Is there a universal parametric city size distribution? Empirical evidence for 70 countries

TL;DR

This study evaluates seven parametric models to describe city size distributions across 70 countries, finding no single best model but highlighting the effectiveness of three-lognormal and three-loglogistic fits.

Contribution

It provides the first comprehensive empirical comparison of multiple parametric models for city size distributions across a diverse set of countries.

Findings

3LN and 3LL are the best fits based on statistical tests.

No single distribution is systematically superior according to AIC and BIC.

Different models perform variably across countries.

Abstract

We study 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.