华中师范大学学报（人文社会科学版）2000，Vol.34Issue(1)：98-102,5.
城市规模分布的三参数Zipf模型 ——Davis二倍数规律的理论推广及其分形性质的实证分析
Three-parameter Zipf's model on city-size distribution:A generalization of Davis'2n-law and demonstrations of its fractal nature
摘要
Abstract
The Davis' number-doubling rule of city hierarchies,which was originally given as,αi＝αi+n.2n，fi＝fi+n.2 -n,is generalized to an universal form,αi＝αi+n.2n，fi ＝fi+n.δ-n(δ1)， from the new expression a three-parameter Z ipf's model is deduced out as follows,P(r)=C(r-α)-dz,where C= a0(f0/lnδ)lnδ／ln2， α＝f0/ln(1/δ),and d z=ln2/lnδ. The last parameter,dz,proved to have a certain nature of fractal dimension(D),i.e.,dz=1/D,so the fractal dimens ion can be expressed as D=lnδ/ln2. This implies that the so-called 2n-law is a special form of 3-parameter Zipf law,in which the Zipf's dimension (dz) as well as the fractal dimension (D) is equal to one,nam ely,dz=(1/D)=1. The results developed by the authors are demonstrated and v erified by the original data presented by K.Davis(1978).关键词
城市体系/城市规模分布/位序-规模法则/分形Key words
urban system/city-size distribution/rank-size ru le/fractals分类
管理科学引用本文复制引用
..城市规模分布的三参数Zipf模型 ——Davis二倍数规律的理论推广及其分形性质的实证分析[J].华中师范大学学报（人文社会科学版）,2000,34(1):98-102,5.基金项目
国家自然科学基金资助项目(49771035) （49771035）
