#### Name

Orlov Alexander Ivanovich

#### Scholastic degree

•

•

•

#### Academic rank

professor

#### Honorary rank

—

#### Organization, job position

Bauman Moscow State Technical University

#### Web site url

—

## Articles count: 129

One of the key provisions of the system fuzzy interval mathematics - the claim that the theory of fuzzy sets is the part of the theory of random sets, thus, part of the probability theory. The article is devoted to the justification of this statement. Proved number of theorems that show that the fuzzy sets and the results of operations on them can be viewed as the projections of random sets and the results of the corresponding operations on them

In practical use of methods of applied statistics we do not apply separate methods for describing data, estimation, testing hypotheses, but we must use deployed whole procedures - the so-called "statistical technology". The concept of "statistical technology" is similar to the concept of "technological process" in the theory and practice of organization of production. It is quite natural that some statistical technology can better meet the needs of the researcher (user, statistics) than others, some - are modern, and others - outdated, some properties are studied, and the others - no. It is important to stress that a qualified and efficient use of statistical methods - this is not one single statistical hypothesis testing and estimation of characteristics or parameters of a given distribution from fixed family. This kind of operations - only the individual building blocks that make up the statistical technology. The procedure of the statistical data analysis - is an information process, in other words, one or other information technology. Statistical information is subject to a variety of operations (series, parallel, or more complex schemes). In this article we discuss statistical technologies and the problem of "docking" algorithms. We introduce the concept of "high statistical technologies" and then we prove the necessity of their development and application. As the examples we have given the researches of Institute of high statistical technologies and econometrics of Bauman Moscow State Technical University. We have also considered a number of education problems in domain of high statistical technologies

Improvement of the organizational structures can increase the efficiency of enterprises. Controlling of personnel in companies such as "Research Institute" is a tool to support personnel decisions; it contributes to the strategic goals and tactical objectives. This article describes the main types of organizational structures, their properties, sociometric research as a tool for management, the stages of implementation of model of controlling of personnel in human resource management system for companies such as "Research Institute". Controlling of personnel is in regulation of HR processes, benchmarking, monitoring the implementation of the goals, taking into account the costs of implementing improved management systems, etc. It aims to determine the quality, efficiency and optimality of specific mechanisms, technologies and methods for the implementation of the HR function. Objectively, the volume of realization of the HR function depends on the presence of a certain quantities of material, labor, financial and other resources, on the objectives of the enterprise at different stages of the life cycle, as well as the number and qualifications of personnel. The quality of realization of the HR function depends on the level of its top-management's understanding of the importance of human resource management in the enterprise, as well as of the skill level of middle management. Controlling of HR function allows us to create an information base for effective management decisions that can help us to optimize the system of personnel management in the circumstances of the market environment, which is a necessary basis for the successful development of enterprises working in the field of high technology products and services

The purpose of mathematical statistics is
development of methods for the data analysis
intended to solve applied problems. Over time,
approaches to the development of data analysis
methods have changed. A hundred years ago, it was
assumed, that the distributions of the data have a
certain type, for example, they are normal
distributions, and on that assumption they developed
a statistical theory. The next stage, in the first place
in theoretical studies there are limit theorems. By
"small sample" we mean a sample, which can not be
applied to conclusions based on the limit theorems.
In each statistical problem there is a need to divide
the final sample sizes into two classes - those for
which you can apply the limit theorems, and those
for which you can not do it because of the risk of
incorrect conclusions. To solve this problem we
often used the Monte Carlo method. More complex
problems arise when studying the effect on the
properties of statistical procedures for data analysis
of various deviations from the original assumptions.
To study such impact, we often used the Monte
Carlo method as well. The basic (and not solved in a
general way) problem of the study of the stability of
the findings in the presence of deviations from the
parametric families of distributions is the problem of
choosing some distributions for using in modeling.
We consider some examples of application of the
Monte Carlo method, relating to the activities of our
research team. We have also formulated basic
unsolved problems

The basic ideas of the developed by us solidary
information economy are analyzed (the original
name - the nonformal informational economy of
the future). Its use as the base of modern
organizational-economic theory in exchange for the
term of “economics” is proved. The core of
researches in the field of the NIEF is forecasting of
development of the future society and its economy,
working out of organizational-economic methods
and models, necessary for the future and intended
for increase of efficiency of managerial processes.
The economy is a science how to make, instead of,
how to divide profit. The basic kernel of the
modern economic theory is an engineering
economy. As the economic component of state
ideology of Russia we offer solidary information
economy. According to the solidary information
economy the modern information technology and
decision theory allow, based on the “open network
society”, to build information and communication
system designed to identify the needs of people and
the organization of production in order to meet
them. To implement this feature we must have
political will of leadership of economic unit, aimed
at transforming the management of this economic
unit. In particular, as is already happening in all
developed countries, the Russian state should
become a major player in the economy

The first statistical publication – the Fourth Book of Moses, “Numbers” in the Old Testament. We trace the development of ideas about the statistics until the twentieth century. The present stage of statistical methods began with parametric statistics by Pearson, Student, Fisher. Scientometrics of statistical researches provides an indication of the accumulated results. Nonparametric statistics appeared in the 1930s, applied statistics in our country - at the turn of 1970-80. We have discussed what gives applied statistics to national economy. Also we have told briefly about the history of statistical methods in
Russia (until Kolmogorov's time)

Some estimators of the probability density function in spaces of arbitrary nature are used for various tasks in statistics of non-numerical data. Systematic exposition of the theory of such estimators had a start in our work [2]. This article is a direct continuation of the article [2]. We will regularly use references to conditions and theorems of the article [2], in which we introduced several types of nonparametric estimators of the probability density. We studied more linear estimators. In this article we consider particular cases - kernel density estimates in spaces of arbitrary nature. When estimating the density of the one-dimensional random variable, kernel estimators become the Parzen-Rosenblatt estimators. Asymptotic behavior of kernel density estimators in the general case of an arbitrary nature spaces are devoted to Theorem 1 - 8. Under different conditions we prove the consistency and asymptotic normality of kernel density estimators. We have studied uniform convergence. We have introduced the concept of "preferred rate differences" and studied nuclear density estimators based on it. We have also introduced and studied natural affinity measures which are used in the analysis of the asymptotic behavior of kernel density estimators. We have found the asymptotic behavior of dispersions of kernel density estimators and considered the examples including kernel density estimators in finite-dimensional spaces and in the space of square-integrable functions

The article analyzes the development of the theory
of statistical control (from the XVIII century to the
present). Prof. M.V. Ostrogradskii (1846) clearly
describes the practical needs (ie, arising from the
quality assurance of large quantities of bags of
flour or pieces of cloth), to meet whom he spent his
research. At the same time Simpson was among the
ideas of probability theory XVIII century.
Therefore prof. M.V. Ostrogradskii may be
regarded as the founder of the theory of statistical
process control (not only in our country but all over
the world). Limit theorems of probability theory
and mathematical statistics have provided a
number of asymptotic results in problems of
statistical quality control, offer based on these best
practices. However, we must find out how much
interest among specialists characteristics are
different from limit for finite sample sizes. Such
research for the synthesis algorithm control plan on
the basis of the limit average output level of defects
is made in this article, and for the synthesis
algorithm control plan on the basis of the
acceptance and the rejection levels of defects - not
yet (clarification of the conditions of applicability
of this algorithm - unsolved problem of applied
mathematics). We have briefly reviewed the
development of our researches on the statistical
control. Control units can be not only some units of
production, but also documents (with internal and
external audit), and standard units of air, water and
soil in the environmental monitoring. One of the
achievements can be regarded as the transfer of
statistical control of production for environmental
monitoring

We have studied the asymptotic behavior of a broad class of nonparametric statistics, which includes statistics of omega-square type and Kolmogorov-Smirnov type. Limit theorems have been proved. We have also developed the method of approximation with step functions. With the help of this method we have obtained a number of necessary and sufficient conditions

The new paradigm of mathematical statistics is based on the transition from parametric to nonparametric statistical methods, the numerical data - to non-numeric, on the intensive use of information technology. Its distinctive features are revealed in comparison with the old paradigm of mathematical statistics in the mid-twentieth century