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

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.