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Pareto Or Log-Normal? Best Fit And Truncation In The Distribution Of All Cities

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  • Giorgio Fazio
  • Marco Modica

Abstract

type="main"> In the literature, the distribution of city size is a controversial issue with two common contenders: the Pareto and the log-normal. While the first is most accredited when the distribution is truncated above a certain threshold, the latter is usually considered a better representation for the untruncated distribution of all cities. In this paper, we reassess the empirical evidence on the best-fitting distribution in relation to the truncation point issue. Specifically, we provide a comparison among four recently proposed approaches and alternative definitions of U.S. cities. Our results highlight the importance to look at issue of the best-fitting distribution together with the truncation issue and provide guidance with respect to the existing tests of the truncation point.

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  • Giorgio Fazio & Marco Modica, 2015. "Pareto Or Log-Normal? Best Fit And Truncation In The Distribution Of All Cities," Journal of Regional Science, Wiley Blackwell, vol. 55(5), pages 736-756, November.
    • Handle: RePEc:bla:jregsc:v:55:y:2015:i:5:p:736-756
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    2. Luckstead, Jeff & Devadoss, Stephen & Danforth, Diana, 2017. "The size distributions of all Indian cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 237-249.
    3. Rafael González‐Val, 2019. "Historical urban growth in Europe (1300–1800)," Papers in Regional Science, Wiley Blackwell, vol. 98(2), pages 1115-1136, April.
    4. Christian Schluter, 2021. "On Zipf’s law and the bias of Zipf regressions," Empirical Economics, Springer, vol. 61(2), pages 529-548, August.
    5. Cieślik Andrzej & Teresiński Jan, 2016. "Does Zipf’s law hold for Polish cities?," Miscellanea Geographica. Regional Studies on Development, Sciendo, vol. 20(4), pages 5-10, December.
    6. Clémentine Cottineau, 2022. "What do analyses of city size distributions have in common?," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(3), pages 1439-1463, March.
    7. Rafael González-Val, 2019. "US city-size distribution and space," Spatial Economic Analysis, Taylor & Francis Journals, vol. 14(3), pages 283-300, July.
    8. Matthias Breuer, 2021. "How Does Financial‐Reporting Regulation Affect Industry‐Wide Resource Allocation?," Journal of Accounting Research, Wiley Blackwell, vol. 59(1), pages 59-110, March.
    9. 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.
    10. Rafael González-Val, 2021. "The Spanish spatial city size distribution," Environment and Planning B, , vol. 48(6), pages 1609-1631, July.
    11. 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.
    12. Marco Bee, 2020. "On discriminating between lognormal and Pareto tail: A mixture-based approach," DEM Working Papers 2020/9, Department of Economics and Management.
    13. John B Parr, 2022. "Singer and the Pareto distribution: A note," Environment and Planning B, , vol. 49(3), pages 1067-1073, March.
    14. Pankaj Bajracharya & Selima Sultana, 2020. "Rank-size Distribution of Cities and Municipalities in Bangladesh," Sustainability, MDPI, vol. 12(11), pages 1-26, June.
    15. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman & Hussain, Saiful Izzuan, 2019. "A robust and efficient estimator for the tail index of inverse Pareto distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 431-439.
    16. Josic Hrvoje & Bašić Maja, 2018. "Reconsidering Zipf’s law for regional development: The case of settlements and cities in Croatia," Miscellanea Geographica. Regional Studies on Development, Sciendo, vol. 22(1), pages 22-30, March.

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