Why Does Zipf's Law Break Down in Rank-Size Distribution of Cities?

TL;DR

This paper analyzes the rank-size distribution of Japanese cities, revealing it consists of two parts with independent power exponents, and explains the breakdown and recovery of Zipf's law over time due to mergers and population changes.

Contribution

It demonstrates that the city rank-size distribution has two independent parts and explains the temporal breakdown of Zipf's law through mergers and demographic shifts.

Findings

Rank-size distribution has two parts with independent power exponents.

Zipf's law holds only during specific periods.

City mergers and population growth influence the distribution.

Abstract

We study rank-size distribution of cities in Japan on the basis of data analysis. From the census data after World War II, we find that the rank-size distribution of cities is composed of two parts, each of which has independent power exponent. In addition, the power exponent of the head part of the distribution changes in time and Zipf's law holds only in a restricted period. We show that Zipf's law broke down due to both of Showa and Heisei great mergers and recovered due to population growth in middle-sized cities after the great Showa merger.