МОДЕЛЮВАННЯ ПОСЛІДОВНОГО ОЦІНЮВАННЯ ПАРАМЕТРА ЗСУВУ АСИМЕТРИЧНО-РОЗПОДІЛЕНИХ ВИПАДКОВИХ ВЕЛИЧИН МЕТОДОМ МАКСИМІЗАЦІЇ ПОЛІНОМА

Abstract

An original approach to finding sequential estimates of the parameter of bias of non-Gaussian asymmetric-distributed random variables is investigated in the paper. The polynomial maximization method (PlMM), which is based on the mathematical apparatus of stochastic Kunchchenko polynomials and a partial description of random variables by higher order statistics (moments or cumulants) is the basis of this approach. The classic approach to solving a posed problem, which is based on simple linear recurrent statistics, that does not take into account the peculiarities of probabilistic data distribution and is optimal only for Gaussian model, is analyzed. Analytical expressions for finding the estimates by polynomial maximization method at the second degree polynomial are obtained. A comparative analysis of the efficiency on the basis of the criterion of the magnitude of asymptotic dispersion of the estimates of various methods parameters is performed. It is shown that theoretical value of the coefficient of the reduction of PlMM-estimates dispersion (in comparison with linear estimates) depends on the magnitude of cumulative coefficients of asymmetry and excess of statistical data. On the basis of the received results, in MATLAB software environment a set of m-functions that realize statistical modeling by Monte-Carlo method of linear and polynomial sequential grading algorithms for the parameter of bias of non-Gaussian random variables with different types of distributions (ex-ponential, gamma, lognormal, Weibull, double-Gaussian ones) is developed. The combination of the obtained results shows that the application of the proposed approach can provide a significant reduc-tion in the time to make decisions when diagnosing the state of technical systems and technological processes.