PROGRESS IN GEOGRAPHY ›› 1999, Vol. 18 ›› Issue (3): 255-262.doi: 10.11820/dlkxjz.1999.03.009

• Original Articles • Previous Articles     Next Articles

A Proof of Davis’ 2\+n law as a Special Equivalent of the Three-parameter Zipf Model

CHEN Yan guang1, LIU Ji sheng2   

  1. 1. Department of Geography, Xinyang Teachers College, Xinyang, Henan 464000, China;
    2. Department of Geography, Northeast Normal University, Changchun 130024, China
  • Received:1998-12-01 Revised:1999-05-01 Online:1999-08-25 Published:1999-08-25

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.

Key words: City size Distribution, Fractal, Fractal dimenson, Urban system

CLC Number: 

  • TU984