Сибирский федеральный университет

Тип публикации: статья из журнала

Год издания: 2014

Ключевые слова: Associative function, Discrete probabilistic distributions, Random set of events, |X|-ary covariance

Аннотация: In this work the class of discrete probabilistic distributions of the II-nd type of random sets of event is investigated. As the tool for constructing of such probabilistic distributions it is offered to use associative functions. There is stated a new approach to define a discrete probabilistic distribution of the II-nd type of a random set on a finite set of N events on the basis of obtained recurrence relation and a given associative function. Advantage of the offered approach is that for definition of probabilistic distribution instead of a totality of 2N probabilities it is enough to know N probabilities of events and a type of associative function. In this paper an |X|-ary covariance of a random set of events is considered. It is a measure of the additive deviation of the events from the independent situation. The process of recurrent constructing a probabilistic distribution II-nd type is demonstrated by the example of three associative functions. The proof of the legitimacy/illegitimacy the obtained distribution by passing to the probabilistic distribution of the I-st type by formulas of Mobius is given. Theorems that establish the form and conditions of the legitimacy of the resulting probabilistic distributions are proved. |X|-ary covariances of random sets of events are found. © Siberian Federal University. All rights reserved.

Журнал: Journal of Siberian Federal University - Mathematics and Physics

Выпуск журнала: Vol. 7, Is. 4

Номера страниц: 500-514

• Lukyanova N.A. (Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, Russian Federation)
• Semenova D.V. (Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, Russian Federation)

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