Article 4321

Title of the article

Extension of statistical Cramer – von Mises tests using Laguerre polynomials while testing the hypothesis of small samples’ normality 


Aleksandr I. Ivanov, Doctor of engineering sciences, associate professor, scientific adviser, Penza Research Institute of Electrical Engineering (9 Sovetskaya street, Penza, Russia), E-mail:
Aleksey P. Ivanov, Candidate of engineering sciences, associate professor, head of the sub-department of technical means of information security, Penza State University (40 Krasnaya street, Penza, Russia), E-mail:
Evgeniy N. Kupriyanov, Postgraudate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: 

Index UDK





Background. The research considers the problem of analyzing small samples using an example of the synthesis of new statistical tests generated by the classical statistical criterion of Cramer – von Mises. Materials and methods. It is proposed to obtain new statistical criteria by strengthening the calculation results according to the classical criterion by multiplying by even orthogonal Laguerre polynomials. Results and conclusions. It is shown that the considered new statistical criteria give solutions that reduce the error probabilities from three to nine times for Laguerre polynomials of 2, 4, 6 orders. With an increase in the order of the Laguerre polynomial, a decrease in the probabilities of errors of the first and second kind of new statistical tests is noted. Three new statistical tests have been added to the family of two previously known statistical tests, with one of the new statistical tests giving responses strongly correlated with the responses of the classical Smironov – Cramer – von Mises test. 

Key words

analysis of small samples, artificial neurons, statistical criteria for testing the hypothesis of normality, orthogonal Laguerre polynomials 

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Дата создания: 09.12.2021 08:46
Дата обновления: 09.12.2021 09:30