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Bulletin of Geography. Socio-economic Series

Zipf ’s Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns
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Zipf ’s Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns

Authors

  • Dariusz Sokołowski Nicolaus Copernicus University https://orcid.org/0000-0003-0361-7017
  • Iwona Jażdżewska University of Łódź https://orcid.org/0000-0002-4554-7486

DOI:

https://doi.org/10.2478/bog-2021-0028

Keywords

cities, city size distribution, weight of cities, Zipf’s Law, rank-size rule, weighted regression

Abstract

The paper aims at presentation of a methodology where the classical linear regression model is modified to guarantee more realistic estimations and lower parameter oscillations for a specific urban system. That can be achieved by means of the weighted regression model which is based on weights ascribed to individual cities. The major shortcoming of the methods used so far – especially the classical simple linear regression – is the treatment of individual cities as points carrying the same weight, in consequence of which the linear regression poorly matches the empirical distribution of cities. The aim is reached in a severalstage process: demonstration of the drawbacks of the linear parameter estimation methods traditionally used for the purposes of urban system analyses; introduction
of the weighted regression which to a large extent diminishes specific drawbacks; and empirical verification of the method with the use of the input data for the USA and Poland.

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Bulletin of Geography. Socio-economic Series

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Published

2021-09-29

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1.
SOKOŁOWSKI, Dariusz and JAŻDŻEWSKA, Iwona. Zipf ’s Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns. Bulletin of Geography. Socio-economic Series. Online. 29 September 2021. No. 53, pp. 147-156. [Accessed 2 July 2025]. DOI 10.2478/bog-2021-0028.
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