On the city size distribution: A finite mixture interpretation

Abstract

Previous studies have shown that city size is lognormally distributed but have not reached a consensus on the shape of the upper tail. Using three datasets of U.S. cities and empirical distribution function statistics, I show that (1) the entire city size distribution is not lognormally distributed; (2) Zipf’s law does not hold generally; and (3) the power-law tail is robust. I then provide an alternative explanation for the observed fat tail: A mixture of lognormal distributions can generate a power law tail. In fact, this fat tail has its statistical origin in Shaked’s theorem. Finally, I provide an urban growth theory to explain how heterogeneous growth factors form a mixture that shapes the aggregate city size distribution.