American Journal of Theoretical and Applied Statistics

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Definition of Probability Characteristics of the Absolute Maximum of Non-Gaussian Random Processes by Example of Hoyt Process

Received: 03 May 2013    Accepted:     Published: 30 May 2013
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Abstract

The technique of a finding of distribution functions of an absolute maximum of non-Gaussian random processes has been illustrated. On an example of Hoyt process the limiting distribution laws of its absolute maximum have been found. By methods of statistical modeling it has been established that the given asymptotic approximations ensure a satisfactory description of the true distributions over a wide range of parameter values of the random process

DOI 10.11648/j.ajtas.20130203.13
Published in American Journal of Theoretical and Applied Statistics (Volume 2, Issue 3, May 2013)
Page(s) 54-60
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Differentiable and Nondifferentiable Random Process, Distribution Function of the Absolute Maximum, Outliers of the Random Process, Statistical Modeling

References
[1] V.I. Tikhonov, V.I. Khimenko, Outliers of Random Process Trajectories [in Russian]. Moscow: Nauka, 1987.
[2] H. Cramer, V. Leadbetter, Stationary and Related Stochastic Processes. New York: Wiley, 1967.
[3] R.L. Stratonovich, Selected Problems of Fluctuation Theory in Radio Engineering [in Russian]. Moscow: Sovet¬skoe Radio, 1961.
[4] Signal detection theory [in Russian]. Moscow: Radio i Svyaz', 1984.
[5] A.P. Trifonov, Yu.S. Shinakov, Joint Discrimination of Signals and Estimation of their Parameters against Background [in Russian]. Moscow: Radio i Svyaz', 1986.
[6] R.S. Hoyt, "Probability functions for modulus and angle of the normal complex variate", BSTJ, 1947, vol. 26, no. 2, p. 318-359.
[7] D.D. Klovsky, Discrete message passing on radio channels [in Russian]. Moscow: Radio i Svyaz', 1982.
[8] O.V. Chernoyarov The statistical analysis of random pulse signals against hindrances under conditions of various prior uncertainty [in Russian] // D.Sc. Thesis. Moscow: Moscow Pedagogical State University, 2011.
[9] V.V. Bykov, Numerical Modeling in Statistical Radio Engineering [in Russian]. Moscow: Sovetskoe Radio, 1971.
[10] J.A. McFadden, "On a class of Gaussian process for which the mean rate of crossing is infinite", J. Roy. Statist. Soc. Ser. B., 1967, vol. 29, no. 3, p. 489-502.
[11] M.V. Fedoryuk, The saddle-point method [in Russian], Moscow: Nauka, 1977.
Author Information
  • Dept. of Radio engineering Devices of the National Research University “MPEI”, Moscow, Russia

  • Dept. of Radio engineering Devices of the National Research University “MPEI”, Moscow, Russia

  • Dept. of Radio engineering Devices of the National Research University “MPEI”, Moscow, Russia

Cite This Article
  • APA Style

    O. V. Chernoyarov, A. V. Salnikova, Ya. A. Kupriyanova. (2013). Definition of Probability Characteristics of the Absolute Maximum of Non-Gaussian Random Processes by Example of Hoyt Process. American Journal of Theoretical and Applied Statistics, 2(3), 54-60. https://doi.org/10.11648/j.ajtas.20130203.13

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    ACS Style

    O. V. Chernoyarov; A. V. Salnikova; Ya. A. Kupriyanova. Definition of Probability Characteristics of the Absolute Maximum of Non-Gaussian Random Processes by Example of Hoyt Process. Am. J. Theor. Appl. Stat. 2013, 2(3), 54-60. doi: 10.11648/j.ajtas.20130203.13

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    AMA Style

    O. V. Chernoyarov, A. V. Salnikova, Ya. A. Kupriyanova. Definition of Probability Characteristics of the Absolute Maximum of Non-Gaussian Random Processes by Example of Hoyt Process. Am J Theor Appl Stat. 2013;2(3):54-60. doi: 10.11648/j.ajtas.20130203.13

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  • @article{10.11648/j.ajtas.20130203.13,
      author = {O. V. Chernoyarov and A. V. Salnikova and Ya. A. Kupriyanova},
      title = {Definition of Probability Characteristics of the Absolute Maximum of Non-Gaussian Random Processes by Example of Hoyt Process},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {2},
      number = {3},
      pages = {54-60},
      doi = {10.11648/j.ajtas.20130203.13},
      url = {https://doi.org/10.11648/j.ajtas.20130203.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.20130203.13},
      abstract = {The technique of a finding of distribution functions of an absolute maximum of non-Gaussian random processes has been illustrated. On an example of Hoyt process the limiting distribution laws of its absolute maximum have been found. By methods of statistical modeling it has been established that the given asymptotic approximations ensure a satisfactory description of the true distributions over a wide range of parameter values of the random process},
     year = {2013}
    }
    

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