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

摘要

We study rank-size distribution of cities in Japan on the basis of dataanalysis. From the census data after World War II, we find that the rank-sizedistribution of cities is composed of two parts, each of which has independentpower exponent. In addition, the power exponent of the head part of thedistribution 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 greatmergers and recovered due to population growth in middle-sized cities after thegreat Showa merger.