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Mat. Zametki, 2006, Volume 80, Issue 2, Pages 220–230 (Mi mz2803)  

This article is cited in 27 scientific papers (total in 27 papers)

The Lack-of-Preference Law and the Corresponding Distributions in Frequency Probability Theory

V. P. Maslov

M. V. Lomonosov Moscow State University, Faculty of Physics

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.

Keywords: frequency probability, frequency dictionary, Zipf–Mandelbrot law, tail of distribution, Shannon entropy, Wiener process, Kolmogorov complexity

DOI: https://doi.org/10.4213/mzm2803

Full text: PDF file (646 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2006, 80:2, 214–223

Bibliographic databases:

UDC: 517.958
Received: 14.03.2006

Citation: V. P. Maslov, “The Lack-of-Preference Law and the Corresponding Distributions in Frequency Probability Theory”, Mat. Zametki, 80:2 (2006), 220–230; Math. Notes, 80:2 (2006), 214–223

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Maslov, “Bose gas of anharmonic oscillators and refinement of the Zipf law”, Theoret. and Math. Phys., 148:3 (2006), 1295–1296  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. V. P. Maslov, “Bose–Einstein-type distribution applied to flicker noise and turbulence”, Theoret. and Math. Phys., 149:2 (2006), 1574–1575  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. V. P. Maslov, “On a new rank distribution”, Math. Notes, 80:3 (2006), 447–448  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. V. P. Maslov, “On the minimization of operational risks”, Math. Notes, 80:4 (2006), 539–541  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. V. P. Maslov, T. V. Maslova, “On Zipf's law and rank distributions in linguistics and semiotics”, Math. Notes, 80:5 (2006), 679–691  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. V. P. Maslov, “Negative asymptotic topological dimension, a new condensate, and their relation to the quantized Zipf law”, Math. Notes, 80:6 (2006), 806–813  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. V. P. Maslov, “Thermal and gas dynamical processes in NPP's after an accident”, Theory Probab. Appl., 51:3 (2007), 513–517  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Maslov V. P., “Minimization of the statistical risk of purchases at the market of realty and consumer durables”, Dokl. Math., 74:3 (2006), 887–888  crossref  zmath  isi  elib  scopus
    9. Maslova T. V., “Zipf's law and Maslov's formula as applied to semiotic systems”, Dokl. Math., 74:3 (2006), 917–920  crossref  zmath  isi  elib  scopus
    10. Maslov V. P., “Quantum linguistic statistics”, Russ. J. Math. Phys., 13:3 (2006), 315–325  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Maslov V. P., Shafarevich A. I., “Rapidly oscillating asymptotic solutions of the Navier–Stokes equations, coherent structures, Fomenko invariants, Kolmogorov spectrum, and flicker noise”, Russ. J. Math. Phys., 13:4 (2006), 414–424  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. Maslov V. P., “On operational risks”, Dokl. Math., 74:3 (2006), 914–916  crossref  mathscinet  zmath  isi  elib  scopus
    13. Maslova T. V., “The application of the construction of Kolmogorov complexity and of a theorem by Maslov to semiotic systems”, Russ. J. Math. Phys., 13:4 (2006), 425–430  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    14. Maslov V. P., Nazaikinskii V. E., “Tunnel canonical operator in thermodynamics”, Funct. Anal. Appl., 40:3 (2006), 173  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    15. V. P. Maslov, “Zeroth-order phase transitions and Zipf law quantization”, Theoret. and Math. Phys., 150:1 (2007), 102–122  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. V. P. Maslov, “A Theorem on Parastatistics and Its Application”, Theoret. and Math. Phys., 150:3 (2007), 436–437  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
    17. V. P. Maslov, “General Notion of a Topological Space of Negative Dimension and Quantization of Its Density”, Math. Notes, 81:1 (2007), 140–144  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    18. V. P. Maslov, “Densities of Lattices Corresponding to Spaces of Positive, Negative, and Variational Dimension, and Their Application to Time Series”, Math. Notes, 81:1 (2007), 222–233  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    19. V. P. Maslov, “Parastatistics and the General Theorem of Probability Theory as Applied to Risk-Free Investments”, Math. Notes, 81:3 (2007), 422–425  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    20. Maslov V. P., “Quantization of topological spaces of negative dimension, parastatistics, and distribution of dependent random variables”, Dokl. Math., 75:3 (2007), 424–427  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    21. Maslov V. P., “Revision of probability theory from the point of view of quantum statistics”, Russ. J. Math. Phys., 14:1 (2007), 66–95  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    22. V. P. Maslov, “Quasithermodynamics and a Correction to the Stefan–Boltzmann Law”, Math. Notes, 83:1 (2008), 72–79  mathnet  crossref  crossref  mathscinet  zmath  isi
    23. V. P. Maslov, “Quasithermodynamic correction to the Stefan–Boltzmann law”, Theoret. and Math. Phys., 154:1 (2008), 175–176  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    24. Maslov V. P., “On the superfluidity of classical liquid in nanotubes. III”, Russ. J. Math. Phys., 15:1 (2008), 98–101  crossref  mathscinet  zmath  adsnasa  isi  elib
    25. Maslov V. P., Maslova T. V., “Synergetics and architecture”, Russ. J. Math. Phys., 15:1 (2008), 102–121  crossref  mathscinet  zmath  adsnasa  isi  elib
    26. M. A. Guzev, E. Yu. Nikitina, “Rangovyi analiz Ugolovnogo Kodeksa RF (na primere ekonomicheskikh prestuplenii)”, Dalnevost. matem. zhurn., 10:2 (2010), 117–129  mathnet
    27. V. P. Maslov, A. I. Shafarevich, “Asymptotic solutions of Navier–Stokes equations and topological invariants of vector fields and Liouville foliations”, Theoret. and Math. Phys., 180:2 (2014), 967–982  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
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