Testing the validity of Zipf and Pareto laws: A multi-method approach

Statistical regularities in the population data, in the form of Zipf’s law for rank-frequency plots and the power-law Pareto distribution functions, have long been observed across various countries and political units and are deemed to be emergent manifestations of complexity in socioeconomic systems. Extensive work on the subject requires continuous revisiting, specifically to test for the range of validity of these statistical patterns, taking into account the data from underrepresented regions. Here, we implement a multi-method approach to assess the regimes of acceptability of the Zipf and Pareto distributions using city-level data from the Philippines from 2000 to 2020. Using the techniques of direct power-law testing, Gibrat’s law validation, and hierarchical scaling law analysis, we find a recurring trend of a 70-30 rule, in which cities within the top 30% of sizes, holding 70% of the total population, show strong Zipfian and Pareto signatures, while the bottom 70%, with the remaining 30% of the total population, manifest significant deviations. By focusing on contemporary data sets in a socioeconomically dynamic setting, the work aims to provide further validation of the empirical law, tying the regimes with the actual conditions on the ground.