Zipf维数和城市规模分布的分维值的关系探讨

Relationship between Zipf dimension and fractal dimension of city-size distribution

城市位序 规模理论和分形理论是研究城市系统的重要基础。前者可以较好地刻画城市的规模分布 ,后者可用来深入地解释城市规模的分布规律。其中 ,城市规模分布的分维值和Zipf维数是这两个基础理论中的重要参数。在研究我国城市规模的分布规律时 ,理论上可认为分维值和Zipf维数的乘积等于 1。但本文认为这种理论上的关系并不能直接套用到统计分析中去 ,如果城市规模分布的分维值和Zipf维数是利用对于样本的OLS (最小二乘法 )估计所得 ,两者的乘积应等于判定系数 (R2 )。最后我们对此结果进行了推导和证明 ,并对其所具有的理论意义和实践价值进行了简要阐述。

China has a long history of urban development and has numerous cities.Macroscopically the congnition of development law of China’s urban system provides an ideal source for enrichment of urban system theoretical research.Furthermore,China,as a developing country on the fast track,is experiencing rapid urban growth.A better understanding of China’s urban system development will be helpful for predicting the city scale(such as,urban land scale,urban population scale)and macro-planning of China’s urban growth. The urban rank-size and the fractal theories are the important bases for studying the urban system.The former can perfectly depict the distribution of urban size,and the latter can be employed to explain the characteristics of distribution of urban size.At the same time,the fractal dimension and the Zipf dimension are the basic parameters of the two theories.But when studying the urban rank-size rule and the fractal,some scholars theoretically believe there is the relationship between Zipf dimension and the fractal dimension of distribution of urban size,that is,their product equals 1.But,we think,if D and q are the results of OLS(Ordinary Least Square)estimation,then their product should be R2(R2,the coefficient of determination).Then,this paper deduces and proves this result. To study the relationship between Zipf dimension and the fractal dimension of distribution of urban size is helpful to understanding the rule of urban rank-size.Moreover,this study is also necessary for grasping urban development in the future characteristics of urban system evolution in the past and predicting in the urban development future because China is experiencing rapid urbanization process.