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Approximation of experimental data distribution by close to gaussian random variable models

Olena Burdukova, Yurii Lega, Oleksandr Havrysh, Tetiana Vorobkalo, Artur Ivashchenko

Abstract

In the paper analytic expressions of approximating functions on the basis of models with perforated cumulant description are obtained. Densities of the distribution of various models, close to the Gaussian random variables, are built, the comparison with empirical distribution density is made and the value of approximation errors for each model class is found. It is shown that the models based on perforated cumulant description are an effective tool for approximating real statistical data of different nature

Keywords:

approximation, number of Edgeworth, cumulant coefficients, close to the Gaussian random variables, perforation of cumulant description

Retrieved from Volume 22, No. 1, 2017

Pages 17-24

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References

  1. Van Trees, H.L. (1977). Detection, estimation, and modulation theory. Vol. 3: Signal processing in radar and sonar and reception of random Gaussian signals in noise (V.T. Goryainov, Ed.; Trans. from English). Moscow: Sovetskoe Radio.
  2. Levin, B.R. (1969). Theoretical foundations of statistical radio engineering. Book 1. Moscow: Sovetskoe Radio.
  3. Kunchenko, Yu.P. (2001). Polynomial estimates of parameters of random variables close to Gaussian. Part 1: Stochastic polynomials, their properties and application for parameter estimation. Cherkasy: ChITI.
  4. Havrysh, O.S., Zabolotnyi, S.V., Burdukova, E.V., & Ivashchenko, A.A. (2015). Criterion of approximation of statistical data by models based on perforated cumulant description. In Signal Processing and Non-Gaussian Processes: Proceedings of the 5th International Scientific and Practical Conference (pp. 14-17). Cherkasy: ChSTU.
  5. Berehun, V.S., Berehun, V.S., & Krasilnikov, O.I. (2010). Approximation methods for finding probability density functions. Electronics and Communications, 4 (57), 51-55.
  6. Zabolotnyi, S.V., & Chepynoha, A.V. (2012). Approximation of empirical distributions of polynomial statistics by poly-Gaussian models. In Modern Technologies in Telecommunications: Proceedings of the 5th International Scientific and Technical Symposium (pp. 86-88). Kyiv: State University of Information and Communication Technologies.
  7. Malakhov, A.N. (1978). Cumulant analysis of non-Gaussian random processes and their transformations. Moscow: Sovetskoe Radio.
  8. Wikipedia. (n.d.). List of countries by life expectancy. Retrieved from https://en.wikipedia.org/wiki/List_of_countries_by_life_expectancy
  9. Statistica.ru. (n.d.). Quality control in confectionery production. Retrieved from http://www.statistica.ru/localportals/industry-analytics/example/1558/

Suggested citation

Burdukova, О., Lega, Yu. , Havrysh, O., Vorobkalo, T., & Ivashchenko, A. (2017). Approximation of experimental data distribution by close to gaussian random variable models. Bulletin of Cherkasy State Technological University, 22(2), 17-24.