Departures from Gibrat's Law, Discontinuities and City Size Distributions

Cities are complex, self-organising, evolving systems and the emergent patterns they manifest provide insight into the dynamic processes in urban systems. This article analyses city size distributions, by decade, from the south-eastern region of the US for the years 1860—1990. It determines if the distributions are clustered into size classes and documents changes in the pattern of size classes over time. A statistical hypothesis test was also performed to detect dependence between city size and growth using discrete probability calculations under the assumption of Gibrat's law. The city size distributions for the south-eastern region of the US were discontinuous, with cities clustering into distinct size classes. The analysis also identified departures from Gibrat's law, indicating variable growth rates at different scales.