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On the use of the Pareto ArcTan distribution for describing city size in Australia and New Zealand

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  • Gómez-Déniz, Emilio
  • Calderín-Ojeda, Enrique

Abstract

The circular inverse of the tangent function is used to simply derive a generalization of the Pareto distribution, the Pareto ArcTan (PAT) distribution. This model includes as limiting cases Pareto and Zipf distributions. This new probabilistic family is used to describe city size data for Australia and New Zealand. Urban agglomerations of these two countries presents similar features, a few large metropolitan areas with a steadily increasing population in the last years and many small cities. The PAT distribution improves the performance of other traditionally used models in urban agglomeration economics such as the classical Pareto, lognormal and the recently proposed Pareto positive stable.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:436:y:2015:i:c:p:821-832
    DOI: 10.1016/j.physa.2015.02.097
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    1. Ertugrul Deliktas & A. Özlem Önder & Metin Karadag, 2013. "The Size Distribution of Cities and Determinants of City Growth in Turkey," European Planning Studies, Taylor & Francis Journals, vol. 21(2), pages 251-263, February.
    2. Bosker, Maarten & Brakman, Steven & Garretsen, Harry & Schramm, Marc, 2008. "A century of shocks: The evolution of the German city size distribution 1925-1999," Regional Science and Urban Economics, Elsevier, vol. 38(4), pages 330-347, July.
    3. Rosen, Kenneth T. & Resnick, Mitchel, 1980. "The size distribution of cities: An examination of the Pareto law and primacy," Journal of Urban Economics, Elsevier, vol. 8(2), pages 165-186, September.
    4. Shunfeng Song & Kevin Honglin Zhang, 2002. "Urbanisation and City Size Distribution in China," Urban Studies, Urban Studies Journal Limited, vol. 39(12), pages 2317-2327, November.
    5. Giesen, Kristian & Zimmermann, Arndt & Suedekum, Jens, 2010. "The size distribution across all cities - Double Pareto lognormal strikes," Journal of Urban Economics, Elsevier, vol. 68(2), pages 129-137, September.
    6. Steven Brakman & Harry Garretsen & Marc Schramm, 2004. "The strategic bombing of German cities during World War II and its impact on city growth," Journal of Economic Geography, Oxford University Press, vol. 4(2), pages 201-218, April.
    7. Anderson, Gordon & Ge, Ying, 2005. "The size distribution of Chinese cities," Regional Science and Urban Economics, Elsevier, vol. 35(6), pages 756-776, November.
    8. Marcelo Resende, 2004. "Gibrat's Law and the Growth of Cities in Brazil: A Panel Data Investigation," Urban Studies, Urban Studies Journal Limited, vol. 41(8), pages 1537-1549, July.
    9. John B. Parr & Keisuke Suzuki, 1973. "Settlement Populations and the Lognormal Distribution," Urban Studies, Urban Studies Journal Limited, vol. 10(3), pages 335-352, October.
    10. Gangopadhyay, Kausik & Basu, B., 2009. "City size distributions for India and China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(13), pages 2682-2688.
    11. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
    12. 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.
    13. Moshe Levy, 2009. "Gibrat's Law for (All) Cities: Comment," American Economic Review, American Economic Association, vol. 99(4), pages 1672-1675, September.
    14. Luckstead, Jeff & Devadoss, Stephen, 2014. "A comparison of city size distributions for China and India from 1950 to 2010," Economics Letters, Elsevier, vol. 124(2), pages 290-295.
    15. 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.
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