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The accuracy of graphs to describe size distributions

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  • Rafael Gonz�lez-Val
  • Arturo Ramos
  • Fernando Sanz-Gracia

Abstract

This article 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 United States, Spain and Italy) over all of the twentieth century. We explain the advantages and disadvantages associated with these graphic methods and derive some statistical properties.

Suggested Citation

  • Rafael Gonz�lez-Val & Arturo Ramos & Fernando Sanz-Gracia, 2013. "The accuracy of graphs to describe size distributions," Applied Economics Letters, Taylor & Francis Journals, vol. 20(17), pages 1580-1585, November.
  • Handle: RePEc:taf:apeclt:v:20:y:2013:i:17:p:1580-1585
    DOI: 10.1080/13504851.2013.829187
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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.
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    Citations

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    Cited by:

    1. Rafael González‐Val, 2019. "Historical urban growth in Europe (1300–1800)," Papers in Regional Science, Wiley Blackwell, vol. 98(2), pages 1115-1136, April.
    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. Miguel Puente-Ajovín & Arturo Ramos & Fernando Sanz-Gracia, 2020. "Is there a universal parametric city size distribution? Empirical evidence for 70 countries," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 65(3), pages 727-741, December.
    4. Rafael González-Val, 2016. "War Size Distribution: Empirical Regularities Behind Conflicts," Defence and Peace Economics, Taylor & Francis Journals, vol. 27(6), pages 838-853, November.
    5. Massing, Till & Puente-Ajovín, Miguel & Ramos, Arturo, 2020. "On the parametric description of log-growth rates of cities’ sizes of four European countries and the USA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    6. Miguel Puente-Ajovín & Arturo Ramos & Fernando Sanz-Gracia, 0. "Is there a universal parametric city size distribution? Empirical evidence for 70 countries," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 0, pages 1-15.
    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.
    8. Arturo Ramos, 2017. "Are the log-growth rates of city sizes distributed normally? Empirical evidence for the USA," Empirical Economics, Springer, vol. 53(3), pages 1109-1123, November.
    9. Campolieti, Michele & Ramos, Arturo, 2021. "The distribution of strike size: Empirical evidence from Europe and North America in the 19th and 20th centuries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    10. 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.
    11. Rafael González-Val, 2021. "The Probability Distribution of Worldwide Forest Areas," Sustainability, MDPI, Open Access Journal, vol. 13(3), pages 1-19, January.
    12. 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.

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    More about this item

    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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