Zipf's law

From PlanningWiki

Originally, Zipf's law stated that, in a corpus of natural language utterances, the frequency of any word is roughly inversely proportional to its rank in the frequency table. So, the most frequent word will occur approximately twice as often as the second most frequent word, which occurs twice as often as the fourth most frequent word, etc. The term has come to be used to refer to any of a family of related power law probability distributions. The "law" was publicized by Harvard linguist George Kingsley Zipf.

In relation to city sizes, Zipf also discovered that city sizes — defined in terms of their populations — follow a very regular pattern, where the largest city in a country tends to be about twice as large as the second-largest city, three times larger than the third-largest city, four times larger than the fourth-largest city, and so on. Because the size increment between successive cities becomes smaller, the result is an urban system characterized by a sprinkling of relatively large cities amidst a sea of small towns. Zip's law has been shown to be true in many countries true across the world, with China, Canada, and South Africa being exceptions.

References

Gibrat, Robert. 1931. Les Inégalités Economiques. Paris: Librairie du Recueil Sirey.

Gabaix, Xavier, and Yannis Ionnides. 2004. "The Evolution of City-Size Distributions." Handbook of Regional and Urban Economics, Volume 4. Henderson & Thisse, Eds. Amsterdam: Elsevier.

Krugman, Paul. 1996. The Self-Organizing Economy. Oxford, England: Basil Blackwell.

Zipf, George. 1949. Human Behavior and the Principle of Least Effort. Cambridge, Mass.: Addison-Wesley.

Newman, Mark. 2005. "Power laws, Pareto distributions and Zipf's Law." In Condensed Matter. http://arxiv.org/abs/cond-mat/0412004

Pumain, Denise. 2006. Hierarchy in Natural and Social Sciences, Methodos Series Number 3, Dordrecht, The Netherlands: Kluwer-Springer.