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On the best functions to describe city size distributions

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  • González-Val, Rafael
  • Ramos, Arturo
  • Sanz-Gracia, Fernando

Abstract

This paper analyses in detail the features offered by a function which is practically new to Urban Economics, the q-exponential, in describing city size distributions. We highlight two contributions. First, we propose a new and simple procedure for estimating their parameters. Second, and more importantly, we explain the characteristics associated with two traditional graphic methods (Zipf plots and cumulative density functions) for discriminating between functions. We apply them to the lognormal and q-exponential, justifying them as the best functions for explaining the entire distribution, and that the relationship between them is of complementarity.

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File URL: http://mpra.ub.uni-muenchen.de/24887/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 21921.

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Date of creation: 07 Apr 2010
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Handle: RePEc:pra:mprapa:21921

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Keywords: city size distribution; q-exponential; lognormal;

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  1. 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.
  2. Kwok Tong Soo, 2004. "Zipf's law for cities: a cross country investigation," LSE Research Online Documents on Economics 19947, London School of Economics and Political Science, LSE Library.
  3. Yannis M. Ioannides & Spyros Skouras, 2009. "Gibrat's Law for (All) Cities: A Rejoinder," Discussion Papers Series, Department of Economics, Tufts University 0740, Department of Economics, Tufts University.
  4. Paul Cheshire & Stefano Magrini, 2006. "Population growth in European cities: Weather matters - but only nationally," Regional Studies, Taylor & Francis Journals, vol. 40(1), pages 23-37.
  5. Xavier Gabaix & Yannis M. Ioannides, 2003. "The Evolution of City Size Distributions," Discussion Papers Series, Department of Economics, Tufts University 0310, Department of Economics, Tufts University.
  6. Sharma, Shalini, 2003. "Persistence and stability in city growth," Journal of Urban Economics, Elsevier, vol. 53(2), pages 300-320, March.
  7. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
  8. Y Ioannides & Henry Overman, 2000. "Zipfs Law for Cities: An Empirical Examination," CEP Discussion Papers dp0484, Centre for Economic Performance, LSE.
  9. William J. Reed, 2002. "On the Rank-Size Distribution for Human Settlements," Journal of Regional Science, Wiley Blackwell, vol. 42(1), pages 1-17.
  10. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
  11. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, vol. 99(4), pages 1676-83, September.
  12. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
  13. Cheshire, Paul, 1999. "Trends in sizes and structures of urban areas," Handbook of Regional and Urban Economics, in: P. C. Cheshire & E. S. Mills (ed.), Handbook of Regional and Urban Economics, edition 1, volume 3, chapter 35, pages 1339-1373 Elsevier.
  14. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
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