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 J. Sib. Fed. Univ. Math. Phys., 2014, Volume 7, Issue 4, Pages 500–514 (Mi jsfu395)

The study of discrete probabilistic distributions of random sets of events using associative function

Natalia A. Lukyanova, Daria V. Semenova

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

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 $2^N$ 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 Möbius 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.

Keywords: random set of events, discrete probabilistic distributions, associative function, $|X|$-ary covariance.

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UDC: 519.213
Accepted: 04.09.2014
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Citation: Natalia A. Lukyanova, Daria V. Semenova, “The study of discrete probabilistic distributions of random sets of events using associative function”, J. Sib. Fed. Univ. Math. Phys., 7:4 (2014), 500–514

Citation in format AMSBIB
\Bibitem{LukSem14} \by Natalia~A.~Lukyanova, Daria~V.~Semenova \paper The study of discrete probabilistic distributions of random sets of events using associative function \jour J. Sib. Fed. Univ. Math. Phys. \yr 2014 \vol 7 \issue 4 \pages 500--514 \mathnet{http://mi.mathnet.ru/jsfu395} 

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This publication is cited in the following articles:
1. N. A. Lukyanova, D. V. Semenova, “Assotsiativnye funktsii Franka v postroenii semeistv diskretnykh veroyatnostnykh raspredelenii sluchainykh mnozhestv sobytii”, PDM, 2016, no. 2(32), 5–19
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