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Zipf law for Brazilian cities

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  • Moura, Newton J.
  • Ribeiro, Marcelo B.

Abstract

This work studies the Zipf law for cities in Brazil. Data from censuses of 1970, 1980, 1991 and 2000 were used to select a sample containing only cities with 30,000 inhabitants or more. The results show that the population distribution in Brazilian cities does follow a power-law similar to the ones found in other countries. Estimates of the power-law exponent were found to be 2.22±0.34 for the 1970 and 1980 censuses, and 2.26±0.11 for censuses of 1991 and 2000. More accurate results were obtained with the maximum likelihood estimator, showing an exponent equal to 2.41 for 1970 and 2.36 for the other 3 years.

Suggested Citation

  • Moura, Newton J. & Ribeiro, Marcelo B., 2006. "Zipf law for Brazilian cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 441-448.
  • Handle: RePEc:eee:phsmap:v:367:y:2006:i:c:p:441-448 DOI: 10.1016/j.physa.2005.11.038
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    References listed on IDEAS

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    1. Katayama, Katsuki & Sakata, Yasuo & Horiguchi, Tsuyoshi, 2002. "Sparse coding for layered neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 532-546.
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    2. Heitor Reis, A., 2008. "Constructal view of the scaling laws of street networks — the dynamics behind geometry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 617-622.
    3. Chen, Yanguang, 2012. "The rank-size scaling law and entropy-maximizing principle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 767-778.
    4. Simos Meintanis, 2009. "A unified approach of testing for discrete and continuous Pareto laws," Statistical Papers, Springer, vol. 50(3), pages 569-580, June.
    5. Jorge Díaz-Lanchas & Carlos Llano & Asier Minondo & Francisco Requena, 2018. "Cities export specialization," Applied Economics Letters, Taylor & Francis Journals, pages 38-42.
    6. Sarabia, José María & Prieto, Faustino, 2009. "The Pareto-positive stable distribution: A new descriptive model for city size data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4179-4191.
    7. Chami Figueira, F. & Moura, N.J. & Ribeiro, M.B., 2011. "The Gompertz–Pareto income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 689-698.
    8. Chen, Yanguang & Wang, Jiejing, 2014. "Recursive subdivision of urban space and Zipf’s law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 392-404.
    9. Valente J. Matlaba & Mark J. Holmes & Philip McCann & Jacques Poot, 2013. "A Century Of The Evolution Of The Urban System In Brazil," Review of Urban & Regional Development Studies, Wiley Blackwell, vol. 25(3), pages 129-151, November.
    10. Kii, Masanobu & Akimoto, Keigo & Doi, Kenji, 2012. "Random-growth urban model with geographical fitness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5960-5970.
    11. Calderín-Ojeda, Enrique, 2016. "The distribution of all French communes: A composite parametric approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 385-394.
    12. Gómez-Déniz, Emilio & Calderín-Ojeda, Enrique, 2015. "On the use of the Pareto ArcTan distribution for describing city size in Australia and New Zealand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 821-832.

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