Formal description of interaction between elements of a complex system

Buslenko, N. P.; Averkin, Alexey

doi:10.1007/bf01068516

Cited by 3 publications

(3 citation statements)

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“…, ), where all components { } are different. A distribution of their sum = 1 + • • • + has the following density and cumulative distribution function for ≥ 0, see [2]:…”

Section: Convolution Of the Exponential Densitiesmentioning

confidence: 99%

On a Parametric Estimation for a Convolution of Exponential Densities

Andronov,

Spiridovska,

Santalova

2023

Contributions to Statistics

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Broad application of the continuous time Markov chain is caused by memoryless property of exponential distribution. An employment of non-exponential distributions leads to remarkable analytical difficulties. The usage of arbitrary nonnegative density approximation by a convolution of exponential densities is a way of considerable interest. Two aspects of the problem solution are considered. Firstly, the parametrical estimation of the convolution on the basis of given statistical data. Secondly, an approximation of fixed non-negative density. An approximation and estimation are performed by the method of the moments, maximum likelihood method, and fitting of a density. An empirical analysis of different approaches has been performed with the use of simulation. The efficiency of the considered approach is illustrated by the task of the queuing theory.

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“…, ), where all components { } are different. A distribution of their sum = 1 + • • • + has the following density and cumulative distribution function for ≥ 0, see [2]:…”

Section: Convolution Of the Exponential Densitiesmentioning

confidence: 99%

On a Parametric Estimation for a Convolution of Exponential Densities

Andronov,

Spiridovska,

Santalova

2023

Contributions to Statistics

View full text Add to dashboard Cite

show abstract

“…The authors of [31] write: «It seems that the concept of complexity for a control theory is as fundamental as the concept of «force» in mechanics or «measure» in mathematics». However, only the author of [32] presented a method and a criterion for estimating the complexity of a structure, which makes it possible to obtain a quantitative estimate of this parameter:…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…In system studies [7][8][9], the concept of «complex system» is used when it becomes impossible or difficult enough to accurately describe and predict the behavior of the system. One of the first definitions of a complex system was given in [10,11], where it was noted that the important properties of complex systems are the possibility of dividing the system into subsystems, as well as the existence of a hierarchical structure. In the practice of research, the allocation of subsystems is carried out in such a way that the goals of the operation of subsystems ensure the possibility of realizing the goals of the functioning of the system as a whole.…”

Section: Introductionmentioning

confidence: 99%