boginski, Vladimir & Butenko, Sergiy & Pardalos, Panos M., 2005. "Statistical analysis of financial networks," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 431-443, February.
    7. Yeşim Güney & Yetkin Tuaç & Olcay Arslan, 2017. "Marshall–Olkin distribution: parameter estimation and application to cancer data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2238-2250, September.
    8. Assistant Professor G. Christopher Crawford & Professor Bill McKelvey, 2018. "Using maximum likelihood estimation methods and complexity science concepts to research power law-distributed phenomena," Chapters, in: Eve Mitleton-Kelly & Alexandros Paraskevas & Christopher Day (ed.), Handbook of Research Methods in Complexity Science, chapter 12, pages 227-253, Edward Elgar Publishing.
    9. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
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    1. Valero, Jordi & Pérez-Casany, Marta & Duarte-López, Ariel, 2022. "The Zipf-Polylog distribution: Modeling human interactions through social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).

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