Size distribution of states, counties, and cities in the USA: New inequality form information

Abstract

In this article, we propose a new approach for studying the patterns of size distribution in settlement systems, based on the analysis of the shape of the Pareto curve (PC). To study the shape of the PC, we used the Gini coefficient, the asymmetry coefficient, and, by analogy with the physics of phase transitions, critical exponent — the index of the PC degree in the neighborhood of zero. An empirical analysis of the PC of various levels of aggregation in the US settlement system has been performed. The form of size distribution of states was studied by decades from 1790 to 2010. The spatial analysis of the PC shape for counties and cities was performed for 2010. The results of an empirical study showed that the PC of the states had left-hand asymmetry over 220 years. The PC of counties and cities had both right-hand and left-hand asymmetries. The obtained results explain in which cases the Pareto distribution having a PC with right-hand asymmetry, and the lognormal distribution with a symmetric PC may not correspond objectively to real settlement systems. As an alternative to power-series distribution and lognormal distribution, we considered an analytically simple two-parameter model with a wide range of PC asymmetry that combines the properties of power-series distribution and lognormal distribution. Verification of the model showed that it adequately described the size of settlements in homogeneous settlement systems.