IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v384y2007i2p613-627.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437107006061
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2007.05.059?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Andrew T. Balthrop, 2021. "Gibrat’s law in the trucking industry," Empirical Economics, Springer, vol. 61(1), pages 339-354, July.
    3. 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.
    4. 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).
    5. Chen, Yanguang, 2012. "Zipf’s law, 1/f noise, and fractal hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 63-73.
    6. 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.
    7. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    8. 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.
    9. 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).
    10. 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.
    11. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:384:y:2007:i:2:p:613-627. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.