Article 4421

Title of the article

MULTIPLICATIVE NEURAL NETWORK COMBINATION OF HURST AND MUROTA-TAKEUCHI STATISTICAL CRITERIA IN CHECKING THE HYPOTHESIS OF NORMALITY OF SMALL SAMPLES 

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
Aleksey P. Ivanov, Candidate of technical sciences, associate professor head of the sub-department of technical means of information security Penza State University (40 Krasnaya street, Penza, Russia), E-mail: ap_ivanov@pnzgu.ru
Evgeniy N. Kupriyanov, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: evgnkupr@gmail.com 

Index UDK

519.24; 53; 57.017 

DOI

10.21685/2307-4205-2021-4-4 

Abstract

Background. The problem of analyzing small samples by combining several statistical criteria created in the last century is considered. The Hirst test, the Anderson-Darling test, and the Murota-Takeuchi test are combined. Materials and methods. It is proposed to combine the considered statistical criteria by multiplying their output states. Already after the multiplicative combination of statistical criteria, it is proposed to quantize their continuous data into discrete states "0" and "1". Results. With a low correlation of the combined statistical criteria, multiplicative neural network generalization gives a significant decrease in their final probability of errors of the first and second kind, in comparison with the previously used concatenation-neural network generalization. In this respect, a simpler concatenation-neural network generalization is less informative. Conclusions. The concatenation-neural network combining of statistical criteria does not work well for criteria of different quality, which is shown by the example of generalization of the three considered statistical criteria. In this respect, multiplicative-neural network generalization of statistical criteria is more advantageous, since it allows increasing the reliability of decisions made for two considered criteria. 

Key words

statistical analysis of small samples, testing the hypothesis of normality, Hurst tests, Anderson-Darling test, Murota-Takeuchi test 

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Дата создания: 16.02.2022 13:07
Дата обновления: 16.02.2022 13:35