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Rank-Size Distribution and the Process of Urban Growth

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From data on French cities' population covering almost two centuries, the viability of rank-size parameters for describing the evolution of city size distributions is tested. We first demonstrate the sensitivity of the Pareto's exponent to the variations of city sample size. The population threshold for which the adjustment of the city size distribution remains stable appears considerably lower than usually admitted. Then it is shown that the non-Paretian behaviour of city size distributions which appears in some censuses can be linked to the particular growth process of middle-sized cities. It can be explained in terms of deviations of Gibrat's law of proportionate effect and modelled in a simple way.

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