AN ALBUM OF NINE CLASSICAL STATISTICAL CRITERIA FOR TESTING THE HYPOTHESIS OF NORMAL OR UNIFORM DISTRIBUTION OF DATA IN SMALL SAMPLES 

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
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 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
Aleksandr V. Bezyaev, Candidate of technical sciences, doctor’s degree student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: tsib@pnzgu.ru
Evgeniy N. Kupriyanov, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: evgnkupr@gmail.com
Andrey G. Bannykh, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: tsib@pnzgu.ru
Konstantin A. Perfilov, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: tsib@pnzgu.ru
Vitaliy S. Lukin, Junior researcher, Regional Training and Research Center "Information Security", Penza State University (40 Krasnaya street, Penza, Russia), E-mail: ibst@pnzgu.ru
Konstantin N. Savinov, Senior lecturer, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: tsib@pnzgu.ru
Svetlana A. Polkovnikova, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: vt@pnzgu.ru
Yuliya I. Serikova, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: vt@pnzgu.ru 

Background. The problem of parallel use of a set of statistical criteria aimed at testing one or another statistical hypothesis is considered. Materials and methods. As a rule, on small samples of 16 experiments, statistical tests give a high value of the probabilities of errors of the first and second kind. However, if we build an equivalent artificial neuron for each of the statistical criteria and combine them into a large network of artificial neurons, then we will get a long code with high redundancy. The reduction of the redundancy of such codes makes it possible to correct the errors of some statistical tests. Results. The paper presents functional dependencies and thresholds used in the software implementation of 9 basic criteria or artificial neurons equivalent to them. Conclusions. On the logarithmic scale of the probabilities of errors of the first and second kind for each criterion and on the logarithmic scale of the number of criteria generalized by the neural network, the self-correcting error correction code “by voting on the majority of bit states” is well described by a linear function. 

classical and new statistical criteria, artificial neurons equivalent to statistical criteria, parallel statistical analysis of small samples, error correction of the neural network output code 

Ivanov A.P., Ivanov A.I., Malygin A.Yu., Bezyaev A.V., Kupriyanov E.N., Bannykh A.G., Perfilov K.A., Lukin V.S., Savinov K.N., Polkovnikova S.A., Serikova Yu.I. An album of nine classical statistical criteria for testing the hypothesis of normal or uniform distribution of data in small samples. Nadezhnost' i kachestvo slozhnykh sistem = Reliability and quality of complex systems. 2022;(1):20–29. (In Russ.). doi:10.21685/2307-4205-2022-1-3