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UDC 621.391

DISTRIBUTION LAWS OF STATISTIC INVARIANT TO SCALE PARAMETER IN SPECTRAL REGION

V. S. Parshin, Dr. Sc. (Tech.), full professor, Heod of the Departament, RSREU, Ryazan; This email address is being protected from spambots. You need JavaScript enabled to view it.

The aim of the research is to show approximation of distribution laws invariant to scale parameter in spectral region for two classes of random variables. For stationary stochastic processes, exact distribution law of invariant statistics in spectral region was obtained and its approximation by a simpler expression was carried out. It is shown that distribution approximation is beta distribution. Accuracy of this approximation was estimated. Also, we obtained distribution law of invariant statistics in spectral region for random pulse signals. It was assumed that statistical characteristics of random variables which determine appearance time and amplitude of pulses are independent from implementation number. Besides we obtained approximated distribution of invariant statistics. It was shown that in this case approximated distribution of invariant statistics is also a beta-distribution.

Key words: unknown scale parameter, spectral density, invariant statistic, distribution law, functional transformation, approximation.

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