MODELING OF PERFORATED RANDOM VARIABLES ON THE BASIS OF MIXTURES OF SHIFTED DISTRIBUTIONS

A.I. Krasilnikov, Cand. Sc. (Phys.-Math.),
Institute of Technical Thermal Physics,
2a Zhelyabov St, Kyiv, 03057, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Èlektron. model. 2018, 40(1):47-62
https://doi.org/10.15407/emodel.40.01.047

ABSTRACT

The use of a family of mixtureû of shifted distributions for the modeling of perforated distributions and random variables has been justified. Peculiarities of simulation of perforated distributions are considered. The cumulant coefficients of mixtures of shifted distributions have been analyzed. The models of perforated random variables on the basis of a two-component mixture of shifted logistic distributions have been constructed.

KEYWORDS

cumulant coefficients, moment-cumulant models, cumulant analysis, perforated distributions, mixtures of distributions.

REFERENCES

1. Malakhov, A.N. (1978), Kumuliantnyi analiz sluchainykh negaussovykh protsessov i ikh preobrazovanii [Cumulant analysis of random non-Gaussian processes and their transformations], Sov. radio, Moscow, USSR.
2. Kunchenko, Yu.P. (2001), Polinomialnye otsenki parametrov blizkikh k gaussovskim sluchainykh velichin. Ch.I. Stokhasticheskie polinomy, ih svoistva i primenenie dlia nakhozhdeniia otsenok parametrov [Parameter polynomial estimations of random variables close to Gaussian. Part I. Stochastic polynomials, their properties and application for finding parameter estimations], ChITI, Cherkassy, Ukraine.
3. Kunchenko, Yu.P. and Zabolotnyi, S.V. (2001), Polinomialnye otsenki parametrov blizkikh k gaussovskim sluchainykh velichin. Ch. II. Otsenka parametrov blizkikh k gaussovskim sluchainykh velichin [Parameter polynomial estimations of random variables close to Gaussian. Part II. Parameters estimation of vandom variables close to Gaussian], ChITI, Cherkassy, Ukraine.
4. Alexandrou, D., De Moustier, C. and Haralabus, G. (1992), Evaluation and verification of bottom acoustic reverberation statistics predicted by the point scattering model, J. Acoust. Soc. Am., Vol. 91, no. 3, pp. 1403-1413.
https://doi.org/10.1121/1.402471
5. Karpov, I.G. (1999), “Approximate identification of distribution laws of hindrances in adaptive receivers with use of a method of the moments”, Radiotekhnika, no. 7, pp. 11-14.
6. Kuznetsov, V.V. (2009), “Use of the moments of the third order in calculations of electric loadings”, Vestnik Samarskogo GTU. Seriia “Tekhnicheskie nauki”, no. 2 (24), pp. 166-171.
7. Wang, H. and Chen, P. (2009), Fault diagnosis method based on Kurtosis wave and information divergence for rolling element bearings, WSEAS Transactions on Systems, Vol. 8, Iss. 10, pp. 1155-1165.
8. Kuznetsov, B.F., Borodkin, D.K. and Lebedeva, L.V. (2013), “Cumulant models of additional errors”, Sovremennye tekhnologii. Sistemnyi analiz.Modelirovanie, no. 1 (37), pp. 134-138.
9. Lukach, E. (1979), Kharakteristicheskie funktsii [Characteristic Functions], Translated by Zolotarev, V.M., Nauka, Moscow, USSR.
10. Kunchenko, Iu.P., Zabolotnii, S.V.,KovalV.V. and Chepynoha,A.V. (2005), “Simulation of excess random variables with a given cumulative description on the basis of the bi-Gaussian distribution”, Visnyk ChDTU, no. 1, pp. 38-42.
11. Zabolotnii, S.V. and Chepynoha, A.V. (2008), “Tetra-Gaussian symmetrically distributed probabilistic models on the basis of a moment description”, Zbirnyk naukovykh prats IPME im. G.Ie. Pukhova NAN Ukrainy, no. 47, pp. 92-99.
12. Chepynoha, A.V. (2010), “Areas of realization of bi-Gaussian models of asymmetric-excess random variables with a perforated moment-cumulant description”, Visnyk ChDTU, no. 2, pp. 91-95.
13. Krasilnikov, A.I. (2013), “Class of non-Gaussian distributions with zero skewness and kurtosis”, Izvestiia vysshikh uchebnykh zavedenii. Radioelektronika, Vol. 56, no. 6, pp. 56-63.
https://doi.org/10.3103/S0735272713060071
14. Krasilnikov, A.I. (2017), “Class of non-Gaussian symmetric distributions with zero coefficient of kurtosis”, Elektronnoe modelirovanie, Vol. 39, no. 1, pp. 3-17.
15. Krasilnikov, A.I. (2016), “Models of asymmetrical distributions of random variables with zero asymmetry coefficient”, Elektronnoe modelirovanie, Vol. 38, no. 1, pp. 19-33.
16. Korolev, V.Iu. (2008), Veroiatnostno-statisticheskii analiz khaoticheskikh protsessov s pomoshchiu smeshannykh gaussovskikh modelei. Dekompozitsiia volatilnosti finansovykh indeksov i turbulentnoi plazmy [Probabilistic-statistical analysis of chaotic processes using mixed Gaussian models. Decomposition of volatility of financial indices and turbulent plasma], Izdatelstvo Instituta problem informatiki RAN, Moscow, Russia.
17. Feller, V. (1984), Vvedenie v teoriiu veroiatnostei i ee prilozheniia [Introduction to probability theory and its applications], Vol. 2., Translated by Prokhorov, Yu.V., Mir, Moscow, USSR.
18. Vadzinskii, R.N. (2001), Spravochnik po veroiatnostnym raspredeleniiam [Reference book on probabilistic distributions], Nauka, St. Petersburg, Russia.
19. Kendall, M. and Stuart, A. (1966), Teoriia raspredelenii [Distribution theory], Translated by Sazonov, V.V. and Shiriaev, A.N., Ed Kolmogorov, A.N., Nauka, Moscow, Russia.

Full text: PDF (in Russian)