08.00.13 Mathematical and instrumental methods of Economics

08.00.13 Mathematical and instrumental methods of Economics
DescriptionThis article is devoted to rating assessment of the socioeconomic situation of the Krasnodar region, presented by such agencies as "RAEKSAnalytics", "Expert RA" and "National Rating Agency". The methodologies used by these agencies were studied and analyzed. A comparison of these methodologies was also conducted. As a result, a number of their shortcomings were identified, including the lack of a complete methodological model in the public domain. Some agencies do not provide links to statistics that are used in the analysis. In the article using the STATISTICA environment, a statistical analysis of data reflecting the level of socioeconomic situation of the Krasnodar region is carried out. Based on the work [12], the article created a discriminant model for assessing the socioeconomic development of urban districts of the Krasnodar region with a confidence of 85%. The study conducted a cluster, discriminant, classification (decision trees), coefficient (proposed by the authors) based on the data of the Federal State Statistics website for the period from 2009 to 2018 in the city districts: Krasnodar, Anapa, Armavir, Gelendzhik, Goryachiy Klyuch, Novorossiysk Sochi. During the study, analyzes such as cluster and classification trees showed poor results, since they are not able to detect latent nonlinear relationships between the study indicators. Using the constructed discriminant model, we have carried out an analysis of the socioeconomic development of urban districts of the Krasnodar region for the period 20092018, which allows us to identify the leaders and the outsiders

08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn onland and underground structures, machines and mechanisms, in many cases, we use rod structural elements made of viscoelastic materials. One of the methods for studying the strength characteristics of rods is the experimental measurement of the velocity of propagation of deformation waves in them and comparing it with theoretically accurate values of the velocity, determined taking into account the real physical and mechanical properties of the material. This comparison allows us to analyze the presence of microdefects in the rods. To assess the economic and operational reliability of building structures using mathematical modeling, we study the characteristics of nonlinear wave processes in viscoelastic rods, which can be used to improve the acoustic diagnostics of material microdefects

08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn previous works, the authors solved the problem of cognitive structuring and formalization of the subject area, synthesis and verification of systemcognitive models, predicting the impact of nomenclature and sales volumes on the profit and profitability of the trading company, decision support for the selection of such nomenclature and sales volumes, which cause a given target profit and profitability of the company. This work is devoted to the study of the simulated subject area by studying its SCmodel

NONNUMERICAL DATA STATISTICS IS A CENTRAL PART OF MODERN APPLIED STATISTICS
08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn 1979, nonnumerical data statistics was singled out as an independent area of applied statistics. Initially, the term "statistics of objects of nonnumerical nature" was used to denote this area of mathematical methods of economics. Our basic nonnumeric statistics textbook is called "NonNumeric Statistics". Nonnumerical data statistics is one of the four main areas of applied statistics (along with number statistics, multidimensional statistical analysis, statistics of time series and random processes). Statistics of nonnumerical data are divided into statistics in spaces of a general nature and sections devoted to specific types of nonnumerical data (statistics of interval data, statistics of fuzzy sets, statistics of binary relations, etc.). Currently, statistics in spaces of a general nature is the central part of applied statistics, and nonnumeric data statistics including it is the main area of applied statistics. This statement is confirmed, in particular, by the analysis of publications in the section "Mathematical Research Methods" of the journal "Industrial Laboratory. Diagnostics of Materials"  the main place of publication of russian studies on applied statistics. This article is devoted to the analysis of the basic ideas of nonnumerical data statistics against the background of the development of applied statistics from the perspective of a new paradigm of mathematical research methods. Various types of nonnumeric data are described. The historical path of statistical science is analyzed. We have discussed the development of statistics of nonnumerical data. The article analyzes basic ideas of statistics in spaces of a general nature: average values, laws of large numbers, extreme statistical problems, nonparametric estimates of the probability density, classification methods (diagnostics and cluster analysis), statistics of the integral type. Some statistical methods for analyzing data lying in specific spaces of nonnumeric nature are briefly considered: nonparametric statistics (real distributions usually differ significantly from normal), statistics of fuzzy sets, theory of expert estimates (the Kemeny median is a sample average of expert orderings), etc. We have also discussed some unsolved problems in statistics of nonnumeric data

PRICING METHOD BASED ON THE ESTIMATION OF DEMAND FUNCTION
08.00.13 Mathematical and instrumental methods of Economics
DescriptionWhen solving some problems of economics and management at an enterprise, it becomes necessary to determine the retail price of a product or service at a known wholesale price or producer price. We offer to determine the retail price based on an analysis of a survey of potential consumers about the maximum possible price for the product or service in question. We calculate the retail price on the basis of optimizing the economic effect equal to the product of the result from the sale of one unit of goods by the demand function, which we estimate by interviewing consumers. To solve the optimization problem, we approximate the demand function using the least squares method. As examples, the linear and power models of the demand function are analyzed. Ways of further development of the proposed approach are discussed. Unresolved scientific problems are formulated. Methods for estimating the demand function in the context of a large number of repetitions of respondents and their tendency to “round numbers” require further elaboration, as a result of which the Kolmogorov criterion cannot be used to determine the accuracy of the restoration of the demand function. Various parametric and nonparametric approaches of regression analysis should be adapted to the problem of restoring the dependence of demand on price, as well as methods for solving the corresponding optimization problems

PROSPECTS FOR EXTENSIVE DEVELOPMENT OF URBAN TRANSPORT INFRASTRUCTURE
08.00.13 Mathematical and instrumental methods of Economics
DescriptionThe development of the city can go in two waysextensive and intensive. Intensive involves a qualitative rethinking of the necessary work, optimization and improvement on the basis of existing infrastructure. An extensive method of development is an increase in physical volumes, for example, an increase in territories. At the moment, the transport system of the city of Krasnodar is extremely busy. The city occupies one of the first places in the number of vehicles, roads with such a traffic load cannot cope, resulting in numerous congestion on the roads. In addition, an average of 150 thousand cars enter the city every day, and this creates an additional burden on the transport system. In the morning there is a large influx of cars from the main entrances to the city. And in the evening there is no less strong loading points of entry into the city, as those who arrived in the morning leave the city. Information technology is designed to save our time and effort. At the same time, one of the problems that "eats" time is traffic jams. You can get from one place to another at one time, but subject to traffic jams, this time can increase several times. Why not use technical and software tools to solve this problem!? Now almost everyone has a smartphone, with a satnav loaded into it. There are many variations of these navigators with approximately the same functionality. But what if the satnav in your smartphone not only chose the shortest path for you, but also helped in unloading traffic throughout the city, reducing traffic congestion to a minimum?

STRATEGY OF RETRO INNOVATIONS IN IMPORT SUBSTITUTION
08.00.13 Mathematical and instrumental methods of Economics
DescriptionUnfavorable changes in exchange rates, sanctions restrictions on the supply to Russia of spare parts necessary for the repair and maintenance of previously imported equipment have led to a significant reduction in the service life of imported machinery and equipment. For the solution, the authors propose to implement the strategy of retroinnovations providing the development of new technologies maintaining in working condition of machinery and equipment in conditions of shortage of spare parts and consumables. To do this, it is necessary to develop technologies for the restoration of complex technical devices in order to extend their service life under the restrictions created by the financial market and sanctions policy. The study of the problem was carried out on the example of the operation of trucks of foreign production, the evaluation of engine life and analyzed the structure of the market. On the basis of the obtained results, a model was proposed, on the basis of which it is possible to form a plan for the production of spare parts for highquality engine repair by domestic enterprises. The strategy of retroinnovations does not solve all the problems of import substitution, but it allows to increase the level of economic security of strategically important economic activities, it creates jobs and provides an opportunity to significantly extend the life of expensive and complex technical devices

08.00.13 Mathematical and instrumental methods of Economics
DescriptionThe instrumental methods of economics include the Monte Carlo method (statistical simulations method). It is widely used in the development, study and application of mathematical research methods in econometrics, applied statistics, organizational and economic modeling, in the development and making management decisions, in the basis of simulation modeling. The new paradigm of mathematical research methods developed by us is based on the use of the Monte Carlo method. In mathematical statistics, limit theorems on the asymptotic behavior of the considered random values were obtained for many methods of data analysis with an unlimited increase in sample volumes. The next step is to study the properties of these random values for finite sample sizes. For such a study, the MonteCarlo method is used. In this article, we use this method to study the properties of statistical criteria for testing the homogeneity of two independent samples. We considered the most used in the analysis of real data criteria  CramerWelch, which coincides with the equality of the sample sizes with Student's criterion; Lord, Wilcoxon (MannWhitney), Wolfowitz, Van der Waerden, Smirnov, type omegasquare (LehmannRosenblatt). The Monte Carlo method allows us to estimate the rates of convergence of distributions of criteria statistics to the limits, to compare the properties of the criteria for finite sample sizes. To use the Monte Carlo method, it is necessary to select the distribution functions of the elements of the two samples. For this purpose, normal and Weibull – Gnedenko distributions are used. The recommendation was received: to test the hypothesis of coincidence of distribution functions of two samples, it is advisable to use the LehmannRosenblatt (type omegasquare) test. If there is reason to assume that the distributions differ mainly by the shift, then the Wilcoxon test and Van der Waerden criteria can also be used. However, even in this case, the omegasquare type test may be more powerful. In the general case, besides the LehmannRosenblatt criterion, the use of the Smirnov criterion is permissible, although for this criterion the real level of significance may differ from the nominal level of significance. We sstudied the frequency of discrepancies of statistical findings on different criteria

08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn modern economic theory, there is no complete classification of innovative approaches to the management of knowledgeintensive and hightech companies and enterprises. Among these approaches, we can highlight situational, structural, process, functional and projectbased approaches. The projectoriented approach, as a purposeful method of future systems forming, is a kind of continuation of the process approach; however, it gives priority not to the process, but to the project, as the main production, innovation and competing business unit. This article provides a brief overview of carried out research in this subject area, analyzes the advantages and opportunities of existing project management validity models, and suggests the author's approach of building a model for identifying and evaluating the potential of modern projectoriented companies and enterprises. This article also shows that the economic efficiency of such companies and enterprises achieving by using the projectbased method both in the integrated system of strategic management and in the main production activities. This leads to an increase in their ability to choose the right way of operational decisionmaking, contributes to the installation of advanced technological and technical equipment, and accelerates the commissioning of new production facilities

08.00.13 Mathematical and instrumental methods of Economics
DescriptionThis work is devoted to revealing some opportunities of the research of a subject to modeling by a research of its model given by the ASCanalysis and the Eidos system