According to the new paradigm of applied mathematical statistics one should prefer non-parametric methods and models. However, in applied statistics we currently use a variety of parametric models. The term "parametric" means that the probabilistic-statistical model is fully described by a finite-dimensional vector of fixed dimension, and this dimension does not depend on the size of the sample. In parametric statistics the estimation problem is to estimate the unknown value (for statistician) of parameter by means of the best (in some sense) method. In the statistical problems of standardization and quality control we use a three-parameter family of gamma distributions. In this article, it is considered as an example of the parametric distribution family. We compare the methods for estimating the parameters. The method of moments is universal. However, the estimates obtained with the help of method of moments have optimal properties only in rare cases. Maximum likelihood estimation (MLE) belongs to the class of the best asymptotically normal estimates. In most cases, analytical solutions do not exist; therefore, to find MLE it is necessary to apply numerical methods. However, the use of numerical methods creates numerous problems. Convergence of iterative algorithms requires justification. In a number of examples of the analysis of real data, the likelihood function has many local maxima, and because of that natural iterative procedures do not converge. We suggest the use of one-step estimates (OS-estimates). They have equally good asymptotic properties as the maximum likelihood estimators, under the same conditions of regularity that MLE. One-step estimates are written in the form of explicit formulas. In this article it is proved that the one-step estimates are the best asymptotically normal estimates (under natural conditions). We have found OS-estimates for the gamma distribution and given the results of calculations using data on operating time to limit state for incisors
Statistical methods are based on the developed theory and demonstrated its usefulness in the sectors of the economy. However, the analysis of the situation in the application of statistical methods shows obvious distress, in which accumulated in our country's scientific potential is not used to the full. As practice shows, it is not enough to develop promising modern theory-based effective mathematical and instrumental methods of controlling. For using such methods in mass, it is necessary that they would be implemented. Management of innovations, i.e. innovation management, quite rightly is currently one of the most debated sections of the economy and the organization of production, of the entire economic science in general. However, the implementation of applied statistics and other statistical methods, more generally, mathematical and instrumental methods of controlling, has its own specifics. It is considered in the article. We have highlighted the developmental vulnerabilities - low scientific level of many individuals applying statistical methods, the lack of organizational structure of applied statistics as a field of applied activities and others. We regret to note that the very idea of the need to establish requirements for the methods of data analysis and project formulations such requirements remained outside the attention of those professionals who need them and were addressed. We have no adequate system of guidance for documents on concrete statistical methods performed on modern scientific level. According to the author, the desired future of applied statistics is reorganization according to the model of Metrology. We have analyzed the application of statistical methods as a specialty. The analysis of state standards on statistical methods and the causes of them blunders are given. We have discussed the status of documents for statistical methods for standardization and quality control.
We discuss a new system of "Six Sigma" for implementation advanced mathematical and instrumental methods of controlling
The quality of a system is seen as an emergent property of systems, due to their composition and structure, and it reflects their functionality, reliability and cost. Therefore, when we speak about quality management, the purpose of management is the formation of pre-defined system properties of the object of management. The stronger the object of the control expresses its system properties, the stronger the nonlinearity manifests of the object: both the dependence of the management factors from each other, and the dependence of the results of the action of some factors from the actions of others. Therefore, the problem of quality management is that in the management process the management object itself changes qualitatively, i.e. it changes its level of consistency, the degree of determinism and the transfer function itself. This problem can be viewed as several tasks: First is the system identification of the condition of the object of management, 2nd – making decisions about controlling influence that changes the composition of the control object in a way its quality maximally increases at minimum costs. To solve the 2nd problem we have proposed an application of the component selection of the object by functions based on the resources allocated for the implementation of different functions; costs associated with the choice of the components and the degree of compliance of various components to their functional purpose. In fact, we have proposed a formulation and a solution of the new generalization of a variant of the assignment problem: "multi backpack", which differs from the known with the fact that the selection has been based not only on the resources and costs, but also with taking into account the degree of compliance of the components to their functional purpose. A mathematical model, which provides a solution to the 1st problem, and reflecting the degree of compliance of the components to their functionality, as well as the entire decision-making process for selections, i.e. 2nd task, has been implemented in the ASC-analysis and in the system called "Eidos" X++". The article also provides a simplified numerical example of the proposed approach with the selection of staff members
The mathematical theory of classification contains a large number of approaches, models, methods, algorithms. This theory is very diverse. We distinguish three basic results in it - the best method of diagnosis (discriminant analysis), an adequate indicator of the quality of discriminant analysis algorithm, the statement about stopping after a finite number of steps iterative algorithms of cluster analysis. Namely, on the basis of Neyman - Pearson Lemma we have shown that the optimal method of diagnosis exists and can be expressed through probability densities corresponding to the classes. If the densities are unknown, one should use non-parametric estimators of training samples. Often, we use the quality indicator of diagnostic algorithm as "the probability (or share) the correct classification (diagnosis)" - the more the figure is the better algorithm is. It is shown that widespread use of this indicator is unreasonable, and we have offered the other - "predictive power", obtained by the conversion in the model of linear discriminant analysis. A stop after a finite number of steps of iterative algorithms of cluster analysis method is demonstrated by the example of k-means. In our opinion, these results are fundamental to the theory of classification and every specialist should be familiar with them for developing and applying the theory of classification
Based on an objective analysis, it must be noted that
in the arsenal of managers, especially foreign ones,
there is practically no fundamentally new methods
and tools. However, promising mathematical and
instrumental methods of controlling actively
developed in our country. In the XXI century it
developed a new paradigm of mathematical methods
of economics and produced more than 10 books,
developed in accordance with this paradigm. The
new paradigm is based on the modern development
of mathematics as a whole - on the system interval
fuzzy math. The new paradigm offers tools used
non-parametric statistics, which suggest that the
distribution functions are arbitrary. In 1979 it was
allocated one of the four major areas of modern
applied statistics - statistics of objects of nonnumeric
nature (statistics of non-numeric data, nonnumeric
statistics). The other three - statistics of
random variables, multivariate statistical analysis,
statistics of random processes and time series.
Statistics of objects of non-numeric nature is central
to the modern mathematical methods of economics.
On the basis of modern information-communication
technologies we have developed a new economic
theory - solidary information economy. New
intellectual tools of controlling include an
automated system-cognitive analysis (ASA) and its
software - the system of "Eidos". 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, the solutions of Einstein's equations for empty space, describing the gravitational field near the Sunlike star have been investigated. We have accounted the own field of the star, the motion of the star around the galactic center, the motion of the galaxy relative to the center of the local supercluster and the expansion of the Universe. The resulting gravitational field near the star has a complex structure, which leads to large-scale geometric turbulence linking large and small scales in this problem
Recently, the process of monetization of the evaluation of scientific activity was initiated, and there is a need for quantitative methods and comparable assessment of the effectiveness and quality of work of a scientist. There are numerous methods to reward for these results. What is common to all these techniques covered is the role of the Hirsch index or h-index. By itself, this index is well founded. However, in connection with the practice of application of h-index in our environment in the minds of the scientific community it has started some kind of mania, which the author proposes to call "Hirsch-mania". This mania is characterized by elevated unhealthy interest to the value of the Hirsch index, especially inadequate artificial exaggeration of this value, as well as a number of negative implications of this interest. In this article we have made an attempt to briefly describe some of the negative effects of this new mental infection that hit the public consciousness of the scientific community. And also we want to identify ways of overcoming at least some of their causes. This is the problem solved in this work. To solve the formulated problem, we propose to apply multi-criteria approach based on information theory, namely those options, which are implemented in an automated system-cognitive analysis (ASC-analysis) and its software tools - intelligent system called "Eidos
The article discusses the question of the concepts of heat
and internal energy of a body. The analysis of these
concepts in the historical aspect and the views of the author,
based on the new photon theory of atomic structure were
presented in this study. The analysis of the historical aspect
of this question tells that the concepts of heat and internal
energy of the body for a long time were associated with the
concept of caloric, which can flow in the substance. The
next step was the identification of the concept of heat with
energy linked with the movement and work. In accordance
with this, Clausius proved the equivalence of heat and work
as the first principle of the theory of heat and introduced the
concept of internal energy, which can be increased in two
ways - making work on body, and summing heat to it. Thus,
energy was the main uniting factor of work and heat. Then,
the kinetic theory of heat, as the energy of motion of
molecules, was developed by Maxwell and caloric model
turned out to be a hindrance in the development of the
theory of heat. In fact, the internal energy of the body is
determined photons, rotating around charged particles in
atoms in their orbitals. The series of photons are combined
into a single photon orbital direction of rotation of the
photons, which are different from each other. Thus, the
body has an internal energy or internal heat. It is due to the
energy of photons, orbiting electrons in the outer shell of
each atom, as well as around the charged particles -
electrons and protons in the nucleus of an atom. This
internal energy may be increased by mechanical action on
the body, leading to an increase in resulting oscillation
frequency of photons around charged particles of atoms and
the internal heat contained in the body can flow of the body
with a higher concentration of heat to the body with a lower
concentration of heat
The aim of this work is to carry out numerical analysis of time behavior of electroconvection in membrane systems, such as a desalting channel of electrodialysis apparatus. The current-voltage curve and the solution flaw were analyzed theoretically using mathematical models of ions transfer taking into account electroconvection in smooth desalting channel consisting of ideally selective anion- and cation-exchange membranes. The Hurst numbers for different parts of the current-voltage curve were calculated in order to determine whether the parts were persistent. The Fourier-analysis of the oscillating term of the current-voltage curve was carried out for the first time so as to determine predominant frequencies in the signal. Frequencies of passing of complexes of vortexes through the cross-section of the desalting channel were calculated. Frequencies of oscillations of concentration profiles were determined. It was found that the frequencies of oscillations of the concentration profiles coincide with the frequencies of passing of complexes of vortexes through the cross-section of the desalting channel. The oscillations of the current-voltage curve were physically interpreted. Namely, it was shown that the main frequency of oscillations of the current-voltage curve corresponds to the frequency of oscillations of the concentration profiles. The oscillations of the concentration profiles, produced by the passing of complexes of vortexes, cause oscillations of conductivity and, consequently, cause oscillations of resistance and of the current density. It was shown that the main frequency of the signal corresponds to the frequency of passing of complexes of vortexes through the cross-section of the desalting channel
In the article we have derived mathematical models of non-stationary transport binary electrolyte in EMS (electromembrane systems: electrodialysis apparatus, electromembrane cell, etc.) for the galvanostatic mode. To be specific, as EMS viewed channel of desalting of EDA (electrodialysis apparatus) and EMS with RMD (rotating membrane disk). We present a formula expressing the intensity of the electric field through the current density and concentration. Also, we have received the differential equation for the current density. The fundamental point here is derived new equation for the unknown vector function of current density of the initial system of equations of Nernst-Planck. In addition, the article shows the output equation for the current density in three dimensions; we have proposed various methods for solving the equation of the current density and the boundary conditions for the current density. The proposed mathematical models of transport binary electrolyte are easy to be generalized to an arbitrary electrolyte. However, the corresponding equations are cumbersome. It should be also noted that the boundary conditions can be varied and depend on the purpose of a particular study in this regard, in this work are just the equation having the general form