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Beyond the Zipf–Mandelbrot law in quantitative linguistics

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  • Montemurro, Marcelo A.

Abstract

In this paper the Zipf–Mandelbrot law is revisited in the context of linguistics. Despite its widespread popularity the Zipf–Mandelbrot law can only describe the statistical behaviour of a rather restricted fraction of the total number of words contained in some given corpus. In particular, we focus our attention on the important deviations that become statistically relevant as larger corpora are considered and that ultimately could be understood as salient features of the underlying complex process of language generation. Finally, it is shown that all the different observed regimes can be accurately encompassed within a single mathematical framework recently introduced by C. Tsallis.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:phsmap:v:300:y:2001:i:3:p:567-578
    DOI: 10.1016/S0378-4371(01)00355-7
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    Cited by:

    1. Ferrer i Cancho, Ramon, 2005. "Decoding least effort and scaling in signal frequency distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 275-284.
    2. 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.
    3. 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.
    4. Miśkiewicz, Janusz & Ausloos, Marcel, 2008. "Correlation measure to detect time series distances, whence economy globalization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6584-6594.
    5. Lambiotte, R. & Ausloos, M. & Thelwall, M., 2007. "Word statistics in Blogs and RSS feeds: Towards empirical universal evidence," Journal of Informetrics, Elsevier, vol. 1(4), pages 277-286.
    6. Ghosh, Dipak & Chakraborty, Sayantan & Samanta, Shukla, 2019. "Study of translational effect in Tagore’s Gitanjali using Chaos based Multifractal analysis technique," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1343-1354.
    7. Bar-Ilan, Judit, 2008. "Informetrics at the beginning of the 21st century—A review," Journal of Informetrics, Elsevier, vol. 2(1), pages 1-52.
    8. Young, D.S., 2013. "Approximate tolerance limits for Zipf–Mandelbrot distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1702-1711.
    9. Rotundo, Giulia, 2014. "Black–Scholes–Schrödinger–Zipf–Mandelbrot model framework for improving a study of the coauthor core score," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 296-301.

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    Keywords

    Zipf–Mandelbrot law; Human language;

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