We report nonparametrically estimated nonlinear stochastic transition kernels for the evolution of the distribution of populations of metropolitan areas, for the period 1900 to 1990, based on US Census data. Comparison of kernels across successive time periods with the kernel for a pooled sample...

We use data for metro areas in the United States, from the US Census for 1900 - 1990, to test the validity of Zipf's Law for cities. Previous investigations are restricted to regressions of log size against log rank. In contrast, we use a nonparametric procedure to calculate local Zipf exponents...