都市人口にみられるZipfの順位法則の成立機構

概要

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We may generally define the rank-size rule by the formula : FR_=f(R) where F_R is the frequency of the event the order of the frequency of which is R(F_R≦F_<R-1>). The Zipf's rank-size rule would be regarded as a type of the rank-size rules which are expressed by the formula shown above. The Zipf's rank-size rule can be applied to urban populations as Lotka, Zipf, Stewart, Simon, Isard, and Tachi have pointed out. An explanation of the mechanism of existence of the Zipf's rank-size rule of urban populations was already tried by Simon. Here, I tentatively tried to make explanations of the mechanism, (a)based on the Miller's model of Zipf's rank-size rule, and (b) based on the assumption that N(λ) (the number of the cities havingthe population λp^*) is m_λN(λ+1), where m_λ=((λ+1)/λ)^α, and α a is a parameter. We have some other rules or model of urban populations, rule of Pareto, Auerbach, Gibrat, Christaller, and Rashevsky, and Beckman's model. And, we can find connections between them.
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