A City-Size Distribution Model Based on the Weber-Fechner Law of Marginal Effects

1981 ◽  
Vol 13 (6) ◽  
pp. 689-701 ◽  
Author(s):  
R Bussière ◽  
T Stovall
Keyword(s):  
Utility Function ◽  
Size Distribution ◽  
Hierarchical Model ◽  
Pareto Distribution ◽  
City Size ◽  
Distribution Model ◽  
Marginal Effects ◽  
City Size Distribution ◽  
Locational Decisions ◽  
Maximum Entropy Distribution

The distribution by size of the cities of a region reflects the locational decisions made by the inhabitants concerned. Some of the factors underlying these decisions have a bearing on city size, and, it is assumed, make up a utility function that varies with city size according to the Weber-Fechner law of marginal effects. Under these conditions, the maximum entropy distribution of the population among the cities of the region gives rise to the hierarchical model described in the paper. Examples are given of calibrations of the model. It is shown that in the applicable statistical range this distribution and the Pareto distribution, although formally different, are quantitatively interchangeable. The derivation presented here may therefore be regarded as providing a new rationale for the Pareto city-size distribution model.

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 The Spanish spatial city size distribution

2020 ◽  
pp. 239980832094186
Author(s):  
Rafael González-Val
Keyword(s):  
Size Distribution ◽  
Pareto Distribution ◽  
City Size ◽  
Large Cities ◽  
Lognormal Distributions ◽  
City Size Distribution ◽  
Distribution Parameters ◽  
Significant Patterns ◽  
New Perspective ◽  
The City

This paper analyses the Spanish city size distribution from a new perspective, focusing on the role played by distance. Using un-truncated data from all cities in 1900 and 2011, we study the spatial distribution of cities and how the city size distribution varies with distance. First, K-densities are estimated to identify different spatial patterns depending on city size, with significant patterns of dispersion found for medium-sized and large cities. Second, using a distance-based approach that considers all possible combinations of cities within a 200-kilometre radius, we analyse the influence of distance on the city size distribution parameters, considering both the Pareto and lognormal distributions. The results validate the Pareto distribution in most of the cases regardless of city size, and the lognormal distribution at short distances.

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.

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