MULTI-CRITERIA VERIFICATION OF THE HYPOTHESIS OF NORMALITY
AND UNIFORMITY OF SMALL SAMPLES USING TERNARY AND BINARY ARTIFICIAL NEURONS 

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. Yunin, Leading specialist, Penza Research Electrotechnical Institute (9 Sovetskaya street, Penza, Russia), E-mail: unin_ap@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
Svetlana A. Polkovnikova, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: 1996svetlanaserikova@gmail.com 

Background. The problem of joint use of three criteria for testing the hypothesis of uniformity and normality is considered: Frotsini (1978), Ali – Chergo – Revis (1992) and a differential version of the Frotsini test (2016). Materials and methods. It is proposed to match each of the studied criteria with an equivalent artificial neuron. Then a neural network of three binary neurons gives a three-bit output code. A network of ternary neurons will produce a six-bit output code. Redundant output codes of neural networks can be convolved with error correction. Results. It is shown that binary artificial neurons make it possible to distinguish between small samples of 16 experiments with a normal or uniform distribution with the same probabilities of errors of the first and second kind – 0,031. Ternary neurons give the same probabilities of errors of the first and second kind at the level of – 0,2303. Due to the independence of the data (Hamming distance spectra do not overlap), it is possible to reduce the error probability to a value of – 0,007. Conclusions. Known code structures with redundancy, capable of detecting and correcting errors, were created mainly for binary codes. Ternary code constructions are poorly studied. It is necessary not only to develop a branch of ternary self-correcting codes, but also a code superstructure that combines binary and ternary neural network self-correcting structures. 

statistical criteria, artificial neurons equivalent to statistical criteria, error correction of the neural network output code 

Ivanov A.I., Yunin A.P., Ivanov A.P., Kupriyanov E.N., Polkovnikova S.A. Multi-criteria verification of the hypothesis of normality and uniformity of small samples using ternary and binary artificial neurons. Nadezhnost' i kachestvo slozhnykh sistem = Reliability and quality of complex systems. 2022;(3):70–77. (In Russ.). doi:10.21685/2307-4205-2022-3-9