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Randomness versus specifics for word-frequency distributions

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  • Yan, Xiaoyong
  • Minnhagen, Petter

Abstract

The text-length-dependence of real word-frequency distributions can be connected to the general properties of a random book. It is pointed out that this finding has strong implications, when deciding between two conceptually different views on word-frequency distributions, i.e. the specific ‘Zipf’s-view’ and the non-specific ‘Randomness-view’, as is discussed. It is also noticed that the text-length transformation of a random book does have an exact scaling property precisely for the power-law index γ=1, as opposed to the Zipf’s exponent γ=2 and the implication of this exact scaling property is discussed. However a real text has γ>1 and as a consequence γ increases when shortening a real text. The connections to the predictions from the RGF (Random Group Formation) and to the infinite length-limit of a meta-book are also discussed. The difference between ‘curve-fitting’ and ‘predicting’ word-frequency distributions is stressed. It is pointed out that the question of randomness versus specifics for the distribution of outcomes in case of sufficiently complex systems has a much wider relevance than just the word-frequency example analyzed in the present work.

Suggested Citation

  • Yan, Xiaoyong & Minnhagen, Petter, 2016. "Randomness versus specifics for word-frequency distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 828-837.
    • Handle: RePEc:eee:phsmap:v:444:y:2016:i:c:p:828-837
    DOI: 10.1016/j.physa.2015.10.082
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    References listed on IDEAS

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    1. Montemurro, Marcelo A., 2001. "Beyond the Zipf–Mandelbrot law in quantitative linguistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(3), pages 567-578.
    2. Xiaoyong Yan & Petter Minnhagen, 2015. "Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-19, May.
    3. Bernhardsson, Sebastian & da Rocha, Luis Enrique Correa & Minnhagen, Petter, 2010. "Size-dependent word frequencies and translational invariance of books," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(2), pages 330-341.
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    Cited by:

    1. Yan, Xiaoyong & Minnhagen, Petter, 2018. "The dependence of frequency distributions on multiple meanings of words, codes and signs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 554-564.
    2. Yan, Xiaoyong & Yang, Seong-Gyu & Kim, Beom Jun & Minnhagen, Petter, 2018. "Benford’s law and first letter of words," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 305-315.
    3. Yan, Xiaoyong & Minnhagen, Petter & Jensen, Henrik Jeldtoft, 2016. "The likely determines the unlikely," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 112-119.

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