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A Universal Rank-Size Law

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  • Marcel Ausloos
  • Roy Cerqueti

Abstract

A mere hyperbolic law, like the Zipf’s law power function, is often inadequate to describe rank-size relationships. An alternative theoretical distribution is proposed based on theoretical physics arguments starting from the Yule-Simon distribution. A modeling is proposed leading to a universal form. A theoretical suggestion for the “best (or optimal) distribution”, is provided through an entropy argument. The ranking of areas through the number of cities in various countries and some sport competition ranking serves for the present illustrations.

Suggested Citation

  • Marcel Ausloos & Roy Cerqueti, 2016. "A Universal Rank-Size Law," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-15, November.
    • Handle: RePEc:plo:pone00:0166011
    DOI: 10.1371/journal.pone.0166011
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    References listed on IDEAS

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    1. Stauffer, Dietrich, 2004. "Introduction to statistical physics outside physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 1-5.
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    Cited by:

    1. Ausloos, Marcel & Eskandary, Ali & Kaur, Parmjit & Dhesi, Gurjeet, 2019. "Evidence for Gross Domestic Product growth time delay dependence over Foreign Direct Investment. A time-lag dependent correlation study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    2. Cerqueti, Roy & Ficcadenti, Valerio, 2022. "Combining rank-size and k-means for clustering countries over the COVID-19 new deaths per million," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    3. Nicola Giuseppe Castellano & Roy Cerqueti & Bruno Maria Franceschetti, 2021. "Evaluating risks-based communities of Mafia companies: a complex networks perspective," Review of Quantitative Finance and Accounting, Springer, vol. 57(4), pages 1463-1486, November.
    4. Ghosh, Abhik & Mallick, Olivia & Chattopadhay, Souvik & Basu, Banasri, 2022. "Strata-based quantification of distributional uncertainty in socio-economic indicators: A comparative study of Indian states," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    5. Nowak, Przemysław & Santolini, Marc & Singh, Chakresh & Siudem, Grzegorz & Tupikina, Liubov, 2024. "Beyond Zipf’s law: Exploring the discrete generalized beta distribution in open-source repositories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 649(C).
    6. Cerqueti, Roy & Lupi, Claudio & Pietrovito, Filomena & Pozzolo, Alberto Franco, 2022. "Rank–size distributions for banks: A cross-country analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    7. Marcel Ausloos & Claudiu Herteliu, 2021. "Statistical Analysis of the Membership Management Indicators of the Church of England UK Dioceses during the Recent (XXth Century) “Decade of Evangelism”," Stats, MDPI, vol. 4(4), pages 1-11, December.
    8. Ausloos, Marcel, 2020. "Rank–size law, financial inequality indices and gain concentrations by cyclist teams. The case of a multiple stage bicycle race, like Tour de France," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    9. Ficcadenti, Valerio & Cerqueti, Roy & Ausloos, Marcel & Dhesi, Gurjeet, 2020. "Words ranking and Hirsch index for identifying the core of the hapaxes in political texts," Journal of Informetrics, Elsevier, vol. 14(3).
    10. Ausloos, Marcel & Cerqueti, Roy & Lupi, Claudio, 2017. "Long-range properties and data validity for hydrogeological time series: The case of the Paglia river," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 39-50.
    11. Roy Cerqueti & Eleonora Cutrini, 2021. "A Framework for Modelling Economic Regional Location Processes Under Uncertainty," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(4), pages 703-725, December.
    12. Pankaj Bajracharya & Selima Sultana, 2020. "Rank-size Distribution of Cities and Municipalities in Bangladesh," Sustainability, MDPI, vol. 12(11), pages 1-26, June.

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