Article 1222

Title of the article

MULTIPLICATIVE UNION OF LEGENDRE POLYNOMIALS WITH THE CLASSICAL VASICEK STATISTICAL TEST
FOR TESTING HYPOTHESES OF UNIFORMITY OR NORMALITY OF SMALL SAMPLE DATA DISTRIBUTIONS 

Authors

Aleksandr I. Ivanov, Doctor of technical sciences, associate professor, senior researcher, Penza Research Electrotechnical Institute (9 Sovetskaya street, Penza, Russia), E-mail: ivan@pniei.penza.ru
Aleksandr V. Bezyaev, Candidate of technical sciences, doctor’s degree student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: tsib@pnzgu.ru
Aleksandr Yu. Malygin, Doctor of technical sciences, professor, head of the Intersectoral testing laboratory of biometric devices and technologies, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: mal890@yandex.ru
Evgeniy N. Kupriyanov, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: evgnkupr@gmail.com 

Abstract

Background. In the last century, about 20 statistical criteria for testing the hypothesis of normal distribution of data and about 20 statistical criteria for testing the hypothesis of uniform distribution of data were created. The article considers a method for synthesizing new statistical criteria by multiplying or dividing their output states. Materials and methods. It is proposed to multiply (divide) the response of the classical almost orthogonal Legendre polynomial to the response of the classical Vasicek statistical test. Results and conclusions. It is shown that the proposed procedures allow two new strong statistical tests to be combined with the Vasicek test. The result is a binary output code with threefold redundancy. Code redundancy folding reduces the probability of occurrence of errors of the first and second kind by 5 times. 

Key words

Vasicek's statistical test, almost orthogonal Legendre polynomial of the second order, artificial neurons equivalent to statistical criteria, synthesis of new statistical tests by multiplying output states of known criteria 

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For citation

Ivanov A.I., Bezyaev A.V., Malygin A.Yu., Kupriyanov E.N. Multiplicative union of Legendre polynomials with the classical Vasicek statistical test for testing hypotheses of uniformity or normality of small sample data distributions. Nadezhnost' i kachestvo slozhnykh sistem = Reliability and quality of complex systems. 2022;(2):5–13. (In Russ.). doi:10.21685/2307-4205-2022-2-1 

 

Дата создания: 01.07.2022 08:59
Дата обновления: 01.07.2022 09:07