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The accuracy of graphs to describe size distributions

Author

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

Abstract

This paper analyses the performance of the graphs traditionally used to study size distributions: histograms, Zipf plots (double logarithmic graphs of rank compared to size) and plotted cumulative density functions. A lognormal distribution is fitted to urban data from three countries (the US, Spain and Italy) over all of the 20th century. We explain the advantages and disadvantages associated with these graphic methods and derive some statistical properties.

Suggested Citation

  • González-Val, Rafael & Ramos, Arturo & Sanz-Gracia, Fernando, 2013. "The accuracy of graphs to describe size distributions," MPRA Paper 48577, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:48577
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    File URL: https://mpra.ub.uni-muenchen.de/48577/1/MPRA_paper_48577.pdf
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    References listed on IDEAS

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    1. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    2. 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.
    3. Stanley, Michael H. R. & Buldyrev, Sergey V. & Havlin, Shlomo & Mantegna, Rosario N. & Salinger, Michael A. & Eugene Stanley, H., 1995. "Zipf plots and the size distribution of firms," Economics Letters, Elsevier, vol. 49(4), pages 453-457, October.
    4. Moshe Levy, 2009. "Gibrat's Law for (All) Cities: Comment," American Economic Review, American Economic Association, vol. 99(4), pages 1672-1675, September.
    5. González-Val, Rafael & Lanaspa, Luis & Sanz, Fernando, 2008. "New Evidence on Gibrat’s Law for Cities," MPRA Paper 10411, University Library of Munich, Germany.
    6. Rafael González-Val & Arturo Ramos & Fernando Sanz-Gracia & María Vera-Cabello, 2015. "Size distributions for all cities: Which one is best?," Papers in Regional Science, Wiley Blackwell, vol. 94(1), pages 177-196, March.
    7. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, vol. 99(4), pages 1676-1683, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Rafael González-Val, 2016. "Historical urban growth in Europe (1300–1800)," Working Papers 2016/8, Institut d'Economia de Barcelona (IEB).
    2. Miguel Puente-Ajovín & Arturo Ramos, 2015. "On the parametric description of the French, German, Italian and Spanish city size distributions," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 54(2), pages 489-509, March.
    3. Rafael González-Val & Arturo Ramos & Fernando Sanz-Gracia, 2014. "A new framework for US city size distribution: Empirical evidence and theory," ERSA conference papers ersa14p633, European Regional Science Association.
    4. repec:spr:empeco:v:53:y:2017:i:3:d:10.1007_s00181-016-1147-8 is not listed on IDEAS
    5. Ramos, Arturo, 2015. "Are the log-growth rates of city sizes normally distributed? Empirical evidence for the US," MPRA Paper 65584, University Library of Munich, Germany.
    6. Puente-Ajovin, Miguel & Ramos, Arturo, 2015. "An improvement over the normal distribution for log-growth rates of city sizes: Empirical evidence for France, Germany, Italy and Spain," MPRA Paper 67471, University Library of Munich, Germany.
    7. Ramos, Arturo & Sanz-Gracia, Fernando & González-Val, Rafael, 2013. "A new framework for the US city size distribution: Empirical evidence and theory," MPRA Paper 52190, University Library of Munich, Germany.

    More about this item

    Keywords

    city size distribution; Zipf plot; lognormal;

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General

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