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| Davis二倍数规律与Zipf三参数模型的等价性证明——关于城市规模分布法则的一个理论探讨 | |
| 引用本文： | 陈彦光,刘继生.Davis二倍数规律与Zipf三参数模型的等价性证明——关于城市规模分布法则的一个理论探讨[J].地理科学进展,1999,18(3):255-262. |
| 作者姓名： | 陈彦光 刘继生 |
| 作者单位： | 1. 信阳师范学院地理系,信阳464000; 2. 东北师范大学地理系,长春130024 |
| 基金项目： | 国家自然科学基金;河南省自然科学基础研究项目 |
| 摘 要： | 本文从城市规模分布的Davis 二倍数规律（2n 规律：ai= ai+ n·2n,fi= fi+ n·2- n）中推导出具有一般意义的三参数Zipf模型：P（r）= C（r- α）- dz,揭示了2n 规律隐含的分形几何性质， 论证了2n 法则为Zipf维数dz= 1 时的特殊情形， 并将2n 规律推广到具有普遍意义的δn 规律， 给出了Zipf维数及分维与邻级倍数δ的数值关系：dz= 1/D= ln2/lnδ。最后从三个方面对文中的理论成果进行了实证分析。 |
| 关 键 词： | 城市体系 城市规模分布 分形 分维 |
| 收稿时间： | 1998-12-01 |
| 修稿时间： | 1999-05-01 |
A Proof of Davis’ 2\+n law as a Special Equivalent of the Three-parameter Zipf Model |
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| Institution: | 1. Department of Geography, Xinyang Teachers College, Xinyang, Henan 464000, China; 2. Department of Geography, Northeast Normal University, Changchun 130024, China |
| Abstract: | The Zipf’s model with three parameters, P(r)=C(r-α) - d z , is deduced from Davis’ 2 n law: a i=a i+n ·2 n, f i=f i+n ·2 -n , by means of a series of mathematical transformation, where d z proves to have some nature of fractal dimension (D) because d z=1/D. The 2 n rule is generalized to δ n rule and δ represents an arbitrary number which is greater than one, namely δ >1. The relationships between δ and the fractal dimensions of city size distributions can be expressed as D=lnδ/ln2 : when δ =2, we have d z =1, so the 2 n rule is only a special case of the three parameter Zipf’s model. The result of the demonstration of Davis’ law as an equivalent of the generalized Zipf’s law is illustrated and verified by some examples including the data in which 2 n rule of urban systems is discovered. |
| Keywords: | Urban system City size Distribution Fractal Fractal dimenson |
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