Does Zipf's law hold for Polish cities?

Abstract

In this paper we study Zipf's law, which postulates that the product of a city's population and its rank (the number of cities with a larger or equal population) is constant for every city in a given region. We show that the empirical literature indicates that the law may not always hold, although its general form, the rank-size rule, could be a good first approximation of city size distribution. We perform our own empirical analysis of the distribution of the population of Polish cities on the largest possible sample to find that Zipf's law is rejected for Poland as the city sizes are less evenly distributed than it predicts.