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last updated: August 2012
998 items collected (including 65 preprints and 130 papers written in non-English languages are included), up from 255 at the previous location at Rockefeller University (1 -> 3.91 )

Zipf's law, named after the Harvard linguistic professor George Kingsley Zipf (1902-1950), is the observation that frequency of occurrence of some event ( P ), as a function of the rank ( i) when the rank is determined by the above frequency of occurrence, is a power-law function Pi ~ 1/ia with the exponent a close to unity (1).

comments on this bibliography:

The year 2002 marked the 100 anniversary of the birth of George Zipf. To honor this occasion, the online web-journal, Glottometrics devoted several volumes to Zipf and Zipf's law: vol 3 vol 4 vol 5

A program related to Zipf's law: zipfR

A small collection of papers on linguistic, cognitive and brain networks

This page is created and maintained by Dr. Wentian Li of Feinstein Institutes for Medical Research, Northwell Health (previously North Shore LIJ Health System). I would like to thank Gabriel Altmann, Rob Axtell, Michael Batty, Claudio Cioffi-Revilla, Bernat Corominas Murtra, Andrew Crompton, Lukasz Debowski, Allen Downey, Clive Downs, Stefan Evert, Ramon Ferrer i Cancho, Xavier Gabaix, Osman Tuna Gokgoz, Sherwin Gooch, Derek Jones, Giorgio Kaniadakis, Jurek Kolasa, Hiroto Kuninaka, Milan Kunz, Vladimir Kuznetsov, Haitao Liu, Dmitrij Manin, Gustavo Martínez-Mekler, Gerardo Naumis, Volker Nitsch, Gowri Shankar, Bill Reed, Jeff Robbins, Ronald Rousseau, Flemming Topsoe, Carlos Urzua, Theo P van der Weide, Guoqing Weng, Ronald Wyllis for recommending papers and various help.

Some other laws

Benford's law: On a wide variety of statistical data, the first digit is d with the probability log10 (1+1/d). This is also referred to as "the first-digit phenomenon." The general significant-digit law is that the first significant digits ddd ... d occur with the probability log10 ( 1 + 1/ddd ... d ). This law was first published by Simon Newcomb in 1881. It went unnoticed until Frank Benford, apparently unaware of Newcomb's paper, concluded the same law and published it in 1938, supported by huge amounts of data. [source: http://www.nist.gov/dads/HTML/benfordslaw.html]

Bradford's law: Journals in a field can be divided into three parts, each with about one-third of all articles: (1) a core of a few journals; (2) a second zone, with more journals; and (3) a third zone, with the bulk of journals. The number of journals is 1:n:n. Bradford formulated his law after studying a bibliography of geophysics, covering 326 journals in the field. He discovered that 9 journals contained 429 articles, 59 contained 499 articles, and 258 contained 404 articles. Although Bradford's Law is not statistically accurate, librarians commonly use it as a guideline. [source: http://www.nist.gov/dads/HTML/bradfordsLaw.html]

Gibrat's law: The growth rate of a company is independent of the company's size. The discussion of Gibrat's law often appears in models to explain the Zipf's law. [source: http://en.wikipedia.org/wiki/Gibrat's_law]

Heaps' law : An empirical rule which describes the vocabulary growth as a function of the text size. It establishes that a text of n words has a vocabulary of size V= K nb where 0 < b < 1. [source: http://encyclopedia.thefreedictionary.com/Heaps'+law ]

Lotka's law : The number of authors making n contributions is about 1/na of those making one contribution, where a is often nearly 2. [source: http://www.nist.gov/dads/HTML/lotkaslaw.html ]

Pareto's principle : The cumulative distribution function (CDF) of incomes, i.e. the number of people whose income is more than x, is an inverse power of x: P[X > x] ~ x-k. Rule of thumb that 20% of a population earns 80% of its income. [source: [ https://www.investopedia.com/terms/p/paretoprinciple.asp, https://www.investopedia.com/terms/1/80-20-rule.asp ] There were also proposals to name it "Juran principle" [source: https://www.juran.com/blog/the-history-of-quality/]

This page is resurrected by Ramon Ferrer i Cancho and Lluis Alemany Puig at Universitat Politecnica de Catalunya (Department de Ciencies de la Computacio) (2021). The current URL is https://wli-zipf.upc.edu UPC CS logo