An expected rank-size rule: A theoretical relationship between the rank size rule and city size distributions

Abstract

This paper investigates a theoretical relationship between the rank-size rule and city size distributions. First, a method of relating a certain city size distribution to ranked city size is formulated by employing order statistics. Second, it is shown that there do not exist city size distributions which satisfy the rank-size rule. Third, an alternative rank-size rule is proposed as E(P r)⌜(r) ⌜(r−y) =c , which is equivalent to the Pareto city size distribution. Last, an alternative statistical test for the rank-size rule is proposed to overcome a shortcoming of the conventional test. Along this line, the Hokkaido region data is analyzed.