Psychonomic Bulletin & Review

, Volume 21, Issue 5, pp 1112–1130 | Cite as

Zipf’s word frequency law in natural language: A critical review and future directions

  • Steven T. PiantadosiEmail author
Theoretical Review


The frequency distribution of words has been a key object of study in statistical linguistics for the past 70 years. This distribution approximately follows a simple mathematical form known as Zipf’s law. This article first shows that human language has a highly complex, reliable structure in the frequency distribution over and above this classic law, although prior data visualization methods have obscured this fact. A number of empirical phenomena related to word frequencies are then reviewed. These facts are chosen to be informative about the mechanisms giving rise to Zipf’s law and are then used to evaluate many of the theoretical explanations of Zipf’s law in language. No prior account straightforwardly explains all the basic facts or is supported with independent evaluation of its underlying assumptions. To make progress at understanding why language obeys Zipf’s law, studies must seek evidence beyond the law itself, testing assumptions and evaluating novel predictions with new, independent data.


Language Zipf’s law Statistics 


Author Note

I’m very grateful to Leon Bergen, Ev Fedorenko, and Kyle Mahowald for providing detailed comments on this paper. Andreea Simona Calude James generously shared the data visualized in Figure 2. I am highly appreciative of Dmitrii Manin, Bob McMurray and an anonymous reviewer for providing extremely helpful comments on this work. Research reported in this publication was supported by the Eunice Kennedy Shriver National Institute Of Child Health & Human Development of the National Institutes of Health under Award Number F32HD070544. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.


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© Psychonomic Society, Inc. 2014

Authors and Affiliations

  1. 1.Brain and Cognitive SciencesUniversity of RochesterRochesterUSA

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