Population patterns in World's administrative units

Area of Science:

• Demography
• Urban Studies
• Statistical Modeling

Background:

• Limited research exists on population distribution within administrative divisions compared to cities.
• Existing models, like the power law, are commonly used for city populations but may not fit administrative data well.

Purpose of the Study:

• To investigate the population distribution of second-level administrative units across 150 countries.
• To propose and validate a new statistical model, the discrete generalized beta distribution (DGBD), for administrative population data.
• To compare the DGBD's performance against the traditional power law model.

Main Methods:

• Analysis of population data for second-level administrative units in 150 countries and territories.
• Development and application of the discrete generalized beta distribution (DGBD) rank-size function.
• Comparative analysis of the DGBD and power law models based on goodness of fit and parameter count.
• Simulation using a computational toy model to explore the origins of the DGBD.

Main Results:

• The DGBD is a statistically sound model for 96% of the analyzed administrative population datasets.
• The DGBD demonstrates superior performance compared to the power law model for administrative divisions in most cases.
• The DGBD also shows advantages when applied to country-level population data (zeroth-level administrative units).
• A simulation model provides evidence that the DGBD can emerge from a specific model of administrative division formation.

Conclusions:

• The discrete generalized beta distribution (DGBD) is a robust and preferred statistical model for describing population distribution in administrative divisions.
• The DGBD offers a better fit than the power law for both sub-national administrative units and country-level populations.
• The proposed computational model helps explain the emergence of the DGBD and its relevance to the evolution of local administrative units and population distribution.