Method of verification of hypothesis about mean value on a basis of expansion in a space with generating element

Serhii W. Zabolotnii; S. S. Martynenko; S. V. Salypa

doi:10.3103/S0735272718050060

Authors

Serhii W. Zabolotnii Cherkasy State Technological University, Ukraine https://orcid.org/0000-0003-0242-2234
S. S. Martynenko Cherkasy State Technological University, Ukraine
S. V. Salypa Cherkasy State Technological University, Ukraine

DOI:

https://doi.org/10.3103/S0735272718050060

Keywords:

statistical hypothesis, stochastic polynomials, generative element, higher order statistics

Abstract

In this paper it is proposed an original method for verification of statistical hypotheses about mean values of random quantities. This method is based on Kunchenko stochastic polynomials tool and probabilistic description on a basis of higher order statistics (moments and/or cumulants). There are represented analytical expressions allowing to optimize decision rules using certain qualitive criterion and calculate decision-making error. It is shown polynomial decision rule in case of polynomial power S = 1 corresponds to classic linear decision rule which is used for comparative analysis. By means of multiple statistical experiments (Monte–Carlo method) obtained results of Neumann–Pierson criterion show proposed polynomial decision rules are characterized by increased accuracy (decrease of the 2nd genus errors probability) in compare to linear processing. The method efficiency increases with increase of stochastic polynomial order increase of degree of random quantities distribution difference from Gaussian probabilities distribution law.

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