A Dynamic Generalization of Zipf's Rank-Size Rule

1982 ◽  
Vol 14 (11) ◽  
pp. 1449-1467 ◽  
Author(s):  
B Roehner ◽  
K E Wiese
Keyword(s):  
Stochastic Model ◽  
Size Distribution ◽  
Urban Growth ◽  
Simple Form ◽  
Deterministic Model ◽  
City Size ◽  
Zipf’S Law ◽  
Zipf's Law ◽  
City Size Distribution ◽  
Zero Growth

A dynamic deterministic model of urban growth is proposed, which in its most simple form yields Zipf's law for city-size distribution, and in its general form may account for distributions that deviate strongly from Zipf's law. The qualitative consequences of the model are examined, and a corresponding stochastic model is introduced, which permits, in particular, the study of zero-growth situations.

scholarly journals Does Zipf’s law hold for Polish cities?

2016 ◽  
Vol 20 (4) ◽  
pp. 5-10 ◽  
Author(s):  
Andrzej Cieślik ◽  
Jan Teresiński
Keyword(s):  
Size Distribution ◽  
Empirical Analysis ◽  
City Size ◽  
Zipf’S Law ◽  
Empirical Literature ◽  
Zipf's Law ◽  
First Approximation ◽  
City Size Distribution ◽  
The City ◽  
Equal Population

Abstract In this paper we study Zipf’s law, which postulates that the product of a city’s population and its rank (the number of cities with a larger or equal population) is constant for every city in a given region. We show that the empirical literature indicates that the law may not always hold, although its general form, the rank-size rule, could be a good first approximation of city size distribution. We perform our own empirical analysis of the distribution of the population of Polish cities on the largest possible sample to find that Zipf’s law is rejected for Poland as the city sizes are less evenly distributed than it predicts.

scholarly journals Economic Transition and the Evolution of City-Size Distribution of China’s Urban System

2021 ◽  
Vol 13 (6) ◽  
pp. 3287
Author(s):  
Jiejing Wang ◽  
Yanguang Chen
Keyword(s):  
Size Distribution ◽  
Economic Transition ◽  
Urban System ◽  
City Size ◽  
Zipf’S Law ◽  
Scaling Exponent ◽  
Urban Hierarchy ◽  
Zipf's Law ◽  
Zipf Distribution ◽  
City Size Distribution

The evolution of city size distribution in China has gained a great deal of scholarly attention. However, little is known about the effect of economic transition on the reorganization of city size distribution in China. Using an urban hierarchy with cascade structure model, we decompose Zipf’s law into two exponential functions that provide a new way of examining the dynamic processes of urban system evolution. This study aims to investigate the dominating latent forces that affect China’s city size distribution through mathematical modeling of the hierarchical scaling laws based on census data of 1982, 1990, 2000, and 2010. A number of features of China’s city size distribution are found. First, the size distribution of Chinese cities displayed a clear trend of evolving toward the Zipf distribution, which is the result of economic transition from planned to market. Second, the rank-size pattern still deviates slightly from the standard Zipf distribution, as indicated by the narrow scaling range and departure of the scaling exponent from the theoretically expected value. We argue that the top-down state regulation is a critical cause of deviation of China’s city size distribution from Zipf’s law.

Toward a More Explicit Stochastic Model of a City-Size Distribution: A Reply to Kim's Critique

1982 ◽  
Vol 14 (8) ◽  
pp. 1121-1124 ◽  
Author(s):  
A Okabe
Keyword(s):  
Stochastic Model ◽  
Size Distribution ◽  
City Size ◽  
Distribution Model ◽  
Population Process ◽  
City Size Distribution

This note is a reply to Kim's critique on my paper concerning Simon's city-size distribution model. First, Kim's critique is shown not to be relevant. Second, to make the debate constructive, a possible direction toward a more general city-size distribution model is shown in the context of a Markov population process.

scholarly journals Investigation of urban regularities for Croatia in the period from 1857 to 2011

2020 ◽  
Vol 71 (4) ◽  
pp. 307-330
Author(s):  
Hrvoje Jošić ◽  
Berislav Žmuk
Keyword(s):  
Size Distribution ◽  
Unit Root ◽  
Urban Economics ◽  
Unit Roots ◽  
City Size ◽  
Zipf’S Law ◽  
Urban Hierarchy ◽  
Zipf's Law ◽  
Gibrat’S Law ◽  
Gibrat's Law

Two main regularities in the field of urban economics are Zipf’s law and Gibrat’s law. Zipf’s law states that distribution of largest cities should obey the Pareto rank-size distribution while Gibrat’s law states that proportionate growth of cities is independent of its size. These two laws are interconnected and therefore are often considered together. The objective of this paper is the investigation of urban regularities for Croatia in the period from 1857 to 2011. In order to estimate and evaluate the structure of Croatian urban hierarchy, Pareto or Zipf’s coefficients are calculated. The results have shown that the coefficient values for the largest settlements in different years are close to one, indicating that the Croatian urban hierarchy system follows the rank-size distribution and therefore obeys Zipf's law. The independence of city growth regarding the city size is tested using penal unit roots. Results for Gibrat's law testing using panel unit root tests have shown that there is a presence of unit root in growth of settlements therefore leading to the acceptance of Gibrat’s law.

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