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.