Truncated lognormal distributions and scaling in the size of naturally defined population clusters
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 dozen individuals to more than 1×106 (which corresponds to the population of the largest cluster).
Á. Corral, F. Udina, E. Arcaute, Truncated lognormal distributions and scaling in the size of naturally defined population clusters, Physical Review E 101 (2020) 042312