A.I. Krasilnikov
Èlektron. model. 2019, 41(3):15-32
ABSTRACT
The properties of the probability density, its parameters, the central moments, and the cumulantThe properties of the probability density, its parameters, the central moments, and the cumulantcoefficients of the Subbotin distribution family were investigated. Based on the properties of thederivative of the probability density and cumulant coefficients, a classification of the Subbotinfamily of distributions was proposed, and criteria for choosing the probability density for approximatingthe distributions of non-Gaussian random variables were established.
KEYWORDS
family of Subbotin distributions, generalized Gaussian distribution, generalizedfamily of Subbotin distributions, generalized Gaussian distribution, generalizednormal distribution, error distribution.
REFERENCES
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3. Subbotin, M.T. (1923), “On the law of frequency of error”, Matematicheskii sbornik, Vol. 31, no. 2, pp. 296-301.
4. Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011), Statistical Distributions. Fourth Edition, John Wiley & Sons, New Jersey.
https://doi.org/10.1002/9780470627242
5. Novitskii, P.V. and Zograf, I.A. (1991), Otsenka pogreshnostei rezultatov izmerenii [Error Estimation in Measurement Results], Energoatomizdat, St. Petersburg, Russia.
6. Shelukhin, O.I. (1999), Negaussovskie protsessy v radiotekhnike [Non-Gaussian Processes in Radio Engineering], Radio i sviaz, Moscow, Russia.
7. Saatci, E. and Akan, A. (2010), “Respiratory parameter estimation in non-invasive ventilation based on generalized Gaussian noise models”, Signal processing, Vol. 90, no. 2, p. 480-489.
https://doi.org/10.1016/j.sigpro.2009.07.015
8. Sharifi, K. and Leon-Garcia, A. (1995), “Estimation of shape parameter for generalized Gaussian distribution in subband decomposition of video”, IEEE Trans. on Circuits and Systems for Video Technology, Vol. 5, no. 1, pp. 52-56.
https://doi.org/10.1109/76.350779
9. Dominguez-Molina, J.A., Gonzalez-Farias, G. and Rodriguez-Dagnino, R.M. (2001), A practical procedure to estimate the shape parameter in the generalized Gaussian distribution, available at: http://www.cimat.mx/reportes/enlinea/I-01-18_eng.pdf
10. Nadarajah, S. (2005), “A generalized normal distribution”, Journal of Applied Statistics, Vol. 32, no. 7, pp. 685-694.
https://doi.org/10.1080/02664760500079464
11. Pogany, T.K. and Nadarajah, S. (2010), “On the characteristic function of the generalized normal distribution”, Comptes Rendus Mathåmatique, 348(3), pp. 203-206.
https://doi.org/10.1016/j.crma.2009.12.010
12. Crowder, G.E. and Moore, A.H. (1983), “Adaptive Robust Estimation Based on a Family of Generalized Exponential Power Distributions”, IEEE Transactions on Reliability, Vol. R-32, no. 5, pp. 488-495.
https://doi.org/10.1109/TR.1983.5221739
13. Varanasi, M.K. and Aazhang, B. (1989), “Parametric generalized Gaussian density estimation”, J. Acoust. Soc. Am., Vol. 86, no. 4, pp. 1404-1415.
https://doi.org/10.1121/1.398700
14. Zabolotnii, S.V., Chepynoha, A.V., Bondarenko, Yu.Yu. and Rud, M.P. (2018), “Polynomial estimates of parameters for data with exponential power distribution”, Visnyk NTUU KPI. Seriia radiotekhnika, radioaparatobuduvannia, no. 75, pp. 40-47.
15. Nardon, M. and Pianca, P. (2009), “Simulation techniques for generalized Gaussian densities”, Journal of Statistical Computation and Simulation, Vol. 79, Issue 11, pp. 1317-1329.
https://doi.org/10.1080/00949650802290912
16. Kalke, S. and Richter, W.-D. (2013), “Simulation of the p-generalized Gaussian distribution”, Journal of Statistical Computation and Simulation, Vol. 83, no. 4, pp. 639-665.
https://doi.org/10.1080/00949655.2011.631187
17. Ianke, E., Emde, F. and Lesh, F. (1964), Spetsialnye funktsii (formuly, grafiki, tablitsy) [Tafeln Höherer Funktionen], Translated by Sedov L.I., Nauka, Moscow, Russia.
18. Dvait, G.B. (1977), Tablitsy integralov i drugie matematicheskie formuly [Tables of Integrals and Other Mathematical Data], Translated by Levi, N.V., Edited by Semendiaev K.A., Nauka, Moscow, Russia.
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