The distribution of all French communes: A composite parametric approach

Abstract

The distribution of the size of all French settlements (communes) from 1962 to 2012 is examined by means of a three-parameter composite Lognormal–Pareto distribution. This model is based on a Lognormal density up to an unknown threshold value and a Pareto density thereafter. Recent findings have shown that the untruncated settlement size data is in excellent agreement with the Lognormal distribution in the lower and central parts of the empirical distribution, but it follows a power law in the upper tail. For that reason, this probabilistic family, that nests both models, seems appropriate to describe urban agglomeration in France. The outcomes of this paper reveal that for the early periods (1962–1975) the upper quartile of the commune size data adheres closely to a power law distribution, whereas for later periods (2006–2012) most of the city size dynamics is explained by a Lognormal model.