The Study of Discrete Probabilistic Distributions of Random Sets of Events Using Associative Function
Natalia A. Lukyanova, Daria V. Semenova · Journal of Siberian Federal University Mathematics & Physics · 2014
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.