Name
Orlov Alexander Ivanovich
Scholastic degree
•
•
•
Academic rank
professor
Honorary rank
—
Organization, job position
Bauman Moscow State Technical University
Web site url
—
Articles count: 155
Classical economic textbooks assume that the effect of a particular company on the environment is infinitely small, in particular, that resources required for an industrial firm are available, and it's only the price to be paid for their involvement. For a large corporation, the situation is quite different. It converts the environment by means of its activity. Objectively existing resource limits are become important. The effects are increased when we consider the economy as a whole thing. Therefore, we have the obvious need for careful consideration of management problems in the real process of interaction between the economy, society and environment. This article is devoted to some approaches to this consideration. We have demonstrated that the economy is the servant of society. In all the economical developed countries in the twentieth century the role of the state in the economy has been increased in 3-5 times. We have discussed the influence of the modern ecological situation on the economy and management. In particular, we predict the end of private enterprise in the classical meaning. We examined the social-ecological aspects of management of the state and personnel of the firm. Discussion of Russian problems we begin with an analysis of the dynamics of the main economic and demographic indicators of Russia, including the total fertility rate in Russia. The system of scenarios of population projections for the period up to 2050 shows the inevitability of significant reduction in the Russian population (in the absence of intensive management actions). We describe two basic scenarios of solving socio-ecological conflicts
The general scheme of modern statistical science is
just like this. Mathematical Statistics is a part of
mathematics that studies the statistical structure (it
itself does not give recipes analysis of statistical
data, however, it is developing methods that are
useful for use in theoretical statistics). Theoretical
Statistics - the science dedicated to the models and
methods of analysis of concrete statistical data.
Applied Statistics (in the narrow sense) is devoted to
the statistical techniques of data collection and
processing (it includes the methodology of statistical
methods, the organization of sample surveys, the
development of statistical techniques, the creation
and use of statistical software). Applications of
statistical methods in concrete fields (in economics
and management - Econometrics, in biology -
Biometrics, in chemistry - Chemometrics, in
technical research - Technometric, in geology,
demography, sociology, medicine, history, etc.).
Often positions 2 and 3 together are called Applied
Statistics. Sometimes position 1 is called Theoretical
Statistics. These terminological differences are
related to the fact that the above-described
development of the considered scientific and applied
field not once, not completely and not always
adequately reflected in the minds of experts.
Meanwhile, there are still textbooks of appropriate
level of representation of the mid-twentieth century.
The article analyzes the post-war development of
the national statistics. We have identified five
"growth points": nonparametrics, robustness,
bootstrap, statistics of interval data, and statistics of
non-numeric data. We have discussed content,
development and the basic ideas of statistics of nonnumeric
data. We have given a number of
unresolved problems of theoretical and applied
statistics
The probabilistic model of grouping data (including multidimensional data) is described. We have also generalized Euler-Maclaurin’s formulas. With its help Sheppard’s corrections and corrections on
grouping for correlation coefficient are received. We have found and studied asymptotical corrections on grouping data generally. Accuracy of approach has been estimated
Currently, 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
We have given a critical analysis of statistical
models and methods for processing text information
in historical records to establish the times when
there were certain events, ie, to build science-based
chronology. There are three main kinds of sources
of knowledge of ancient history: ancient texts, the
remains of material culture and traditions. The
specific date of the extracted by archaeologists
objects in most cases can not be found. The group of
Academician A.T. Fomenko has developed and
applied new statistical methods for analysis of
historical texts (Chronicle), based on the intensive
use of computer technology. Two major scientific
results were: the majority of historical records that
we know now, are duplicated (in particular,
chronicles, describing the so-called "Ancient Rome"
and "Middle Ages", talking about the same events);
the known historical chronicles tell us about real
events, separated from the present time for not more
than 1000 years. It was found that chronicles
describing the history of "ancient times" and
"Middle Ages" and the chronicle of Chinese history
and the history of various European countries do not
talk about different, but about the same events. We
have the attempt of a new dating of historical events
and restoring the true history of human society
based on new data. From the standpoint of statistical
methods of historical records and images of their
fragments – they are special cases of non-numeric
objects of nature. Therefore, developed by the group
of A.T. Fomenko computer-statistical methods are
the part of non-numerical statistics. We have
considered some methods of statistical analysis of
chronicles applied by the group of A.T. Fomenko:
correlation method of maximums; dynasties method;
the method of attenuation frequency; questionnaire
method codes. New chronology allows us to
understand much of the battle of ideas in modern
science and mass consciousness. It becomes clear
the root cause of cautious attitude of the West
towards Russia
The article is devoted to the discussion of the
organization of clinical-statistical studies and
experiments. We have considered the examples of
the application of statistical methods in scientific
medical research. Under the clinical-statistical
research we understand specially organized
collection and analysis of medical data about the
course of disease in patients, research of the
dynamics of objective and subjective indicators of
the state of reaction to these or other therapeutic
effects. We study one, two or more groups of
individuals (patients or healthy), conclusions are
drawn on the whole group, but not for each
individual patient. The purpose of research - to
transfer the conclusions reached for the sample to
the general population, i.e., clinical and statistical
study focused on the production of useful
recommendations concerning those patients who fall
into the field of view of doctors after the end of the
study. There are two main types of research -
prospective and retrospective. The first related to the
analysis of the last patients, the second - to
monitoring the course of their disease in the future.
We have considered typical mistakes in the
organization of clinical-statistical studies. When
planning a research, we usually distinguish the
experimental and control groups, which are identical
or similar in all respects except for the studied
factors (exposure). We discuss the various options
for blind methods and consider the application of
statistical models and methods in scientific medical
research. We have analyzed examples of confidence
estimation of proportion (probability) and the
homogeneity test of probabilities. For statistical
modeling we use the Poisson distribution in the case
of small probability. With its help, we analyze
statistical data on the opisthorchiasis
Fuzzy sets are the special form of objects of nonnumeric
nature. Therefore, in the processing of the
sample, the elements of which are fuzzy sets, a
variety of methods for the analysis of statistical data
of any nature can be used - the calculation of the
average, non-parametric density estimators,
construction of diagnostic rules, etc. We have told
about the development of our work on the theory of
fuzziness (1975 - 2015). In the first of our work on
fuzzy sets (1975), the theory of random sets is
regarded as a generalization of the theory of fuzzy
sets. In non-fiction series "Mathematics.
Cybernetics" (publishing house "Knowledge") in
1980 the first book by a Soviet author fuzzy sets is
published - our brochure "Optimization problems
and fuzzy variables". This book is essentially a
"squeeze" our research of 70-ies, ie, the research on
the theory of stability and in particular on the
statistics of objects of non-numeric nature, with a
bias in the methodology. The book includes the
main results of the fuzzy theory and its note to the
random set theory, as well as new results (first
publication!) of statistics of fuzzy sets. On the basis
of further experience, you can expect that the theory
of fuzzy sets will be more actively applied in
organizational and economic modeling of industry
management processes. We discuss the concept of
the average value of a fuzzy set. We have
considered a number of statements of problems of
testing statistical hypotheses on fuzzy sets. We have
also proposed and justified some algorithms for
restore relationships between fuzzy variables; we
have given the representation of various variants of
fuzzy cluster analysis of data and variables and
described some methods of collection and
description of fuzzy data
The 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
The 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)
System paradigm is discussed conformably to
functioning of controlling institution of a large-scale
agro-industrial system. Presently the systemacity
became the general platform of fundamental and
applied, scientific and practical elaborations and
projects. Now in the sphere of system researches
surge of interest in questions of classification is
observed. Apparently, it is connected with
accumulation of results of private researches in all
areas of this discipline and with inevitable
transdisciplinary crossings of their practical
applications. So, undoubted intervention of high
technologies to the agrarian sphere is observed. The
efficiency of this introduction, certainly, depends on
coordination of actions of developers of various
subject domains. On the basis of the objective
analysis it must be noted that in the arsenal of
managers, especially foreign ones, there is
practically no fundamentally new methods and tools
of controlling. So says the executive director of
Russian Association of Controllers prof. S. G. Falco.
However, promising mathematical and instrumental
methods of controlling actively developed in our
country. It is necessary to implement them. For
example, managers should be used advanced
mathematical and instrumental methods of
controlling. These methods are based on the modern
development of mathematics as a whole - on the
system interval fuzzy math. Considered methods are
developed in accordance with the new paradigm of
mathematical methods of research. It includes new
paradigms of applied statistics, mathematical
statistics, mathematical methods of economics,
methods of analysis of statistical and expert data in management and control. In the XXI century there
were more than 10 books issued, developed in
accordance with the new paradigm of mathematical
methods of research. The systems approach to
solving specific applications often requires going
beyond the economy. Very important are the
procedures for the introduction of innovative
methods and tools. In this article we consider the
above research results in their interconnection