Doubling the number of statistical Cramer – von Mises criterion by differentiating small samples with normal and uniform distribution of biometric data 

Aleksandr I. Ivanov, Doctor of engineering sciences, associate professor, scientific adviser, Penza Scientific Research Electrotechnical Institute (9 Sovetskaya street, Penza, Russia), E-mail: ivan@pniei.penza.ru
Aleksandr Yu. Malygin, Doctor of engineering 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
Svetlana A. Polkovnikova, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: 1996svetlanaserikova@gmail.com 

Background. In the last century, 4 statistical tests were created that can be combined into the Cramer – von Mises criterion. The purpose of this work is to double the number of this criteria, the criteria under consideration. Materials and methods. It is proposed to perform numerical differentiation of small sample data before calculations. In the synthesis of new statistical criteria according to the Cramer-von Mises scheme, the derivative of the input data is compared with the density of the distribution of normal data. Results and conclusions. It is shown that the new statistical criteria proposed in the work have about 10 times less probability of errors of the first and second kind. In addition, they are weakly correlated with the classical statistical criteria of the same family. 

Kramer – von Mises statistical criterion, Smirnov – Kramer – von Mises criterion, Anderson – Darling criterion, Frozini criterion, artificial neurons, synthesis of new statistical criteria 

Ivanov A.I., Malygin A.Yu., Polkovnikova S.A. Doubling the number of statistical Cramer – von Mises criterion by differentiating small samples with normal and uniform distribution of biometric data. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki = University proceedings. Volga region. Engineering sciences. 2022;(1):53–61. (In Russ.). doi:10.21685/2072-3059-2022-1-5