Сomparative Analysis of Polynomial Maximization and Maximum Likelihood Estimates for Data with Exponential Power Distribution

Authors

  • S. V. Zabolotnii Cherkasy State Business College, Ukraine
  • A. V. Chepynoha Cherkasy State Technological University, Ukraine
  • A. M. Chorniy Cherkasy State Technological University, Ukraine
  • A. V. Honcharov Cherkasy State Technological University, Ukraine

DOI:

https://doi.org/10.20535/RADAP.2020.82.44-51

Keywords:

exponential power distribution, stochastic polynomials, high-order statistics, parameter estimation

Abstract

The work is devoted to the estimate accuracy comparative analysis of the experimental data parameters with exponential power distribution (EPD) using the classical Maximum Likelihood Estimation (MLE) and the original Polynomial Maximization Method (PMM). In contrast to the parametric approach of MLE, which uses the description in the form of probability density distribution, PMM is based on a partial description in the of higher-order statistics form and the mathematical apparatus of Kunchenko's stochastic polynomials. An algorithm for finding PMM estimates using 3rd order stochastic polynomials is presented. Analytical expressions allowing to determine the variance of PMM-estimates of the asymptotic case parameters and EPD parameters with a priori information are obtained. It is shown that the relative theoretical estimates accuracy of different methods significantly depends on the EPD shape parameter and matches only for a separate case of Gaussian distribution. The effectiveness of different approaches (including valuation of mean values estimates) both with and without a priori information on EPD properties was investigated by repeated statistical tests (through Monte Carlo Method). The greatest efficiency areas for each of methods depending on EPD shape parameter and sample data volume are constructed.

Author Biographies

S. V. Zabolotnii, Cherkasy State Business College

Doctor of Technical Sciences, Professor of Computer Engineering and Information Technologies Department

A. V. Chepynoha, Cherkasy State Technological University

Ph.D., Associate Professor of Informatics, Information Security and Documentation Department

A. M. Chorniy, Cherkasy State Technological University

Ph.D., Associate Professor of Radio Engineering, Telecommunication and Robotic Systems Department

A. V. Honcharov, Cherkasy State Technological University

Ph.D., Associate Professor of Radio Engineering, Telecommunication and Robotic Systems Department

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Published

2020-09-30

Issue

82

Section

Theory and Practice of Radio Measurements

License

Copyright (c) 2020 S. V. Zabolotnii, A. V. Chepynoha, A. M. Chorniy, A. V. Honcharov

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