Date of Publication

4-22-2025

Document Type

Master's Thesis

Degree Name

Master of Science in Applied Physics

Subject Categories

Physics

College

College of Science

Department/Unit

Physics

Defense Panel Chair

Emmanuel T. Rodulfo

Abstract/Summary

Zipf's law is a statistical rule where after ordering a collection of objects by size in descending order, the second object is one-half of the largest, the third is one-third, and so on. It has been extensively studied for city size distributions of various urban systems across different territories. The current work aims to examine the validity of Zipf's law for Philippine cities and municipalities for different time periods, given the literature gap in the case of the country. The data will consist of city-level data from the Philippine Statistics Authority census for 2000, 2010, 2015, and 2020. Three approaches will be used: linear regression, Gibrat's law, hierarchical scaling law. As a complement to the first approach, power law behavior of the city sizes will also be assessed. Data truncation will be considered in the various analyses to be performed. Zipf's law can be used to assess the condition of the urban system, and when applicable, allows for the projections of city population.

The linear regression and hierarchical scaling law approaches provide evidence supporting Zipf's law for the truncated dataset or the upper tail of the size distribution. On the other hand, all three approaches give evidence contrary to the law for the untruncated data. The upper tail comprises roughly the top 30% of LGUs and consists of around 70% of the entire population across several years. This range also shows three signatures of complex systems: Zipf-like behavior in the rank-size distribution, a power law in the frequency distribution, and fractality. Furthermore, the upper tail does not strictly conform to Zipf's law, but it has incrementally become more uneven over the years. This may be explained by the above-average growth rates for the largest city sizes. The smallest city sizes, in contrast, tend to have below-average rates. Based on the difference in the results of the two datasets, the statistics suggest that the power law behavior is essential for a Zipf-like characteristic to hold. Furthermore, the results from the three approaches indicate that Philippine urban system is gradually becoming more concentrated.

Keywords: Zipf’s law, Gibrat’s law, hierarchical scaling law, Philippine urban system, complex systems

Abstract Format

html

Language

English

Format

Electronic

Keywords

Zipf's law

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Embargo Period

4-21-2027

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Available for download on Wednesday, April 21, 2027

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