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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. Ioannides, Yannis M. & Overman, Henry G., 2003. "Zipf's law for cities: an empirical examination," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 33(2), pages 127-137, March.
  2. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, American Economic Association, vol. 99(4), pages 1676-83, September.
  3. Gabaix, Xavier & Ioannides, Yannis M., 2004. "The evolution of city size distributions," Handbook of Regional and Urban Economics, Elsevier, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378 Elsevier.
  4. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, American Economic Association, vol. 94(5), pages 1429-1451, December.
  5. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, Oxford University Press, vol. 3(4), pages 343-372, October.
  6. Kwok Tong Soo, 2004. "Zipfs Law for Cities: A Cross Country Investigation," CEP Discussion Papers, Centre for Economic Performance, LSE dp0641, Centre for Economic Performance, LSE.
  7. Sharma, Shalini, 2003. "Persistence and stability in city growth," Journal of Urban Economics, Elsevier, vol. 53(2), pages 300-320, March.
  8. Paul Cheshire & Stefano Magrini, 2005. "Population Growth in European Cities - Weather Matters, but only Nationally," ERSA conference papers ersa05p12, European Regional Science Association.
  9. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
  10. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 114(3), pages 739-767, August.
  11. William J. Reed, 2002. "On the Rank-Size Distribution for Human Settlements," Journal of Regional Science, Wiley Blackwell, Wiley Blackwell, vol. 42(1), pages 1-17.
  12. Yannis M. Ioannides & Spyros Skouras, 2009. "Gibrat's Law for (All) Cities: A Rejoinder," Discussion Papers Series, Department of Economics, Tufts University, Department of Economics, Tufts University 0740, Department of Economics, Tufts University.
  13. 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.
  14. Cheshire, Paul, 1999. "Trends in sizes and structures of urban areas," Handbook of Regional and Urban Economics, Elsevier, in: P. C. Cheshire & E. S. Mills (ed.), Handbook of Regional and Urban Economics, edition 1, volume 3, chapter 35, pages 1339-1373 Elsevier.
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