Development of modern models and methods of the theory of statistical hypothesis testing

Abstract

Typical problems of the theory of statistical hypothesis testing are considered. All these problems belong to the same object area and are formulated in a single system of axioms and assumptions using a common linguistic thesaurus. However, different approaches are used to solve each of these problems and a unique solution method is developed. In this regard, the work proposes a unified methodological approach for formulating and solving these problems. The mathematical basis of the approach is the theory of continuous linear programming (CLP), which generalizes the known mathematical apparatus of linear programming for the continuous case. The mathematical apparatus of CLP allows passing from a twopoint description of the solution of the problem in the form {0; 1} to a continuous one on the segment [0; 1]. Theorems justifying the solution of problems in terms of CLP are proved. The problems of testing a simple hypothesis against several equivalent or unequal alternatives are considered. To solve all these problems, a continuous function is introduced that specifies a randomized decision rule leading to continuous linear programming models. As a result, it becomes possible to expand the range of analytically solved problems of the theory of statistical hypothesis testing. In particular, the problem of making a decision based on the maximum power criterion with a fixed type I error probability, with a constraint on the average risk, the problem of testing a simple hypothesis against several alternatives for given type II error probabilities. The method for solving problems of statistical hypothesis testing for the case when more than one observed controlled parameter is used to identify the state is proposed

Devising the policy of funds allocation in the decision-making process under the budget and tax management

“…At the macro level, its financing takes place at the expense of the State Budget of Ukraine. Thus, there is a problem of optimal allocation of limited resources, which can be considered as a problem of mathematical programming since this scientific area considers the use of mathematical methods for solving optimization economic problems [16][17][18]. The study has formed a methodical approach to the definition of PLSP in a region and its components (Fig.…”

“…It should be added that the objective function ( 5) is additive, and its components are functions that are convex upwards. That is why, to solve the optimization problem ( 5), (1), one can use the method of sequential distribution, which makes it possible to obtain the optimal solution [16].…”

Analysis of semi-Markov systems with fuzzy initial data

“…as the result of observing the modal value of the fuzzy number T ij in the corresponding session. The totality of these observations can be used to determine the membership function of this fuzzy number T ij with the implementation of the proposed methodology (4) (17). As a result of processing the set Φ m (T ij ), the set <m m , α m , β m > will be obtained.…”