The power of the entropy-parametric criterion for testing statistical hypotheses in control systems and information processing - V.G. Polosin (Известия высших учебных заведений. Поволжский регион:Технические науки, 2022)
Background. The use of the entropy-parametric criterion as a decisive rule implies the occurrence of errors of the second kind, capable of causing substantial material damage in technical, medical, information-measuring and control systems. To prevent errors of the second kind, it is necessary to a priori assess the ability of the entropyparametric criterion to detect minor effects and changes in the state of an object. The purpose of the work is to estimate the power of the entropy – parametric criterion, which takes into account the informational and probabilistic properties of the samples of measurement results. Materials and methods. The theoretical and methodological basis of the research is an analysis of the entropy-parametric criterion in space centered relative to the competing hypothesis of the estimates of the entropy coefficient and the counter-process, given to their standard deviations. Results. As a result of the geometric interpretation of the mutual arrangement of hypotheses, mathematical expressions are obtained for calculating the probability of an error of the second kind and the power of the entropy – parametric criterion depending on the position of the null hypothesis in the centered space of the competing hypothesis. Conclusions. It is shown that in the anisotropic spaces of the above estimates of the entropy coefficient and the counter-process centered on the alternative hypothesis, the power of the entropy criterion depends on the direction of the position of the null hypothesis. Recommendations are given on the choice of the probability of making a second kind of error, limiting the area in which the null hypothesis is considered invalid with a probability of 80 %.