Abstract
We studied the parametric description of the city size distribution (CSD) of 70 different countries (developed and developing) using seven models, as follows: the lognormal (LN), the loglogistic (LL), the double Pareto lognormal (dPLN), the two-lognormal (2LN), the two-loglogistic (2LL), the three-lognormal (3LN) and the three-loglogistic (3LL). Our results show that 3LN and 3LL are the best densities in terms of non-rejections out of standard statistical tests. Meanwhile, according to the information criteria AIC and BIC, there is no systematically dominant distribution.
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Notes
Data from the World Bank for the year 2011.
The log-likelihoods of the 2LN and 3LN can be maximized in a relatively simple way by an Expectation-Minimization (EM) algorithm (see, e.g, McLachlan and Krishnan (2008)). However, the results are the same to the approach taken here up to, say, a precision of \(10^{-4}\).
We have taken this idea from an anonymous referee. We thank them for such an appropriate observation.
In this line of reasoning, Pumain et al. (2015) also emphasize that, apart from the time period and some non-essential peculiarities, the urbanization process of the BRICS resembles that of Europe and the United States.
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Financial support from Ministerio de Economía y Competitividad (ECO2017-82246-P) and support by Aragon Government (ADETRE Consolidated Group) is acknowledged.
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Puente-Ajovín, M., Ramos, A. & Sanz-Gracia, F. Is there a universal parametric city size distribution? Empirical evidence for 70 countries. Ann Reg Sci 65, 727–741 (2020). https://doi.org/10.1007/s00168-020-01001-6
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DOI: https://doi.org/10.1007/s00168-020-01001-6