MODELS OF ASYMMETRICAL DISTRIBUTIONS OF RANDOM VARIABLES WITH ZERO ASYMMETRY COEFFICIENT

A.I. Krasilnikov

Èlektron. model. 2018, 38(1):19-34
https://doi.org/10.15407/emodel.38.01.019

ABSTRACT

The use of mixtures of distributions for finding possible asymmetrical distributions with zero asymmetry coefficients has been substantiated as based on the method of randomization. Mathematical models of asymmetric distributions with zero asymmetry coefficients have been analyzed; the models were obtained by the randomization of the shift and scale parameters of the basic distribution function. The examples of finding such distributions are given. The obtained results
allow realizing the mathematical and computer modeling of asymmetric distributions with zero asymmetry coefficients.

KEYWORDS

asymmetric distributions, cumulant coefficients, coefficient of skewness, mixtures of distributions, conjugate distributions.

REFERENCES

1. Novitskii, P.V. and Zograf, I.A. (1991), Otsenka pogreshnostei rezultatov izmerenii [Error estimation in measurement results], Energoatomizdat, St. Petersburg, Russia.
2. 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
3. Shelukhin, O.I. (1998), Negaussovskie protsessy v radiotekhnike [Non-Gaussian processes in radio engineering], Radio i svyaz, Moscow, Russia.
4. Marchenko, B.G., Matsiuk, O.V. and Fryz, M.Ye. (2005), Matematychni modeli y obrobka sygnaliv v oftalmolohii [Mathematical models and processing of signals in ophthalmology], Ternopil Ivan Pul’uj National Technical University, Ternopil, Ukraine.
5. Potapov, A.A., Gilmutdinov, A.Kh. and Ushakov, P.A. (2008), “System principles and element base of fractal radioelectronics. Part 2. Methods of synthesis, models and application prospect”, Radiotekhnika i elektronika, Vol. 53, no. 11, pp. 1347-1394.
6. Palagin, V.V. (2010), “Adaptation of moment quality criterion for the multiple-choice task of verification of hypotheses when using the polynomial decision rules”, Elektronnoe modelirovanie, Vol. 32, no. 4, pp. 17-33.
7. Krasilnikov, A.I. (2014), Modeli shumovykh signalov v sistemakh diagnostiki teploenergeticheskogo oborudovaniya [Models of noise signals in the systems of diagnostics of heatand-power producing equipment], Institute of Engineering Thermophysics of NAS of Ukraine, Kyiv, Ukraine.
8. Babak, S.V., Myslovich, M.V. and Sysak, R.M. (2015), Statisticheskaya diagnostika elektrotekhnicheskogo oborudovaniya [Statistical diagnostics of the electrotechnical equipment], Institute of Electrodynamics of NAS of Ukraine, Kyiv, Ukraine.
9. Bostandzhiyan, V.A. (2009), Raspredelenie Pirsona, Dzhonsona, Veibulla i obratnoe normalnoe. Otsenivanie ikh parametrov [Pearson, Johnson, Weibull distribution and the reverse normal. Estimation of their parameters], Institute for Problems of Chemical Physics of RAS, Chernogolovka, Russia.
10. Senatov, V.V. (2009), Tsentralnaya predelnaya teorema: Tochnost approksimatsii i asimptoticheskie razlozheniya [Central limit theorem: Approximation accuracy and asymptotic decompositions], Knizhnyi dom «Librokom», Moscow, Russia.
11. Korolev, V.Yu. (2004), Smeshannye gaussovskie veroyatnostnye modeli realnykh protsessov [ThemixedGaussian probabilisticmodels of real processes],Maks Press, Moscow,Russia.
12. Malakhov, A.N. (1978), Kumulyantnyi analiz sluchainykh negaussovykh protsessov i ikh preobrazovanii [Cumulant analysis of random non-Gaussian processes and their transformations], Sovetskoe radio, Moscow, Russia.
13. Kunchenko, Yu.P. (2001), Polinomialnye otsenki parametrov blizkikh k gaussovskim sluchainyh velichin. Ch. I. Stokhasticheskie polinomy, ikh svoistva i primenenie dlya nakhozhdeniya otsenok parametrov [Parameter polynomial estimations of random variables close to Gaussian. Part I. Stochastic polynomials, their properties and application for finding the parameter estimations], ChITI, Cherkassy, Ukraine.
14. De Carlo, L.T. (1997), “On the meaning and use of kurtosis”, Psychological Methods, Vol. 2, no. 3, pp. 292-307.
https://doi.org/10.1037/1082-989X.2.3.292
15. 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.
16. Krasilnikov, A.I., (2002), “Poisson moments of infinitely divisible distributions”, Elektronika i svyaz, no. 15, pp. 84-88.
17. Marchenko, B.G. and Shcherbak, L.N. (1993), “Moment problem and cumulant analysis”, Otbor i obrabotka informatsii, Vol. 9 (85), pp. 12-20.
18. 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
19. Jondeau, E. and Rockinger, M. (2001), “Gram-Charlier densities”, Journal of Economic Dynamics and Control, Vol. 25, pp. 1457-1483.
https://doi.org/10.1016/S0165-1889(99)00082-2
20. Jondeau, E. and Rockinger, M. (2003), “Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements”, Journal of Economic Dynamics and Control, Vol. 27, pp. 1699-1737.
21. Krasilnikov, A.I. and Pilipenko, K.P (2007), “Unimodal two-component Gaussian mixture. Excess kurtosis”, Elektronika i svyaz, no. 2 (37), pp. 32-38.
22. Chepynoha, A.V. (2010), “Areas of realization of bi-Gaussian models of skewness-excess random variables with the punched moment-cumulant description”, Visnyk ChDTU, no. 2, pp. 91-95.

Full text: PDF (in Russian)