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
In the article we have considered A. N. Kolmogorov and N. V. Smirnov papers dedicated to one-sided and two-sided goodness-of-fit and homogeneity tests. It has been shown that the term "Kolmogorov - Smirnov test" used incorrectly. We have also given the recommendations on use of the terms "Kolmogorov test", "Smirnov test", "test of Kolmogorov-Smirnov type" and discussed omega-square test (Cramer-von Mises–Smirnov test). Typical errors in the application of these criterions have been considered, in particular to test for normality of the distribution of measurement results
In the article we have considered the basic idea of asymptotic mathematical statistics of interval data, in which the elements of a sample are not the numbers, but the intervals. Algorithms and conclusions of interval data statistics fundamentally different from
the classical ones. The results related to the basic concepts of notna and rational sample sizes are listed. Interval data statistics as an integral part of the system of fuzzy interval mathematics is shown
The concept of risk-controlling is based on the general theory of risk. The current state of risk-management in our country is reviewed. We also discuss the research on risk-controlling made in the BMSTU Laboratory of economic-mathematical methods in controlling
We consider the nonparametric problem of reneval dependence, which is described by the sum of a linear trend and periodic function with a known period. We obtain the asymptotic distribution of the parameter estimates and the trend component. The methods of estimating the periodic component and designing in-terval forecast. In the model of the points of observa-tion, natural for applications, justified by the condi-tions of use. In particular, we prove an asymptotically unbiased estimate of the coefficient of the linear term
This article briefly reviews the classical concept of functional dependence in mathematics, determines the limitations of this concept for adequate modeling of reality and formulates the problem, consisting in search of such generalization of the concept of func-tions, which is more suitable for the adequate reflec-tion of causal relationships in the real domain. Also, it discusses theoretical and practical solving the prob-lem, consisting in: (a) we suggest the universal method of calculating the amount of information in the value of argument about the meaning of the function, i.e. cognitive functions which is independent from the subject area; b) we offer software tools: Eidos intelli-gent system, allowing in practice to carry out these calculations, i.e. to build cognitive functions based on a fragmented noisy empirical data of high dimension. We also offer the concepts of nonreducing, partially and completely reduced direct and inverse, positive and negative cognitive functions and the method of formation of reduced cognitive function, which is a generalization of known weighted least-squares meth-od on the basis of observation the amount of infor-mation in the values of the argument about the values of the functions accounting
The new results of the sample average values in different spaces and rules of large numbers for them are given in the article. We also introduced the weighted average values of type I corresponding to the sample, and type II, corresponding to the set of order statistics. The evolution of ideas about the Kemeny distance and the Kemeny median is traced. The modified Kemeny median, convenient for computation and avoiding the effect of the "center of the bagel hole" is proposed. As a generalization of the Kemeny median, we introduced and studied the empirical and theoretical values in the spaces of arbitrary origin. For them, we proved the rules of large numbers
About thirty-five years ago, the statistics of non-numerical objects was highlighted as an independent field of mathematical statistics. This article analyzes the basic ideas in this area, and relevant publications on the background of the development of applied statistics, and in connection with the system fuzzy interval mathematics
The requirements for the project design stages of creating rocket and space technology are specified. The algorithm of estimation the feasibility of such projects is proposed based on their innovation and investment components
We have proposed the general scheme for studying the stability of the conclusions obtained by mathematical methods and models regarding tolerance deviations of the original data and background models. The concrete problems of stability are discussed: towards a change of data, its size and distributions, to allowable transformations measurement scales, to the temporal characteristics (time of start of the project, the planning horizon). Reducing the uncertainty can be conducted by changing the type of data, i.e. with the aid of the transition to non-numerical data.
The models of concrete management processes of industrial organizations are considered on the examples of stability characteristics of investment projects to change the discount factors and in models of inventory management to change in the coefficients of the model and batch size production
We introduce the concept of "controlling organizational-economic methods". We define the terms in the sequence "the problem - the model - the method - the conditions of applicability". We have described the basic organizational-economic model of industrial firm; by means of this model we have discussed the problems of development of modern organizational-economic methods. We have demonstrated the relevance of the theory and methodology of organizational-economic modeling. For example, we consider the application of statistical methods at various stages of the life cycle of the product, the problem of internal risks in an industrial firm and accounting for inflation in the analysis of activities of the organization