The purpose of the article is to attract the attention of professional environment to the problems of statistical thinking formation in Russia. Unfortunately, at present there is not yet a clear understanding of the scientific definition of “statistical thinking”, which brings notable difficulties in the process of developing a mechanism and taking into account the peculiarities of the formation of statistical thinking in society, especially among young rising generations. The paper concludes that in the existing circumstances it is extremely important to consolidate the efforts of the statistical community aimed at concretizing the content of statistical thinking and solving the problems related to the extended reproduction of its direct carriers. 

Improving the living standards of citizens and improving the investment climate are the key benchmarks of any state.

The purpose of this study is to analyze the relationship between quality of life and the growth of bank deposits in the regions of Russia.

Materials and methods. The integral index of the quality of life of the population of the Russian regions from 2011 to 2021 was assessed using the method of principal components based on blocks of variables reflecting not only material but also spiritual and moral spheres of society. The authors analyzed the presence of correlation between the integral index of the quality of life and the volume of bank deposits. Assuming that the integral index of the quality of life can have a significant impact on the growth of bank deposits, panel data models with fixed and random effects were constructed and analyzed. The data from the Federal State Statistics Service (Rosstat) and from open Russian Internet resources on banking analytics were used in the paper.

Results. The paper shows that despite the presence of a stable correlation between the value of the integral index of the quality of life and the estimate of the volume of deposits, the quality of life does not have a significant impact on the growth of bank investments. Regional inflation is expected to have a negative impact on deposit growth.

Conclusion. The increase in free cash stimulates the population to choose the most reliable ways of their preservation and multiplication, for example, bank deposits. However, improving the quality of their lives, the population may begin to consider other, albeit less reliable, but perhaps more profitable areas of investment, such as real estate or mutual funds. In addition, today the compensation for deposits in a bank, in respect of which an insured event has occurred, is paid to the depositor in the amount not exceeding 1.4 million rubles, which encourages agents to consider other investment instruments, if the available free cash exceeds the above amount. In conditions when the growth rates of consumer prices exceed the return on deposits, their real return becomes negative, which means that the population will look for alternative ways of investment. Analysis that takes into account different types of investment by regions of the country is currently a difficult task due to the aggregation and non-transparency of this type of data. We also note that the turbulent period starting from 2022, characterized by a sharp increase in interest rates, requires separate consideration.

Growing competition among domestic manufacturers under the pressure of sanctions requires special attention to the issues of product range optimization. In changing conditions, manufacturers are forced to constantly monitor sales, analyze data and optimize the product range, excluding ineffective types of products and adding new types that are in demand in the sales market.

Purpose of research: to identify the possibilities of game theory in managing the product range, to provide recommendations for its use in the process of forming an assortment policy. The relevance of the research topic is due to the need of manufacturers to improve the mechanisms for managing the range of manufactured products.

The following materials and methods of game modeling were used in the study: designing a set of players, designing a set of player strategies, quantitative assessment of the elements of the payoff matrix, techniques for reducing the degree of uncertainty, methods for choosing optimal strategies under conditions of complete and partial uncertainty, as well as generalizing the experience of using game models in the analysis of various economic situations.

The focus is on game modeling that complements the mathematical and statistical methods traditionally used to formulate an assortment policy: mathematical programming methods - the task of optimizing an assortment given resource constraints, such as budget and stocks of raw materials used in the production process; multi-criteria choice methods - the task of taking into account several criteria when making decisions on the product assortment, such as product quality, product price, product demand, etc.; statistical analysis methods (the task of analyzing available sales data and identifying trends - regression analysis to forecast demand for manufactured products, identify relationships between various factors, such as product demand and prices, marketing efforts, seasonality, etc.; cluster analysis to segment products and customers based on previously identified characteristics, such as customer preferences and age, as well as associative analysis to identify relationships between products - determining product groups that can be presented together in the assortment); methods of time series analysis and simulation modeling (the task of forecasting demand for products based on available sales data; the task of fictitious implementation of various assortment management scenarios and quantitative assessment of their consequences).

Results. Game models of product assortment management of the basic level (taking into account the presence of a product type in the formed assortment) and advanced level (taking into account not only the presence of a product type in the formed assortment, but also its quantity) were constructed, an approach to quantitative assessment of the consequences of decisions made to change the assortment of manufactured products was proposed. The sensitivity of the optimal strategy for forming the product assortment to the dynamics of the decision maker’s attitude to risk and the level of trust in information was established.

Conclusion. The scientific novelty of the study consists in developing an approach to managing the assortment of manufactured products, the basis of which is the justification of the optimality of the game strategy. The practical significance of the study lies in expanding the application of applied and research capabilities of game modeling to issues of managing the assortment of manufactured products, as well as improving the tools for analyzing the enterprise’s assortment policy (aspects of the width and depth of the assortment). Eight factors of the strategic assortment policy were identified and substantiated.

Purpose of the study. Within the framework of this study, attention is focused on the assessment of convergence using the budget revenues of the regions of Russia per capita as a key index. Currently, research in the field of economic growth and macroeconomics remains in the center of attention of the scientific community and government agencies, as they play a key role in shaping the development strategies of regions and countries as a whole. In this context, one of the essential aspects is the assessment of convergence, that is, the process of convergence of economic indexes between different regions.

Materials and methods. The study examines key methods and models of spatial econometric analysis, such as unconditional convergence, global Moran indexes, etc. Much attention is paid to the interpretation and formation of economically sound conclusions based on the results of econometric modeling.

Results. This article is devoted to the application of spatial econometric analysis in the context of the study of differentiation of economic development of Russian regions. Spatial regression analysis is a tool for studying the relationships between various economic variables in various geographical areas, while considering various dependencies and spatial autocorrelation.

Conclusion. The results of the study have empirical significance for political and economic decision-making at the regional and national levels. The article provides an important contribution to the methodology of econometric analysis in macroeconomics, expanding the understanding of the relationships between economic variables in various geographical areas. 

When developing distributed computing systems with parallel data processing, there is a problem of assessing the impact of workload values and structure on its performance indexes. One of the key points in this problem is to assess the impact of various prioritization disciplines on the time characteristics of emerging request queues in the system, for which statistical methods of data analysis are used.

The goal of this study is to develop a method for constructing a simulation model that will allow estimating the time characteristics of the system depending on changing workload values and a priorityprocessing algorithm. The method is based on the joint use of the developed simulation model, which describes in detail the functioning of the system of the considered class in time, taking into account conflict situations arising during parallel processing of information, and experimentally obtained individual time characteristics of the system.

Materials and methods. The model is implemented in the GPSS language. All stages of applying the presented method are considered. Examples of workload for modeling are given. Justifications for using the presented data, as well as the principles by which they were selected, are given. For the analyzed class of problems, simulation modeling of the computing system was carried out. During the construction of the simulation model of the system a specialized data acquisition device as source of requests; a switch for which a request queue with different priorities is simulated; a data processing device, which is the final recipient of the data were selected as simulation functional nodes.

The types of algorithms used to solve the request prioritization problem are taken from common prioritization algorithms typical for the Quality of Service (QoS), used in modern switching equipment. Three prioritization algorithms were considered: without using priorities as a standard; priority queue; Weighted Round Robin as a more complex algorithm.

Data on the processing time of various types of requests were obtained experimentally using the Wireshark network traffic analysis tool. The obtained times, as well as the intensity of requests for request processing and the ratio of requests of different types are parameters of the created model and can be changed to simulate another system with a similar architecture.

Results. Based on the analysis of the obtained modeling results, the influence of various disciplines for processing request priorities in queues on the system performance indexes is shown. Regenerative model analysis method is used to analyze the obtained data. The obtained method allows for a detailed analysis of the system’s time characteristics, taking into account the prioritization of requests when they are processed in queues.

Conclusion. The conducted research analysis shows the impossibility of obtaining these metrics by means of analytical modeling, which emphasizes the novelty of the study. The method obtained during the study is used in the development of systems of the presented class, which emphasizes its practical significance and relevance. 

Purpose of the study. The aim of the study is to develop a new method for finding an optimal portfolio of securities based on suboptimization using a sparse covariance matrix, and to create a program based on it to automate the procedure for selecting an investment strategy.

Materials and methods. The paper presents one of the possible formalizations of a two-criterion investment problem – setting the problem for the maximum expected portfolio yield with an upper limit on the standard deviation. At the same time, the calculation of the standard deviation of a portfolio with a sparse matrix of covariances of financial instruments’ yields is justified. A solution to a two-criterion problem based on the use of the Karush-Kuhn-Tucker optimality conditions is given. All necessary primary calculations and studies are performed in Microsoft Excel; the functions of the Python programming language are used for automation and implementation of the graphical interface.

Results. The analysis of the methods used to make investment decisions was carried out and the use of each of them for specific stock market data was justified. To automate analytical approaches to finding the optimal investment strategy with full, partial and absent correlation dependence, a program and a graphical interface were created using the Python programming language libraries. The software product was tested on the example of the investment process with real data of the Russian stock market. The initial data in this study were quotes of shares of Russian companies for the period from 01.01.2019 to 31.12.2021, taken from the Yahoo Finance website. The choice of each of the shares was based on the results of the fundamental and technical analysis.

Conclusion. As a result of the conducted research, it was established that the proposed method of finding the optimal strategy using a sparse covariance matrix is a suitable tool for an active investment strategy. The technical implementation of the proposed method - the use of the Python programming language to create a graphical interface – allows automating the process of constructing an investment strategy.

Purpose. Modeling systems and programming platforms provide broad opportunities for the use of statistical tools in research activities. Since the normal distribution is one of the most common distribution laws, the criterion for checking the sample for normality is in high demand among statistical assessment tools, among which the Epps-Pulley test has the status as one of the most powerful tests to check the deviation of the distribution from the normal one. There are a number of implementations of this test in the R and Python languages. However, this test is not implemented in one of the most popular Matlab modeling software. Thus, the purpose of this study is to develop a software implementation of the Epps-Pulley criterion in the Matlab environment and verify the correctness of the performed calculations.

Materials and methods. We implemented the calculation of EppsPulley statistics by two methods – classical, using cycles, and matrix-vector, using linear algebra operations. The classical method requires calculating the intermediate values necessary to obtain the criterion statistics using two independent cycles, the second cycle being a double one, in which one cycle is nested within the other. The matrix-vector method requires fewer lines of code by performing calculations using linear algebra operations on matrices and vectors. We obtained critical statistical values for the sample size ranging from 8 to 1000 elements with two-dimensional linear interpolation of tabular values. We used an approximation by a beta function of the third kind for a sample of over 1000 elements.

Results. An assessment of the computational efficiency of the methods showed that the cyclic approach is about three times higher than the matrix-vector approach in terms of consumed time, which is presumably associated with the processing of insignificant elements in triangular matrices when performing component-by-component operations. The correctness of the software implementation of the Epps-Pulley criterion was tested on several examples, which confirmed the compliance of the calculated values of the criterion statistics, as well as the critical values of statistics, with known data. We carried out a criterion statistical evaluation based on the empirical values of the error of the first kind. We obtained the error values correspondence to the specified significance levels. We performed comparative estimates of the Epps-Pulley test with the Anders-Darling and Shapiro-Wilk tests in terms of the criterion empirical power. Evaluation results are tabulated. The software implementation of the Epps-Pulley test is published on the MATLAB Central Internet resource and is available for free use. 

The article examines the problems of studying transaction costs through the prism of the concept of an “extended enterprise” in the digital economy, defines evolutionary approaches to the study of transaction costs, classifies the classification features of transaction costs, the structure and methods of accounting for transaction costs, and also proposes a model of the relationship between transaction and transformation costs in analog and digital economies, which allows a more comprehensive consideration of changes in t transaction costs in digital coordinates.