Abstract
Whereas there has been an extended discussion concerning city population distribution, little has been said about that of administrative divisions. In this work, we investigate the population distribution of second-level administrative units of 150 countries and territories and propose the discrete generalized beta distribution (DGBD) rank-size function to describe the data. After testing the balance between the goodness of fit and number of parameters of this function compared with a power law, which is the most common model for city population, the DGBD is a good statistical model for 96% of our datasets and preferred over a power law in almost every case. Moreover, the DGBD is preferred over a power law for fitting country population data, which can be seen as the zeroth-level administrative unit. We present a computational toy model to simulate the formation of administrative divisions in one dimension and give numerical evidence that the DGBD arises from a particular case of this model. This model, along with the fitting of the DGBD, proves adequate in reproducing and describing local unit evolution and its effect on the population distribution.
Highlights
The inhabitable area of the world is divided into politically distinct units, which may be countries or dependent territories
Does a power law hold for the administrative unit population as it does for big cities? Are there any traces of ubiquitous behaviour? What is the effect on the population distribution of external agents delineating artificial boundaries for administrative territories? In this paper, we seek to answer these questions by addressing two main issues: (i) we provide a description and characterization of population distribution for secondary administrative divisions (SAUs on) for a set of 150 countries; in particular, we discuss the validity of power laws and propose applying a two-parameter rank-size function to fit the data; and (ii) we propose a computational one-dimensional toy model to describe the process of administrative unit formation and development, from which our two-parameter representation arises
We investigated the topic of the formation, evolution and population distribution of administrative units for different countries and territories around the world
Summary
The inhabitable area of the world is divided into politically distinct units, which may be countries or dependent territories. We seek to answer these questions by addressing two main issues: (i) we provide a description and characterization of population distribution for secondary administrative divisions (SAUs on) for a set of 150 countries; in particular, we discuss the validity of power laws and propose applying a two-parameter rank-size function to fit the data; and (ii) we propose a computational one-dimensional toy model to describe the process of administrative unit formation and development, from which our two-parameter representation arises.
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