Skip to main content
Log in

The lack-of-preference law and the corresponding distributions in frequency probability theory

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We obtain two new distributions in frequency probability theory and demonstrate them, in particular, in the example of frequency dictionaries. One of these distributions gives a logarithmic correction to the Zipf-Mandelbrot law, and the other describes the “tails” of the distribution.

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. Mathematical Encyclopedic Dictionary [in Russian], Sovetskaya Entsiklopediya, Moscow, 1988.

  2. 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 the stock market,” Mat. Zametki [Math. Notes], 78 (2005), no. 6, 870–877.

    Google Scholar 

  3. V. P. Maslov, “Nonlinear averaging in economics,” Mat. Zametki [Math. Notes], 78 (2005), no. 3, 377–395.

    MathSciNet  Google Scholar 

  4. V. P. Maslov, “A refinement of Zipf’s law for frequency dictionaries,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 405 (2005), no. 5, 591–594.

    Google Scholar 

  5. V. P. Maslov, Quantum Economics [in Russian], Nauka, Moscow, 2005.

    Google Scholar 

  6. E. A. Asarin and A. V. Pokrovskii, “Application of Kolmogorov complexity to the analysis of the dynamics of controllable systems,” Avtomat. i Telemekh. [Automat. Remote Control] (1986), no. 1, 25–33.

  7. E. Mendelson, Introduction to Mathematical Logic, Van Nostrand, Toronto-New York-London, 1966; Russian transl.: Nauka, Moscow, 1976.

    Google Scholar 

  8. A. A. Karatsuba, “The complexity of computations,” Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.], 211 (1995), 186–202.

    MATH  MathSciNet  Google Scholar 

  9. L. D. Landau and E. M. Lifshits, Statistical Physics [in Russian], Nauka, Moscow, 1964.

    Google Scholar 

  10. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco, 1982.

    MATH  Google Scholar 

  11. V. P. Maslov and V. E. Nazaikinskii, “Tunnel canonical operator and thermodynamics,” Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.] (2006) (to appear).

  12. British National Corpus, ftp.itri.bton.ac.uk/pub/bnc.

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Matematicheskie Zametki, vol. 80, no. 2, 2006, pp. 220–230.

Original Russian Text Copyright © 2006 by V. P. Maslov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maslov, V.P. The lack-of-preference law and the corresponding distributions in frequency probability theory. Math Notes 80, 214–223 (2006). https://doi.org/10.1007/s11006-006-0130-7

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11006-006-0130-7

Key words

Navigation