There is More than a Power Law in Zipf

被引:90
作者
Cristelli, Matthieu [2 ,3 ]
Batty, Michael [1 ,4 ]
Pietronero, Luciano [2 ,3 ,5 ]
机构
[1] UCL, Ctr Adv Spatial Anal, London W1T 4TJ, England
[2] Univ Roma La Sapienza, Dept Phys, I-00185 Rome, Italy
[3] CNR, Inst Complex Syst, I-00185 Rome, Italy
[4] Arizona State Univ, Sch Geog Sci & Urban Planning, Tempe, AZ 85287 USA
[5] London Inst Math Sci, London W1K 2NY, England
基金
英国工程与自然科学研究理事会;
关键词
SIZE DISTRIBUTION; CITIES; DISTRIBUTIONS; TAILS;
D O I
10.1038/srep00812
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf's Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto's or Benford's, but contrary to popular belief, from a distribution of, say, city sizes and a simple random sampling, one does not obtain Zipf's law for the largest cities. This pathology is reflected in the fact that Zipf's Law has a functional form depending on the number of events N. This requires a fundamental property of the sample distribution which we call 'coherence' and it corresponds to a 'screening' between various elements of the set. We show how it should be accounted for when fitting Zipf's Law.
引用
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页数:7
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