PRECISION STATISTICS: NEUROET NETWORKING OF CHI-SQUARE TEST AND SHAPIRO–WILK TEST
IN THE ANALYSIS OF SMALL SELECTIONS OF BIOMETRIC DATA 

Ivanov Alexander Ivanovich, doctor of technical sciences, associate professor, senior researcher, Penza Scientific and Research Electrotechnical Institute (440000, 9 Soviet square, Penza, Russia), E-mail: bio.ivan.penza@mail.ru
Vjatchanin Sergej Evgenevich, associate professor, head of sub-department of radio-space communications, Penza State University (440026, 40 Krasnaya street, Penza, Russia), E-mail: ivo@.pnzgu.ru
Malygina Elena Aleksandrovna, candidate of technical sciences, researcher, interdisciplinary laboratory testing of biometric devices and technologies, Penza State University (440026, 40 Krasnaya street, Penza, Russia), E-mail: e-mail: ivo@.pnzgu.ru
Lukin Vitaliy Sergeevich, postgraduate student, Penza State University (440026, 40 Krasnaya street, Penza, Russia), E-mail: ivo@.pnzgu.ru 

519: 24; 53; 57.017 

10.21685/2307-4205-2019-2-4 

The aim of the paper is a neural network generalization of the Chi-square test and the Shapiro–Wilk test for the analysis of small samples of biometric data. It is shown that any of the statistical criteria can be represented in the form corresponding to a neuron having an input sorter, an adder and some functional converter. The generalization of two statistical criteria is accomplished by tuning the output quantizers of two neurons. The setting is always ambiguous for a predetermined value of the confidence probabilities of the generalized decisions. It is shown that the usual form of presentation of statistical criteria in the form of computational formulas and the tables of quantiles of confidence probability of the equivalent to their neural network description if the tables of the ratio of quantization thresholds providing a given level of confidence in a neural network generalization are given. 

the Chi-square test; the Shapiro–Wilk test; the neural network generalization of statistical criteria