- Issue
- Journal of Siberian Federal University. Mathematics & Physics. 2014 7 (4)
- Authors
- Lukyanova, Natalia A.; Semenova, Daria V.
- Contact information
- Lukyanova, Natalia A.:Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia;; Semenova, Daria V.:Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia;
- Keywords
- random set of events; discrete probabilistic distributions; associative function; |X|-ary covariance
- Abstract
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 M¨obius 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
- Pages
- 500–514
- Paper at repository of SibFU
- https://elib.sfu-kras.ru/handle/2311/16497
Journal of Siberian Federal University. Mathematics & Physics / The Study of Discrete Probabilistic Distributions of Random Sets of Events Using Associative Function
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