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

Lucien Benguigui*, Efrat Blumenfeld-Lieberthal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)613-627
Number of pages15
JournalPhysica A: Statistical Mechanics and its Applications
Issue number2
StatePublished - 15 Oct 2007
Externally publishedYes


  • City size distribution (CSD)
  • Exponent α
  • Power law


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