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Random Texts Do Not Exhibit the Real Zipf's Law-Like Rank Distribution

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  • Ramon Ferrer-i-Cancho
  • Brita Elvevåg

Abstract

Background: Zipf's law states that the relationship between the frequency of a word in a text and its rank (the most frequent word has rank , the 2nd most frequent word has rank ,…) is approximately linear when plotted on a double logarithmic scale. It has been argued that the law is not a relevant or useful property of language because simple random texts - constructed by concatenating random characters including blanks behaving as word delimiters - exhibit a Zipf's law-like word rank distribution. Methodology/Principal Findings: In this article, we examine the flaws of such putative good fits of random texts. We demonstrate - by means of three different statistical tests - that ranks derived from random texts and ranks derived from real texts are statistically inconsistent with the parameters employed to argue for such a good fit, even when the parameters are inferred from the target real text. Our findings are valid for both the simplest random texts composed of equally likely characters as well as more elaborate and realistic versions where character probabilities are borrowed from a real text. Conclusions/Significance: The good fit of random texts to real Zipf's law-like rank distributions has not yet been established. Therefore, we suggest that Zipf's law might in fact be a fundamental law in natural languages.

Suggested Citation

  • Ramon Ferrer-i-Cancho & Brita Elvevåg, 2010. "Random Texts Do Not Exhibit the Real Zipf's Law-Like Rank Distribution," PLOS ONE, Public Library of Science, vol. 5(3), pages 1-10, March.
  • Handle: RePEc:plo:pone00:0009411
    DOI: 10.1371/journal.pone.0009411
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    Cited by:

    1. Marcelo A Montemurro & Damián H Zanette, 2013. "Keywords and Co-Occurrence Patterns in the Voynich Manuscript: An Information-Theoretic Analysis," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-9, June.
    2. Chen, Yanguang, 2012. "Zipf’s law, 1/f noise, and fractal hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 63-73.
    3. Espitia, Diego & Larralde, Hernán, 2020. "Universal and non-universal text statistics: Clustering coefficient for language identification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).

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