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.
Highlights
Current information and measurement technologies trends are focused on the use and software systems development that will provide a solution to the problem of statistical processing the experimental results in any form of recorded measurements and necessarily includes modern statistical analysis methods
EPD is offered as an alternative to the Gaussian distribution law assumption for measurement error probability while the model of exponential power distribution is applied [4]
Since the distribution of experimental data is usually symmetric according to its center, the exponential power distribution can be claimed as a model of error measurement distribution law
Summary
Turning to the description of random variables using the probability density distribution, we have at present the use of the most accurate method for obtaining estimates – the method of maximum likelihood This approach produces problems associated with nonlinearity of processing [9, 11, 12]. The researcher is often faced with the task of choosing either a simpler method, which may not satisfy the accuracy, or cumbersome calculations that require the implementation of complex computational procedures To solve this dilemma this paper proposes to apply an original approach to statistical parameter estimation, which is based on the polynomial maximization method (PMM) by describing random variables in the form of a finite moments or cumulants number [18]. The analysis procedure involves obtaining both: theoretical expressionsfor parameters estimates variance ratio and the comparison of estimates variances empirical values using statistical modeling by the Monte Carlo method
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