IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v675y2025ics0378437125004790.html

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

Author

Listed:
  • Ordoñez, Dylan Marcus T.
  • Batac, Rene C.

Abstract

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.

Suggested Citation

  • Ordoñez, Dylan Marcus T. & Batac, Rene C., 2025. "Testing the validity of Zipf and Pareto laws: A multi-method approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 675(C).
    • Handle: RePEc:eee:phsmap:v:675:y:2025:i:c:s0378437125004790
    DOI: 10.1016/j.physa.2025.130827
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437125004790
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2025.130827?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Chen, Yanguang, 2012. "The rank-size scaling law and entropy-maximizing principle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 767-778.
    2. Perlada, Camille D. & Orden, Alfiero K. & Cirunay, Michelle T. & Batac, Rene C., 2021. "Quantifying the organization of urban elements through the statistical distributions of their spatial spreading metrics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    3. Chen, Yanguang, 2012. "The mathematical relationship between Zipf’s law and the hierarchical scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3285-3299.
    4. Ekrem Aydiner & Andrey G. Cherstvy & Ralf Metzler, 2019. "Money distribution in agent-based models with position-exchange dynamics: the Pareto paradigm revisited," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(5), pages 1-4, May.
    5. Michelle T. Cirunay & Rene C. Batac, 2018. "Statistical signatures of the spatial imprints of road network growth," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(10), pages 1-16, October.
    6. Rosen, Kenneth T. & Resnick, Mitchel, 1980. "The size distribution of cities: An examination of the Pareto law and primacy," Journal of Urban Economics, Elsevier, vol. 8(2), pages 165-186, September.
    7. Aydiner, Ekrem & Cherstvy, Andrey G. & Metzler, Ralf, 2018. "Wealth distribution, Pareto law, and stretched exponential decay of money: Computer simulations analysis of agent-based models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 278-288.
    8. Felix Auerbach & Antonio Ciccone, 2023. "The Law of Population Concentration," Environment and Planning B, , vol. 50(2), pages 290-298, February.
    9. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2018. "Zipf’s law and city size distribution: A survey of the literature and future research agenda," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 75-92.
    10. Hernandez, Edward Russel & Sy, Patricia Breanne & Cirunay, Michelle T. & Batac, Rene C., 2024. "Power-law distributions of urban tree cover," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    11. Antonino A. Paguirigan & Marc Jordan G. Angco & Johnrob Y. Bantang, 2017. "A fragmentation model of earthquake-like behavior in internet access activity," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 28(07), pages 1-14, July.
    12. Jeff Alstott & Ed Bullmore & Dietmar Plenz, 2014. "powerlaw: A Python Package for Analysis of Heavy-Tailed Distributions," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-11, January.
    13. Lämmer, Stefan & Gehlsen, Björn & Helbing, Dirk, 2006. "Scaling laws in the spatial structure of urban road networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 89-95.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kiona Moria Aguana & Rene C. Batac, 2026. "Emergence of power-law statistics in the co-authorship networks of Philippine physics researchers," Scientometrics, Springer;Akadémiai Kiadó, vol. 131(1), pages 665-685, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Grachev, Gennady A., 2022. "Size distribution of states, counties, and cities in the USA: New inequality form information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    2. Batac, Rene C. & Cirunay, Michelle T., 2022. "Shortest paths along urban road network peripheries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    3. Hernandez, Edward Russel & Sy, Patricia Breanne & Cirunay, Michelle T. & Batac, Rene C., 2024. "Power-law distributions of urban tree cover," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    4. Perlada, Camille D. & Orden, Alfiero K. & Cirunay, Michelle T. & Batac, Rene C., 2021. "Quantifying the organization of urban elements through the statistical distributions of their spatial spreading metrics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    5. Hasan Engin Duran, 2025. "The future of urban hierearchy and Zipf law: ARIMA and BATS forecasting," Letters in Spatial and Resource Sciences, Springer, vol. 18(1), pages 1-14, December.
    6. SHIDA, Yoshisada, 2021. "Does the Currency Crisis Veil the Impact of Economic Sanctions under an Authoritarian Regime? An Inquiry into Russia," RRC Working Paper Series 91, Russian Research Center, Institute of Economic Research, Hitotsubashi University.
    7. Hasan Engin Duran & Andrzej Cieślik, 2021. "The distribution of city sizes in Turkey: A failure of Zipf’s law due to concavity," Regional Science Policy & Practice, Wiley Blackwell, vol. 13(5), pages 1702-1719, October.
    8. Lang, Wei & Long, Ying & Chen, Tingting & Li, Xun, 2019. "Reinvestigating China’s urbanization through the lens of allometric scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1429-1439.
    9. Miguel Puente-Ajovín & Marcos Sanso-Navarro & María Vera-Cabello, 2022. "The distribution of urban population and economic activity in the European Union and the United States," Letters in Spatial and Resource Sciences, Springer, vol. 15(3), pages 517-522, December.
    10. Angelina Hackmann & Torben Klarl, 2020. "The evolution of Zipf's Law for U.S. cities," Papers in Regional Science, Wiley Blackwell, vol. 99(3), pages 841-852, June.
    11. Kazuhiro Kumo & Elena Shadrina, 2021. "On the Evolution of Hierarchical Urban Systems in Soviet Russia, 1897–1989," Sustainability, MDPI, vol. 13(20), pages 1-17, October.
    12. Piotr Gabrielczak & Tomasz Serwach, 2019. "Firm-size distribution in Poland – is power law applicable?," Lodz Economics Working Papers 3/2019, University of Lodz, Faculty of Economics and Sociology.
    13. Borba, Jhordan Silveira & Gonçalves, Sebastian & Anteneodo, Celia, 2025. "Inequality in a model of capitalist economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 664(C).
    14. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2019. "Zipf’s law, the coherence of the urban system and city size distribution: Evidence from Pakistan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 87-103.
    15. Montebruno, Piero & Bennett, Robert J. & van Lieshout, Carry & Smith, Harry, 2019. "A tale of two tails: Do Power Law and Lognormal models fit firm-size distributions in the mid-Victorian era?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 858-875.
    16. Inho Hong & Woo-Sung Jung & Hang-Hyun Jo, 2019. "Gravity model explained by the radiation model on a population landscape," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-13, June.
    17. Pankaj Bajracharya & Selima Sultana, 2020. "Rank-size Distribution of Cities and Municipalities in Bangladesh," Sustainability, MDPI, vol. 12(11), pages 1-26, June.
    18. Stepinski, Tomasz F. & Dmowska, Anna, 2020. "Complexity in patterns of racial segregation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    19. Pengfei Li & Ming Lu, 2021. "Urban Systems: Understanding and Predicting the Spatial Distribution of China's Population," China & World Economy, Institute of World Economics and Politics, Chinese Academy of Social Sciences, vol. 29(4), pages 35-62, July.
    20. Cirunay, Michelle T. & Batac, Rene C., 2023. "Evolution of the periphery of a self-organized road network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:675:y:2025:i:c:s0378437125004790. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.