name
Orlov Alexander Ivanovich
Scholastic degree
•
•
•
Academic rank
professor
Honorary rank
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Organization, job position
• Bauman Moscow State Technical University
Research interests
статистические методы, организационно-экономическое моделирование. Разработал новую область прикладной статистики — статистику объектов нечисловой природы
Web site url
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Current rating (overall rating of articles)
0
TOP5 co-authors
Articles count: 155
Сформировать список работ, опубликованных в Научном журнале КубГАУ
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SYSTEM FUZZY INTERVAL MATHEMATICS - A PROMISING AREA OF THEORETICAL AND COMPUTATIONAL MATHEMATICS
01.00.00 Physical-mathematical sciences
DescriptionThe article b riefly considers the prospects of some “points of growth” in the modern theoretical and computational mathematics: the numbers and sets, i.e. the base of modern mathematics; mathematical, pragmatic and computer numbers; from the usual sets - to unclear; the theory of fuzzy sets and “fuzzy dou-bling” of mathematics; the mix of fuzzy set theory to the theory of random sets; interval numbers as a spe-cial case of fuzzy sets; development of interval mathematics (interval doubling of mathematics); the system as a generalization of a multitude; the systematic generalization of mathematics and tasks emerging; the systematic generalization of operations on sets (on the example of the operation of the Boolean association); the systematic generalization of the concept of functions and functional dependencies participation; cognitive function; the matrix of knowledge as fuzziness with an estimated degree of truth of showing data systems arguments on the system of values of the function; modification of the method of least squares for the approximation of cognitive functions; development of the idea of the systematic generalization of mathematics in the field of information theory – system emergent information theory; information measures of the level of consistency; ratios of emergence; direct and opposite, direct and indirect logical reasoning with an estimated level of truth; intellectual system of Eidos X++ as a toolkit that implements the ideas of system of a fuzzy interval sum of mathematics
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SYSTEM OF MODELS AND METHODS OF TESTING THE HOMOGENEITY OF TWO INDEPENDENT SAMPLES
08.00.13 Mathematical and instrumental methods of Economics
DescriptionThe new paradigm of mathematical research methods allows us to give a systematic analysis of various statements of statistical analysis problems and methods for solving them, based on a probabilistic-statistical model of generating data accepted by the researcher. Methods for testing the homogeneity of two independent samples - a classic area of mathematical statistics. For more than 110 years since the publication of the fundamental Student’s article, various criteria have been developed for testing the statistical hypothesis of homogeneity in various statements, and their properties have been studied. However, the need for streamlining the totality of the scientific results found is urgent. It is necessary to analyze the whole variety of problem statements for testing the statistical hypotheses of the homogeneity of two independent samples, as well as the corresponding statistical criteria. This analysis is devoted to this article. It contains a summary of the main results concerning the methods for testing the homogeneity of two independent samples, and a comparative study of them, allowing the system to analyze the diversity of such methods in order to select the most appropriate for processing specific data. Based on the basic probabilistic-statistical model, the main statements of the problem of testing the homogeneity of two independent samples are formulated. A comparative analysis of the Student and Cramer - Welch criteria, designed to test the homogeneity of mathematical expectations, is given, a recommendation on the widespread use of the Cramer - Welch criterion is substantiated. From nonparametric methods for testing homogeneity, the criteria of Wilcoxon, Smirnov, Lehmann - Rosenblatt are considered. Dismantled two myths about the Wilcoxon criteria. Based on the analysis of the publications of the founders, the incorrectness of the term "Kolmogorov – Smirnov criterion" is shown. To verify absolute homogeneity, i.e. coincidence of the distribution functions of samples, it is recommended to use the Lehmann - Rosenblatt criterion. The current problems of the development and application of nonparametric criteria are discussed, including the difference between nominal and real significance levels, making it difficult to compare power of criteria, and the need to take into account coincidences of sample values (from the point of view of the classical theory of mathematical statistics, the probability of coincidences is 0)
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REAL AND NOMINAL SIGNIFICANCE LEVELS IN STATISTICAL HYPOTHESIS TESTING
01.00.00 Physical-mathematical sciences
DescriptionIn the statistical hypothesis testing, critical values often point to a priori fixed (nominal) significance levels. As such, typically researcher uses the values of three numbers 0.01, 0.05, 0.1, to which may be added a few levels: 0.001, 0.005, 0.02, and others. However, for the statistics with discrete distribution functions, which, in particular, include all nonparametric statistical tests, the real significance levels may be different from the nominal, differ at times. Under the real significance level we refer to the highest possible significance level of discrete statistics, not exceeding a given nominal significance level (ie, the transition to the next highest possible value corresponding discrete statistical significance level is greater than a predetermined nominal). In the article, we have discussed the difference between nominal and real significance levels on the example of nonparametric tests for the homogeneity of two independent samples. We have also studied two-sample Wilcoxon test, the criterion of van der Waerden, Smirnov two-sample two-sided test, sign test, runs test (Wolfowitz) and calculated the real significance levels of the criteria for nominal significance level of 0.05. The study of the power of these statistical tests is accomplished by means of Monte Carlo method. The main conclusion: the use of nominal significance levels instead of real significance levels for discrete statistics is inadmissible for small sample sizes
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DISTANCES IN THE SPACES OF STATISTICAL DATA
01.00.00 Physical-mathematical sciences
DescriptionThe core of applied statistics is statistics in spaces of arbitrary nature, based on the use of distances and optimization problems. This article discusses the various distances in spaces of statistical data, in particular, their conclusions on the basis of appropriate systems of axioms. The conditions and proofs of theorems first published in scientific periodicals
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DISTRIBUTIONS OF REAL STATISTICAL DATA ARE NOT NORMAL
01.00.00 Physical-mathematical sciences
DescriptionIn the training courses on the theory of probability and mathematical statistics there are various parametric families of distributions of numerical random variables considered. Namely, we have been studying the families of normal distributions, log-normal distributions, exponential distributions, gamma distributions, Weibull-Gnedenko distributions, etc. All of them depend on one, two or three parameters. Therefore, for a complete description of the distribution it is sufficient to know or estimate one, two or three numbers. Parametric theory of mathematical statistics is widely developed, where it is assumed that the distribution of observations belong to one or another parametric family of distributions. This tradition comes from Karl Pearson, who in the early twentieth century proposed the use of four parametric family of distributions. The above families of distributions - are the subsets of a four-parametric family of Pearson. Unfortunately, parametric families exist only in the minds of the authors of textbooks on probability theory and mathematical statistics. In real life, they are not. Therefore, modern applied statistics and econometrics mainly use non-parametric methods, in which the distribution of observations can have arbitrary form. First, on an example of a normal distribution, we are discussing the impossibility of practical use of parametric families of distributions to describe specific statistical data. We give the results of research of metrologists and estimation of convergence in limit theorems. Then we discuss how the parametric methods can use for reject outlying observations. It is very unstable the significance levels for a fixed rejection rule and the parameter of the rejection rules for a fixed level of significance. Consequently, the rejection of the classic rules of mathematical statistics is not sciencebased
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01.00.00 Physical-mathematical sciences
DescriptionWe should have trained staff to implement innovative strategies. Therefore, it is natural, that a lot of attention is paid to the staffing of the management processes of innovative activity at the enterprises of the rocket and space industry (RCP). Training and human resources management in accordance with current legislation should be based on professional standards. The content of professional standards should reflect the results of forecasting scientific and technical progress in the field, for example, in the RCP. It is necessary to forecast trends in the use of information and communication technologies in solving management problems in the socio-economic sphere in order to reflect these developments in professional standards. The approach to solving this problem is the subject of this article. What should the professional standard be like in the RCP? The main problem lies in the fact that although the standard is to be enacted in the near future, its actual impact on the industry will start in 5 - 10 years and will continue for at least another 10 years, ie, until the 2030s. Professional standards should come from "Education through Science" concept, ie, knowledge, skills, competences, provided by a professional standard, should be based on modern scientific achievements. For example, mathematical methods of research should be based on a new paradigm in the area of knowledge and statistical data analysis methods must meet high statistical techniques. For the development of professional standards in the field of the RCP it is necessary to predict the characteristics of the qualification (level of knowledge, skills and experience) required the employee to carry out professional activities in the RCP in 2020 - 2030. Modern information and communication technologies are creating a fundamentally new situation in the organization of the economy. We have an ability to manage the work of organizational units, scattered throughout the world, from a single center. The requirement of presence in the workplace is mainly a relic of the past. We have a lot of advantages in a remote work
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PREDICTIVE POWER – THE BEST INDICATOR OF THE QUALITY OF THE DIAGNOSTIC ALGORITHM
01.00.00 Physical-mathematical sciences
DescriptionInexpediency of use of probability of correct diagnostics as a quality indicator of diagnostic algorithm is shown. The new indicator - the prognostic strength based on Mahalanobis distance between classes is offered and studied. We have found asymptotic distribution of the prognostic strength; the way of testing of adequacy of its application has been specified. In a problem of testing of two simple hypotheses the prognostic strength connection is established with Hellinger distance
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FORECAST OF INFORMATION AND COMMUNICATION TECHNOLOGIES
01.00.00 Physical-mathematical sciences
DescriptionForecasting of scientific and technical progress is necessary to make grounded management decisions. In this article, we forecast the development of information and communication technologies in order to solve a particular but important issue of design of professional standards in the aerospace industry. We identify the factors affecting the development of information and communication (computer) technologies, with their help determine the trends of development of these technologies over the next two decades. The main trend - the maximum cheaper production of computer (or network) components, combined with an increase in their capacity. One way to reduce the cost of production is the "centralization" - combining several components into one. The third trend - the desire to reduce the size of computers. The size of a future computer could be a device the size of a pencil, a pin or button, as the system unit has a negligible size, keyboard and display are virtual, transfer any amount of information through a virtual office online. The development of secure free copying will lead to increased use of this free software and technologies "rental program" over the Internet. We predict an increase in reliability and intensive programs while maintaining the general principles of the interface. Revolutionary changes are expected production (machines, sensors), and household appliances
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01.00.00 Physical-mathematical sciences
DescriptionCurrently, the majority of scientific, technical and economic studies use statistical methods developed mainly in the first third of the XX century. They constitute the content of common textbooks. However, mathematical statistics are rapidly developing in the next 60 years. In some situations there is a need of the transition from classical to modern methods. As an example, we discuss the problem of testing the homogeneity of two independent samples. We have considered the conditions of applicability of the traditional method of testing the homogeneity based on the use of Student's t-statistic, as well as more up-to-date methods. We describe a probabilistic model of generation of statistical data in the problem of testing the homogeneity of two independent samples. In terms of this model the concept of "homogeneity" ("no difference"), can be formalized in different ways. High degree of homogeneity is achieved if the two samples are taken from one and the same population (absolute homogeneity). In some cases it is advisable to testing the coincidence of some characteristics of the elements of the sample - mathematical expectations, medians, variances, coefficients of variation, and others (testing the homogeneity of characteristics). To test the homogeneity of mathematical expectations is often recommended classic t-test. It is believed that the samples taken from a normal distributions with equal variances. It is shown that for scientific, technical and economic data the preconditions of two-sample t-test usually are not performed. To test the homogeneity of mathematical expectations instead of t-test we have offered to use the Cramer-Welch test. We have considered the consistent nonparametric Smirnov and Lehmann-Rosenblatt tests for absolute homogeneity
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MANAGEMENT PROBLEMS IN SMALL PRODUCTION COMPANIES AT EARLY LIFECYCLE STAGES
DescriptionIn 1970 in the journal publications of "Forbes" and "Business week" the term of "startup" appeared, which later became popular in the scientific and business literature. Startups are the organizations, which create a new product or service under conditions of high uncertainty. In the last 25-30 years, due to Russia's transition from a planned economy to the mixed, many researchers and practitioners in the field of management, economics and entrepreneurship are concerned of some questions of small business, including production. It is particularly acute problem of deaths of Russian small businesses: only three out of a hundred small businesses manage to survive for more than 3 years. In addition, one of the main reasons, why we have such statistics, is management deficiencies and administrative errors, which are studied in this article. We are primarily interested in small manufacturing plants and problems of development in the early stages of the life cycle. In the literature, it has been given just little attention. A small production company is a company associated with the production organization or incorporation of the product / technology in the production process. We regard the small production companies at an early stage of development, working in the field of mechanical engineering, instrumentation, energy, telecommunications, robotics, materials production. In this work, we analyze the first foreign and then domestic research on small business, discuss the problems of management of small industrial enterprises in the early stages of the life cycle (based on the results of our questionnaire studies) and as an example, consider the story of a startup - All-Union Center of statistical methods and Informatics of Central Board of the All-Union economic society (now - Institute of high statistical technologies and econometrics of Bauman Moscow State Technical University)