Truncated lognormal distributions and scaling in the size of naturally defined 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).

Presented (in part) by Elsa Arcaute at the Conference on Complex Systems (CCS) 2019, Singapore

References in corpus (5)

• Power-law distributions in empirical data
• Laws of Population Growth
• The statistical physics of Cities
• Universality of rain event size distributions
• The Mean/Max Statistic in Extreme Value Analysis

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