城市规模分布的Weibull模型:理论基础与实证分析

A Weibull-type model on city-size distributions: the revised result and its empirical analysis of Curry's entropy-maximizing model

基于城市地理系统的分数维思想,修正了Curry的最大熵模型,得到关于城市规模分布的Weibull模型:M(i≤P)/n=1-exp[-(P/u)v],并论证了约束性参数与Zipf维数的内在关系,从而从新的角度解释了城市等级体系的分形性质及其数理特征.利用河南省多年(1990～1996)的城市人口数据对本文发展的数学模型进行验证,取得了令人满意的结果.

The entropy maximization model on rank-size rule of urban hierarchies presented by L. Curry (1964) is revised and improved and a new model of city-size distributions is advanced as follows:M(i≤P)/n=1-exp, which is identical in form to the Weibull's distribution. On the other hand, as for P<u, the new model can be re-expressed approximately as M(i≤P)=n(P/u)~v, where i is the size of a city, P represents the threshold value of city size, u denotes the mean size of cities in an urban system, n implies the number of cities, M means number of the cities sizes of which are greater than the threshold value P, and v as a power exponent has some nature and meaning of fractal dimension. An empirical analysis is made based on the system of cities in Henan Province, China, and the results show that the new model given in the paper can be employed to characterize size distributions of cities in real world more effectively than the well-known Zipf's law.