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The Zipf-Polylog distribution: Modeling human interactions through social networks

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

Abstract

The Zipf distribution attracts considerable attention because it helps describe data from natural as well as man-made systems. Nevertheless, in most of the cases the Zipf is only appropriate to fit data in the upper tail. This is why it is important to dispose of Zipf extensions that allow to fit the data in its entire range. In this paper, we introduce the Zipf-Polylog family of distributions as a two-parameter generalization of the Zipf. The extended family contains the Zipf, the geometric, the logarithmic series and the shifted negative binomial with two successes, as particular distributions. We deduce important properties of the new family and demonstrate its suitability by analyzing the degree sequence of two real networks in all its range.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:603:y:2022:i:c:s037843712200454x
    DOI: 10.1016/j.physa.2022.127680
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    References listed on IDEAS

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    1. Wang, Zhenhua & Ren, Ming & Gao, Dong & Li, Zhuang, 2023. "A Zipf's law-based text generation approach for addressing imbalance in entity extraction," Journal of Informetrics, Elsevier, vol. 17(4).

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