A.P. Samoylenko - Associate Professor, Department of Radio and Telecommunication Systems, Federal State-Owned Autonomy Educational Establishment of Higher Education «Southern Federal University» E.B. Gorbunova - Post-Graduate Student, Department of Radio and Telecommunication Systems, Federal State-Owned Autonomy Educational Establishment of Higher Education «Southern Federal University». E-mail: kattag@rambler.ru

In order to predict the reliability of avionics complex it is necessary to estimate the probability density function for the available sample without resorting to grouping the data and evaluate the accuracy of assessment compared to conventional methods. To solve the above problem the non-parametric simulation method of constructing the probability density of the random variable is proposed. The method consists in generating complementary «pseudo-samples» around each element of the original sample, followed by the histogram construction. To construct a probability density the histogram is interpolated by cubic splines with subsequent normalization. The authors investigated the complementary arrays parameters and chose their values ensuring the best recovery of the desired probability density. The dynamics of standard deviation evaluation shift caused by the sample processing is also investigated. It is shown that the proposed method can reduce the standard deviation estimation error to a 3-10% in comparison with the estimates made for the primary sample. The research results outlined in this article were obtained with the financial support of the Ministry of Education and Science of the Russian Federation in the framework of the state task №2014/74 «Development of diagnostics of the state of biological and technical objects with the use of algorithms for analysis of non-stationary signals». Studies conducted in the SFU FSAEI VPO.

 

1. Kobzar A.I. Prikladnaja matematicheskaja statistika. Dlja inzhenerov i nauchnykh rabotnikov. M.: FIZMATLIT. 2006. 816 s.
2. Gaskarov D. V., SHapovalov V.I. Malaja vyborka. M.: Statistika. 1978. 248 s.
3. Krjanev A.V. Lukin G.V. Matematicheskie metody obrabotki neopredelennykh dannykh. M.: FIZMATLIT. 2003. 216 s.
4. Samojjlenko A.P., Gorbunova E.B. Tekhnologii prognozirovanija nadezhnosti REHA pri ogranichennykh obemakh statisti­cheskikh dannykh. Rostov-na-Donu: Izd-vo JUFU. 2014. 153 s.
5. CHavchanidze V.V., Kumsishvili V.A. Ob opredelenii zakonov raspredelenija na osnove malogo chisla nabljudenijj // V kn.: Primenenie vychislitelnojj tekhniki dlja avtomatizacii proizvodstva (Trudy soveshhanijj 1959 g.). M.: Mashgiz. 1961. S. 71-75.
6. Parsen E. On estimation of a probabilities for sums of bounded random variables // Annals of Mathematical Statistics. 1962. V. 33. P. 1065-1076.
7. Rosenblatt M. Remarks on some nonparametric estimates of a density function // Annals of Mathematical Statistics. 1956. V. 27. P. 832-835.
8. EHfron B., Diakonis P. Statisticheskie metody s intensivnym ispolzovaniem EHVM // V mire nauki. 1983. № 7. C. 60-74.
9. Tikhonov A.N., Goncharskijj A.V., Stepanov V.V., JAgola A.G. CHislennye metody reshenija nekorrektnykh zadach. M.: Nauka. 1990. 232 s.
10. Gaskarov D. V., Golinkevich T.A., Mozgalevskijj A.V. Prognozirovanie tekhnicheskogo sostojanija i nadezhnosti REHA / Pod red. T.A. Golinkevicha. M.: Sov. radio. 1974. 224 s.