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Size Distributions for All Cities: Which One is Best?

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  • González-Val, Rafael
  • Ramos, Arturo
  • Sanz, Fernando
  • Vera-Cabello, María

Abstract

This paper analyses in detail the features offered by three distributions used in urban economics to describe city size distributions: lognormal, q-exponential and double Pareto lognormal, and another one of use in other areas of economics: the log-logistic. We use a large database which covers all cities with no size restriction in the US, Spain and Italy from 1900 until 2010, and, in addition, the last available year for the rest of the countries of the OECD. We estimate the previous four density functions by maximum likelihood. To check the goodness of the fit in all periods and for the thirty-four countries we use the Kolmogorov-Smirnov and Cramér-von Mises tests, and compute the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). The results show that the distribution which best fits the data in most of the cases (86.76%) is the double Pareto lognormal.

Suggested Citation

  • González-Val, Rafael & Ramos, Arturo & Sanz, Fernando & Vera-Cabello, María, 2013. "Size Distributions for All Cities: Which One is Best?," MPRA Paper 44314, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:44314
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    More about this item

    Keywords

    city size distribution; double Pareto lognormal; log-logistic; q-exponential; lognormal;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General

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