Universal City-size distributions through rank ordering

TL;DR

This paper introduces a two-parameter discrete generalized beta distribution to model global city size distributions, revealing a universal pattern across diverse countries and providing insights into urban growth and randomness.

Contribution

It proposes a novel two-parameter distribution model that fits city size data worldwide better than power laws and enables analysis of urban evolution over time.

Findings

The DGB distribution fits city size data across multiple countries better than power law.

A universal pattern in city size distributions is observed globally.

Entropy analysis offers insights into the randomness of city sizes.

Abstract

We consider a two-parameter discrete generalized beta (DGB) distribution and propose its universal applications to study the size-distribution of the urban agglomerations across various countries in the world, where the urban agglomerations include the small and mid-sized cities along with the heavily populated cities. Our proposition is validated by an exhaustive study with the 3 decades' census data for India and China and census data of USA for a time window of 8 years. Moreover, we have studied the city size distributions for many different countries, like Brazil, Italy, Sweden, Australia, Uganda etc., from all the continents around the world according to the availability of the data. The detailed analyses exhibit a unique global pattern for the city size distributions, from low to high size, across the world with various geographic and economic conditions. Further analyses based on the entropy of the distribution provide insights on the underlying randomness and spreads of the city sizes within a country. The DGB distribution, a typical rank order (RO) distribution, through its two parameters, not only fits the data on wider range of city sizes better than the well-known power law for all the countries considered, it also helps us to characterize, discriminate and study their evolution over time.