Estimation of parameters of poly-gaussian models by polynomial maximization method

Authors

DOI:

https://doi.org/10.15587/1729-4061.2014.23156

Keywords:

polygaussian distribution, polynomial maximization method, moment-cumulant description, statistical modeling

Abstract

A promising direction for solving various problems of processing random sequences and signals is the use of poly-Gaussian models (Gaussian mixtures). To estimate the parameters of these models, the polynomial maximization method (Kunchenko’s method) is first proposed in the paper. This method uses a moment-cumulant description of random variables. It is positioned as an alternative between the method of moments and the maximum likelihood method. The results of estimating the parameters for approximating the frequency distribution by the bi-Gaussian model are given in the paper. The coefficients of reducing the variance estimate were calculated and the approximation adequacy using the chi-square criterion was estimated. According to the results of the conducted studies it may be concluded about the great advantage of Kunchenko’s method over the method of moments and its approximation of the efficiency to the maximum likelihood method. Further studies are aimed at estimating the parameters of poly-Gaussian models of higher orders and developing random sequences on their basis.

Author Biographies

Анатолий Владимирович Чепинога, Cherkassy state technological university Chekhova, 42, f.528, Cherkassy, Ukraine, 18006

Assistant

Department of the radio engineering

Сергей Васильевич Заболотний, Cherkassy state technological university Rizdvyana, 62, f.58, Cherkassy, Ukraine, 18005

Candidate of engineering sciences, associate professor

Department of the radio engineering

Елена Владимировна Бурдукова, Cherkassy state technological university S.Smirnova, 2, f.131, Cherkassy, Ukraine, 18021

Engineer

Department of the radio engineering

References

  1. Литвак, М. Я. Полигауссовские модели негауссовской случайно-шероховатой поверхности [Текст] / М. Я. Литвак, В. И. Малюгин // Журнал технической физики. – 2012. – Т. 82, № 4. – С. 99–107.
  2. Чикрин, Д. Е. Построение эффективных систем регулировки мощности в каналах связи с негауссовым комплексом помех [Текст] / Д. Е. Чикрин, В. И. Малюгин // Радиотехнические и телекоммуникационные системы. – 2011. – № 4. – С. 78–80.
  3. Melnykov, V. Finite mixture models and model-based clustering [Text] / V. Melnykov, R. Maitra // Statistics Surveys. – 2010. – № 4. – P. 80–116.
  4. Delay and Doppler Estimation of Gaussian Mixtures Using Moment [Text] : 17th inter. conf. // Systems, Signals and Image Processing. Proceedings Chair Fabiana R. Leta. — Rio de Janeiro: IWSSIP, 2010. – 532 p.
  5. Ибатуллин, Э. А. Оценивание параметров полигауссового распределения плотностей вероятности сигналов методом максимального правдоподобия [Текст] / Э. А. Ибатуллин // Электронный научно-технический журнал “Информационные технологии и телерадиокоммуникации”. – 2005. – № 5 (1). – С. 25–32
  6. Королев, В. Ю. Разделение смесей вероятностных распределений при помощи сеточных методов моментов и максимального правдоподобия [Текст] / В. Ю. Королев, А. Л. Назаров // Автомат. и телемех. – 2010. – № 3. – С. 98–116.
  7. Xu, D. Continuous empirical characteristic function estimation of mixtures of normal parameters [Text] / D. Xu, J. Knight // Econometric Reviews. – 2011. – Vol. 30, Issue 1. – P. 25–50.
  8. Kunchenko, Y. P. Polynomial parameter estimation of close to Gaussian random variables [Text] / Y. P. Kunchenko. – Aachen: Shaker, 2002. – 396 p.
  9. Кунченко, Ю. П. Стохастические полиномы [Текст] / Ю. П. Кунченко. – К.: Наукова думка, 2006. – 275 с.
  10. Kelley, C. T., Solving Nonlinear Equations with Newton’s Method, no 1 in Fundamentals of Algorithms [Text] / C. T. Kelley. – Philadelphia: SIAM, 2003. – 104 p.
  11. Greenwood, P. E. A guide to chi-squared testing [Text] / P. E. Greenwood, M. S. Nikulin. – New York: Wiley, 1996. – 280 p.
  12. Чепинога, А. В. Аналіз ефективності застосування чисельних методів для пошуку параметрів полігаусових моделей [Текст] / А. В. Чепинога // Вісник Інженерної академії України. – 2010. – № 2. – С. 135–139.
  13. Litvak, M. Y., Malugin, V. I. (2012). Poligaussian model of nonGaussian random rough surface. Technical Physics, Vol. 82, 4, 99–107.
  14. Chikrin, D. E. (2011). Building effective systems for power control in the communication channels with non-Gaussian complex noise. Radio Engineering and telecommunications systems. 4, 78–80.
  15. Melnykov, V., Maitra, R. (2010). Finite mixture models and modelbased clustering. Statistics Surveys. 4, 80–116.
  16. Gholizadeh, M. H., Amindavar, H. (2010). Delay and Doppler Estimation of Gaussian Mixtures Using Moment. 17th International Conference on Systems, Signals and Image Processing, 465–468.
  17. Ibatullin, E. A. (2005). Parameter Estimation of poligaussian probability density signals by maximum likelihood. Information Technologies and teleradiocommunication, 5 (1), 25–32.
  18. Korolev, V. Y., Nazarov, A. (2010). Separating mixtures of probability distributions using the grid method of moments and maximum likelihood. Automatic. and telemechanics, 3, 98–116.
  19. Xu, D., Knight J. (2011). Continuous empirical characteristic function estimation of mixtures of normal parameters. Econometric Reviews. Vol. 30, 1, 25–50.
  20. Kunchenko, Y. P. (2002). Polynomial parameter estimation of close to Gaussian random variables. Shaker, 396.
  21. Kunchenko, Y. P. (2006). Stochastic polynomials. Science Dumka, 275.
  22. Kelley, C. T. (2003). Solving Nonlinear Equations with Newton’s Method, no 1 in Fundamentals of Algorithms. SIAM, 104.
  23. Greenwood, P. E., Nikulin, M. S. (1996). A guide to chi-squared testing. Wiley, 280.
  24. Chepinoga, A. V. (2010). Analysis of the efficacy of numerical methods for finding parameters of poligaussian models. Journal of Engineering Academy of Ukraine, 2, 135–139.

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Published

2014-04-09

How to Cite

Чепинога, А. В., Заболотний, С. В., & Бурдукова, Е. В. (2014). Estimation of parameters of poly-gaussian models by polynomial maximization method. Eastern-European Journal of Enterprise Technologies, 2(4(68), 43–46. https://doi.org/10.15587/1729-4061.2014.23156

Issue

Vol. 2 No. 4(68) (2014): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2014 Анатолий Владимирович Чепинога, Сергей Васильевич Заболотний, Елена Владимировна Бурдукова

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