Population patterns in World's administrative units

While there has been an extended discussion concerning city population distribution, little has been said about administrative units. Even though there might be a correspondence between cities and administrative divisions, they are conceptually different entities and the correspondence breaks as artificial divisions form and evolve. In this work we investigate the population distribution of second level administrative units for 150 countries and propose the Discrete Generalized Beta Distribution (DGBD) rank-size function to describe the data. After testing the goodness of fit of this two parameter function against power law, which is the most common model for city population, DGBD is a good statistical model for 73% of our data sets and better than power law in almost every case. Particularly, DGBD is better than power law for fitting country population data. The fitted parameters of this function allow us to construct a phenomenological characterization of countries according to the way in which people are distributed inside them. We present a computational model to simulate the formation of administrative divisions and give numerical evidence that DGBD arises from it. This model along with the DGBD function prove adequate to reproduce and describe local unit evolution and its effect on population distribution.