Method of Verification of Hypothesis about Mean Value on a Basis of Expansion in a Space with Generating Element
- Authors: Zabolotnii S.W.1, Martynenko S.S.1, Salypa S.V.1
-
Affiliations:
- Cherkasy State Technological University
- Issue: Vol 61, No 5 (2018)
- Pages: 222-229
- Section: Article
- URL: https://journals.rcsi.science/0735-2727/article/view/177211
- DOI: https://doi.org/10.3103/S0735272718050060
- ID: 177211
Cite item
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.
About the authors
Serhii W. Zabolotnii
Cherkasy State Technological University
Author for correspondence.
Email: zabolotni@ukr.net
Ukraine, Cherkasy
S. S. Martynenko
Cherkasy State Technological University
Email: zabolotni@ukr.net
Ukraine, Cherkasy
S. V. Salypa
Cherkasy State Technological University
Email: zabolotni@ukr.net
Ukraine, Cherkasy