The purpose of this paper is to compare the shortcomings of the widely used inequality coefficients that appear when working with real (ie, knowingly incomplete) data and searching for alternative quantitative methods for describing inequalities that lack these shortcomings.

Research methods:

– consideration of an extensive range of as full as possible real data on the population distribution by income, expenditure, property (ie data on the economic structure of society);

– revealing the specific shortcomings of these data on the economic structure of society, finding out which information is missing or presented disproportionately;

– comparison of the values of the most widely used indices of inequality calculated on real data on the economic structure, with a view to establishing the suitability of these indicators for problems of inequality estimation;

– development of an index of inequality that adequately describes the real economic structure of society.

Research data:

– official data of Rosstat and the Federal Tax Service on incomes of Russian citizens;

– specialized sites of announcements about the prices for real estate and cars;

– Credit Suisse Research Institute data on the distribution of Russian citizens by property level;

– Forbes data on income and wealth of the richest people in Russia.

It is shown that the income data are essentially incomplete and fragmentary – the width of the income range (i.e., the income of therichest member of society) is known, but the filling of rich cohorts is not known, since the incomes of the richest members of society are hidden.

We proposed the next (criteria as) requirements for an inequality index:

–  possibility of calculating the index of inequality for arbitrary quantization;

– invariance of the value of the inequality index for different quantization of the same data;

– sensitivity of the index to the width of the income range.

It is noted that only the exponential function describes societies with high social inequality enough well (the intensity of the exponential distribution is more than 10).

For the presented population distributions, the next indices of inequality are calculated:

– decile coefficient of funds;

– Gini coefficient;

– Pareto index;

– indicators of total entropy (zero, first or Tayle index, and second orders);

– the ratio of maximum income (property value) to the modal;

– intensity of exponential distribution.

It is shown, that:

– the value of the Pareto index does not have a unique relationship with the inequality;

– the coefficients of the funds (decile, quintile, etc.) are not computable for arbitrary quantization, and therefore are unsuitable for comparing data from various sources and have different quantization;

– The Gini index requires complete data on the rich;

– from all considered criteria of inequality the first three indicators of the total entropy, as well as the ratio of maximum income (property) to the modal strongly depend on data quantization.

Therefore they are unsuitable for comparison data from various sources with different quantization. It is concluded that the intensity of the exponential distribution does not possess the listed disadvantages and can be recommended as an index of inequality.

The purpose of the study is to assess the readiness of the Russian higher education system to move to the digital level based on the statistical researches of education. The way to the digital economy becomes decisive in the development of Russian education and covers all its stages. Within the framework of the state program “Education development” the project “Modern Digital Educational Environment” is being realized, for the secondary education the “Digital School” project is being developed, and in the program of development of the digital economy a separate direction “Personnel and Education” is emphasized. Digitalization of education becomes the next stage after the informatization stage in the technological development of education. It is necessary to assess the current level of informatization of higher education.

Materials and methods of research. The presented study of the assessment of the readiness of Russian higher education to the digital economy is based on the methodology, proposed by the World Bank, which includes an assessment of five groups of indicators: the use of information technology in the learning process; training of teaching staff for the use of information technology in education; informatization of education management; information infrastructure of higher education; normative and legal support of the digitalization of education. The methodology includes the combination and interpretation of the different statistical data because the appropriate study of digitalization of education requires the specific approach. The factual basis of the research is the data of official statistics and universities.

The results, on the one hand, indicate a high level of provision of universities with personal computers and access to the Internet, and on the other hand, a lack of automation of the administrative and educational processes of the university. Despite the constant development of technologies and the emergence of new educational web tools, and a multi-year state policy on the information educational space formation, its potential is partly used by universities. Only one third of university students are trained using e-learning or distance education technologies. At the same time, non-state educational institutions provide most of the educational services available to online listeners. In general, the share of online education in the market of educational services is low and is 1.8% for higher education programs and 6.7% for additional professional education. 82% of students, enrolled in programs with exclusive use of e-learning are students of non-state universities. The use of technology, even in the form of blended learning, in addition to the corresponding IT infrastructure, requires the appropriate training of lecturers and students. The training of lecturers in the use of IT in education, including training directly to work with IT, should be supplemented by teaching methodical work in the information educational space.

Conclusion. The study shows that the Russian education system has created the necessary reserve for the creation of IT infrastructure, regulatory support, and best practices in the field of IT application in the educational process, which should become the basis for the participation of Russian universities in the digital economy. At the same time, the differences between information technologies (IT) and digital are not obvious, in many respects, these concepts are identical, differences arise when considering the totality of the information technologies and resources involved. Digitalization assumes that practically all the computing devices are involved in information support, including consumers, who, for example, install mobile applications in order to use the services. Involving a large number of devices with the ability to connect to the Internet allows you to organize the collection and processing of a large amount of digital data. The basis of digitalization is the created IT infrastructure and the degree of informatization in educational institutions.

The article is devoted to an assessment of the potential for modernization of the Russian economy in the face of external challenges that make it difficult for domestic companies to access international financial markets and technologies. The relevance of the study is due to the need to search for own resources for the required large-scale modernization. The purpose of the study is to assess the production and financial potential in the modernization process. This goal predetermines the solution of such problems as analysis of the current state of the production base, assessment of financial resources for the production upgrade, identification of opportunities and risks in the implementation of modernization processes. In this connection, the authors focus on analyzing the factors constraining modernization processes, such as: a low level of capital accumulation, inadequate development of the financial services market, and uneven spatial accessibility of credit institutions.

The methodological apparatus for analyzing the production and financial potential is based on the allocation of basic non-financial sectors of the economy and the financial market, using the methods of detailing, grouping, vertical and horizontal analysis, comparison and synthesis. In addition, graphical analysis is used. The empirical basis of the study was the statistical indicators of the Federal State Statistics Service for the branches of the economy and the data of the Central Bank of the Russian Federation on the state of the banking sector. The theoretical basis was the works of well-known scientists, dedicated to the issues of re-industrialization and the development of strategic priorities for innovative modernization of the Russian economy.

The article compares the dynamics of investment in fixed assets with the rate of increase in depreciation of production assets, analyzes the sources of financing investment activities in the part of updating production systems, and assesses the methods of state regulation of the banking sector as one of the main external suppliers of investment resources in non-financial sectors of the economy. The quality of regulation of financial market institutions is assessed from the standpoint of its diversification and ensuring greater accessibility to the borrowed capital of not only business but also the population.

Based on the results of the analysis, factors that limit the scope for large-scale structural modernization of the economy are identified. It is revealed that the pace of renewal of fixed capital is insufficient and does not contribute to reducing the wear and tear of production assets in the basic sectors of the Russian economy. The availability of borrowed capital for the modernization of production systems is differentiated in a spatial aspect. The functioning institutions of the financial market also do not ensure equal access to credit resources for small and medium-sized businesses.

The scientific novelty of this study is that the authors identified the main problems of the process of modernization and implementation of innovative developments in the context of high levels of depreciation of production systems and inadequate investment resources. In addition, worthy of attention is the conclusion that the structure of the financial services market is inadequate for the scale of structural modernization and it needs to be diversified. The results of the research can find practical application in the development of modernization strategies in the leading sectors of the economy.

Quality of life is one of the most important characteristics that reflects a comprehensive description of the level and living conditions. Nowadays quality of working life is an integral feature of “Quality of Life”. Quality of working life identifies working conditions and labor management. The quality of working life allows us to determine the working conditions, its organization from the perspective of the optimal realization of the abilities of employees.

The article analyzes the domestic approaches to the definition and evaluation of the quality of working life. The conducted research allowed the authors to draw the following conclusions: the quality of working life is characterized by a multitude of indicators, and the required condition for studying the quality of working life is the development of techniques that allow the evaluation of the studied category.

The goal is to evaluate the quality of working life in Russia.

Methods. A number of indicators are presented to estimate the quality of working life of employees in the Russian Federation. According to the authors, those indicators are employment, labor safety, work safety, salary, and competence level and workforce productivity. The analysis that is based on data from Federal State Statistics Service has been done in view of gender factors and federal district differences. According to this analysis, the general part of workforce has jobs with harmful or dangerous working conditions. Extractive and process industries are considered the most hazardous.

The article describes the method of integrated assessment of working life quality, based on the study of social and labor sphere of the Federal districts of Russia. Based on this author’s method, the integral indicators of the quality of working life of the population of the Russian Federation in the context of Federal districts are calculated and analyzed and the rating of each of them is determined.

Results. The article notes that the quality of working life reflects not only the working conditions and its payment, but also the relations in the working collective, the motivation of the personnel to work. The most important motivational factors and characteristics of the socio-psychological climate of the enterprise are determined. The set of indicators, proposed by the authors and the methods of assessing the quality of the working life of the population can be useful to local governments for determining the rating of the quality of working life of officers in municipalities, and thus for making various managerial decisions.

Purpose of research. The work is devoted to the study of socio-economic differentiation in Russia and its impact on the financial situation of the population, its subjective perception, as well as on the psychosocial well-being of individuals. To achieve this goal, the following tasks are to be solved: clustering of regions of the Russian Federation, based on socio-economic indexes; studying the interrelation between the level of socio-economic development of the region and the financial situation of residents; studying the interrelation between the level of socio-economic development of the region and the subjective perception by individuals of their financial situation; studying the interrelation between the level of socio-economic development of the region and the psychosocial well-being of individuals.

Materials and methods. The information base of the study includes: regional data, published by the State Committee on Statistics in the digest “Russian Federation Regions”, household survey data “Russian monitoring of the economic situation and health of the population HSE” (RLMS-HSE). Russia Longitudinal Monitoring Survey of Higher School of Economics is a representative socio-economic survey of Russian households, in which the content structure of the used questionnaires meets the standard, adopted in the world practice.

The study uses the following methods: cluster analysis (k-means method), statistical groupings, Kruskal-Wallis and Mann-Whitney statistical tests.

Results. The study showed that:

– the Russian Federation regions are very heterogeneous in terms of socio-economic development – specific indicators for the regions may differ significantly. It should be taken into account in the study of any social and economic problems, including the problems of income inequality;

– Russian regions can be divided into four clusters. Analysis of the petal diagram of clusters made it possible to reveal their features and give them generalized characteristics. The first cluster includes regions with very high investment, fixed assets and GRP per capita. The second cluster includes regions with an average level of development. The third cluster includes regions with a high level of development. The fourth cluster includes depressive regions;

– There is a clear correlation between the level of socio-economic development of the region of residence and the objective financial situation of residents: the incomes of respondents, living in the leading regions are significantly higher than the incomes of respondents of other clusters; the incomes of respondents, living in depressed regions are lower than the incomes of respondents of other clusters;

– Individuals’ perception of their financial situation and their concerns are practically the same in all clusters and do not correlate with the level of socio-economic development of the region of residence;

– The level of economic development of the region of residence does not have a significant direct impact on psychosocial well-being – individuals from different clusters feel almost equally satisfied with life and almost equally happy.

Study purpose. Existing approaches to forecasting dynamics of financial markets, as a rule, reduce to econometric calculations or technical analysis techniques, which in turn is a consequence of preferences among specialists, engaged in theoretical research and professional market participants, respectively. The main study purpose is developing a predictive economic-mathematical model that allows combining both approaches. In other words, this model should be estimated using traditional methods of econometrics and, at the same time, take into account the impact on the pricing process of the effect of clustering participants on behavioral patterns, as the basis of technical analysis. In addition, it is necessary that the created economic-mathematical model should take into account the phenomenon of existing historical trading levels and control the influence they exert on price dynamics, when it falls into local areas of these levels. Such analysis of price behavior patterns in certain areas of historical repeating levels is a popular approach among professional market participants. Besides, an important criterion of developing model’s potential applicability by a wide range of the interested specialists is its general functional form’s simplicity and, in particular, its components.

Materials and methods. In the study, the market of the pound sterling exchange rate against the US dollar (GBP/USD) for the whole period of 2017 was chosen as the considered financial series, in order to forecast it. The presented economic-mathematical model was estimated by classical Kalman filter with an embedded neural network. The choice of these assessment tools can be explained by their wide capabilities in dealing with non-stationary, noisy financial market time series. In addition, applying Kalman filter is a popular technique for estimation local-level models, which principle was implemented in the newly model, proposed in article.

Results. Using chosen approach of simultaneous applying Kalman filter and artificial neural network, there were obtained statistically significant estimations of all model’s coefficients. The subsequent model application on GBP/USD series from the test dataset allowed demonstrating its high predictive ability comparing with added random walk model, in particular judging by percentage of correct forecast directions. All received results have confirmed that constructed model allows effectively taking into account structural features of considered market and building good forecasts of future price dynamics.

Conclusion. The study was focused on developing and improving apparatus of forecasting financial market prices dynamics. In turn, economic-mathematical model presented in that paper can be used both by specialists, carrying out theoretical studies of pricing process in financial markets, and by professional market participants, forecasting the direction of future price movements. High percentage of correct forecast directions makes it possible to use proposed model independently or as a confirmatory tool.

The aim of the research is the analytical description of one of the modules of the organizational and technical system, designed for the formation of sensual images and their transformation into concepts-representations. Within the framework of the computer paradigm in organizational and technical systems, such obvious principles as digital representation of information and its processing with the use of algorithms implemented by computing means are used. The success of the computer paradigm application is certainly impressive, but there are clearly situations in which human consciousness operates much more efficiently, interpreting the unconventional, the new situation with the aim of formulating an adequate response. In this regard, attempts to model some mechanisms of human consciousness within the framework of the cognitive approach are of great interest. In accordance with the ideas of cognitive theory in the human brain, images (schemes, categories, gestalts, systems, archetypes, etc.) are formed and then are processed. It is assumed that the resulting images are those effects that are then processed, perceived, used by the organizational and technical system for the formation of concepts-representations. Concept representation is a generalized sensual-visual image of the object or phenomenon and is characterized by a number of features, the number of which may vary in the course of the system operation.

The method of Markov chains is used to study the statistical characteristics of the mechanism of formation of concepts-representations. It is assumed that the formation of sensual images and their transformation into concepts-representations occurs at random moments of time. The module of concept-representation formation can be in one of two states that correspond to the logic of its functioning – either its state does not change, or when a new concept-representation is formed, the state of the module changes. A stochastic matrix of one step transient probabilities, characterizing changes in the module states and corresponding initial probabilities of states is introduced. Because of application of the theory of Markov chains with two states, the relations for the probabilities of the module states through an arbitrary number of steps, as well as asymptotic expressions for the probabilities of states are given. The graphs of the module state probabilities change depending on the number of circuit steps, initial probabilities, probabilities of one-step transitions of the stochastic matrix are presented.

Analytical expressions and corresponding graphs for the average number of stays in the module of a particular state are obtained, which are interpreted as the average number of corrections of essential features of concepts-representations. The asymptotic relations for the number of corrections are obtained, and the error of the approximate asymptotic relations is estimated.

Thus, the paper formulates a very general model of the random process of formation of sensual images and their transformation into concepts-representations. The key task of the practical application of the model is to analyze the logic of the functioning of a particular organizational and technical system and to determine on this basis the parameters appearing in the model.

Statistics agencies are the main data provider on the economic position of the macroeconomic level. Most economic decisions on a national scale are based on statistical data. Data processing is a key business process for statistical agencies. At the same time, the quality of statistical data supplied by Rosstat is not always high enough. There are adjustments, a discrepancy between data sets describing the same economic phenomenon is revealed. The purpose of the work is to describe the methods of collecting and processing statistical information that will contribute to improving the quality of the presented data. From the information point of view, the statistical agency is engaged in the organization of information exchange between data providers and consumers, acts as a data aggregator. To organize the information exchange within community you need to create a semantic space to ensure the meaningful filling of the data. The main role in the semantic space is played by the identifiers of objects. The article considers the unified identifiers of statistical accounting objects as a method of collecting and processing statistical information and improving its quality. The international statistical practice use methods of standardizing the turnover of statistical data. Information standards are designed to unify identifiers and namespace for participants of the statistical information turnover and to provide a single semantic space. If you use of unified identifiers, the procedures for processing statistical data become transparent, it allow you grouping by different sections, as well as decomposition of aggregated data into components.

The results of the work are recommendations on the use of Core component of the information infrastructure for the collection and analysis of statistical data. In the existing information infrastructure of the Russian digital economy, there are a number of data sources, the use of which will improve the quality of collection and processing of statistical data. To create a semantic space of statistical data in the Russian Federation, the most important section is the registers of Core Components. The use of registers will allow you to organize the binding of statistical data from different domains, as well as to implement the link of aggregated data with microdata. Significant progress is observed in the marking of goods, which allows you to track object’s movement through all stages of the life cycle, as well as the location. The government of the Russian Federation initiated a project on labeling of goods, and this information gives an opportunity to get a clear picture of a significant part of the economy. An additional information source of statistical data can be the corporate sector, where actively used tracking systems that monitor the goods, vehicles, containers, warehousing.

Conclusion: There are several options for creation of the semantic space for statistical data. World experience is guided by the use of the Web architecture, which involves the technological identifiers. Semantics of statistical data can be ensured by using the potential of the information infrastructure, which will solve a number of problems of statistical accounting.