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
Volume 2, Issue 3, May 2013, Pages: 54-60
Received: May 3, 2013; Published: May 30, 2013
Views 3238      Downloads 155
Authors
O. V. Chernoyarov, Dept. of Radio engineering Devices of the National Research University “MPEI”, Moscow, Russia
A. V. Salnikova, Dept. of Radio engineering Devices of the National Research University “MPEI”, Moscow, Russia
Ya. A. Kupriyanova, Dept. of Radio engineering Devices of the National Research University “MPEI”, Moscow, Russia
Article Tools
PDF
Follow on us
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
Keywords
Differentiable and Nondifferentiable Random Process, Distribution Function of the Absolute Maximum, Outliers of the Random Process, Statistical Modeling
To cite this article
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, American Journal of Theoretical and Applied Statistics. Vol. 2, No. 3, 2013, pp. 54-60. doi: 10.11648/j.ajtas.20130203.13
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.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186