Skip to main content
Log in

On Zipf’s law and rank distributions in linguistics and semiotics

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

A number of formulas of linguistic statistics are refined. The notions of real and virtual cardinality of a sign are introduced. We show that a formula refining Zipf’s law for the occurrence frequencies in frequency dictionaries can be extended to arbitrary sign objects, i.e., semiotic systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Bibliography

  1. S. M. Gusein-Zade, “On the frequency distribution of Russian letters,” Problemy Peredachi Informatsii [Problems Inform. Transmission], 23 (1988), no. 4, 102–107.

    MathSciNet  Google Scholar 

  2. M. B. Malyutov, “A survey of methods and examples of text atribution,” Obozrenie Prikladnoi i Promyshlennoi Matematiki, 12 (2005), no. 1, 41–77.

    Google Scholar 

  3. N. A. Morozov, “Linguistic spectra: a tool for distinguishing plagiarisms from true works of known authors. A stylemetric study,” Izv. Otd. Russ. Yazyka i Slovesnosti Imper. Akad. Nauk, XX (1915), no. 4.

  4. A. A. Markov, “On an application of the statistical method,” Izv. Imper. Akad. Nauk, Ser. VI, X (1916), no. 4, 239.

    Google Scholar 

  5. M. V. Arapov, E. N. Efimova, and Yu. A. Shreider, “On the meaning of rank distributions,” Nauchn. Tekhn. Inform., Ser. 2 (1975), no. 1, 9–20; http://kudrinbi.ru/public/442/index.htm.

  6. V. P. Maslov, “On a general theorem of set theory resulting in the Gibbs, Bose-Einstein, and Pareto distributions and the Zipf-Mandelbrot law for stock market,” Mat. Zametki [Math. Notes], 78 (2005), no. 6, 870–877.

    MathSciNet  Google Scholar 

  7. V. P. Maslov, “Linguistic statistics,” Russ. J. Math. Phys., 13 (2006), no. 3, 315–325.

    Article  Google Scholar 

  8. V. P. Maslov, “The lack-of-preference law and the corresponding distributions in frequency probability theory,” Mat. Zametki [Math. Notes], 80 (2006), no. 2, 220–230.

    Google Scholar 

  9. S. P. Kapitsa, S. P. Kurdyumov, and G. G. Malinetskii, Synergetics and Forecasts of the Future [in Russian], Editorial URSS, Moscow, 2001.

    Google Scholar 

  10. Semiotics: Semiotics of Language and Literature [in Russian], Raduga, Moscow, 1983.

  11. A. N. Kolmogorov, “Theory of information transmission,” in: Works of Session of Akad. Nauk SSSR on Production Automation [in Russian], Moscow, 1957.

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Matematicheskie Zametki, vol. 80, no. 5, 2006, pp. 718–732.

Original Russian Text Copyright © 2006 by V. P. Maslov, T. V. Maslova.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maslov, V.P., Maslova, T.V. On Zipf’s law and rank distributions in linguistics and semiotics. Math Notes 80, 679–691 (2006). https://doi.org/10.1007/s11006-006-0189-1

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11006-006-0189-1

Key words

Navigation