Truncated lognormal distributions and scaling in the size of naturally defined population clusters

TL;DR

This study analyzes the size distribution of population clusters in a European region, revealing that lognormal distributions better describe the data than power-law models, especially across a wide range of cluster sizes.

Contribution

It demonstrates that population cluster sizes follow lognormal distributions over a broad range, challenging the common assumption of power-law behavior in such data.

Findings

Cluster populations span six orders of magnitude.

Lognormal fits outperform power-law models across the entire range.

Limited applicability of Zipf's law to high-population clusters.

Abstract

Using population data of high spatial resolution for a region in the south of Europe, we define cities by aggregating individuals to form connected clusters. The resulting cluster-population distributions show a smooth decreasing behavior covering six orders of magnitude. We perform a detailed study of the distributions, using state-of-the-art statistical tools. By means of scaling analysis we rule out the existence of a power-law regime in the low-population range. The logarithmic-coefficient-of-variation test allows us to establish that the power-law tail for high population, characteristic of Zipf's law, has a rather limited range of applicability. Instead, lognormal fits describe the population distributions in a range covering from a few dozens individuals to more than one million (which corresponds to the population of the largest cluster).