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A dynamic model for city size distribution beyond Zipf's law

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  • Benguigui, Lucien
  • Blumenfeld-Lieberthal, Efrat

Abstract

We present a growth model for a system of cities. This model recovers not only Zipf's law but also other kinds of city size distributions (CSDs). A new positive exponent α, which yields Zipf's law only when equal to 1, was introduced. We define three classes of CSD depending on the value of α: larger than, smaller than, or equal to 1. The model is based on a random growth of the city population together with the variation of the number of cities in the system. The striking result is the peculiar behavior of the model: it is only statistical deterministic. Moreover, we found that the exponent α may be larger, smaller or equal to 1, just like in real systems of cities, depending on the rate of creation of new cities and the time elapsed during the growth. It is to our knowledge the first time that the influence of the time on the type of the distribution is investigated. The results of the model are in very good agreement with real CSD. The classification and model can be also applied to other entities like countries, incomes, firms, etc

Suggested Citation

  • Benguigui, Lucien & Blumenfeld-Lieberthal, Efrat, 2007. "A dynamic model for city size distribution beyond Zipf's law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 613-627.
    • Handle: RePEc:eee:phsmap:v:384:y:2007:i:2:p:613-627
    DOI: 10.1016/j.physa.2007.05.059
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    Citations

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    Cited by:

    1. Rafael González-Val, 2011. "Deviations from Zipf’s Law for American Cities," Urban Studies, Urban Studies Journal Limited, vol. 48(5), pages 1017-1035, April.
    2. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    3. Jiejing Wang & Yanguang Chen, 2021. "Economic Transition and the Evolution of City-Size Distribution of China’s Urban System," Sustainability, MDPI, vol. 13(6), pages 1-15, March.
    4. Grachev, Gennady A., 2022. "Size distribution of states, counties, and cities in the USA: New inequality form information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    5. Andrew T. Balthrop, 2021. "Gibrat’s law in the trucking industry," Empirical Economics, Springer, vol. 61(1), pages 339-354, July.
    6. Kwong, Hok Shing & Nadarajah, Saralees, 2019. "A note on “Pareto tails and lognormal body of US cities size distribution”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 55-62.
    7. Chen, Yanguang, 2021. "Exploring the level of urbanization based on Zipf’s scaling exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    8. Dimitrios TSIOTAS, 2016. "City-Size Or Rank-Size Distribution? An Empirical Analysis On Greek Urban Populations," Theoretical and Empirical Researches in Urban Management, Research Centre in Public Administration and Public Services, Bucharest, Romania, vol. 11(4), pages 5-16, November.
    9. Chen, Yanguang, 2012. "Zipf’s law, 1/f noise, and fractal hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 63-73.
    10. Chen, Yanguang, 2016. "The evolution of Zipf’s law indicative of city development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 555-567.
    11. Tomaz Ponce DENTINHO & Cristina SERBANICA, 2020. "Space justice, demographic resilience and sustainability. Revelations of the evolution of the population hierarchy of the regions of Romania from 1948 to 2011," Eastern Journal of European Studies, Centre for European Studies, Alexandru Ioan Cuza University, vol. 11, pages 27-44, June.

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