Article collection "Mathematical Problems of Cybernetics" №12, Moscow, 2003

Authors:Kolpakov R.M.

On discrete transformations of finite distributions with rational pronabilities

Abstract:

The paper concerns discrete transformations of finite-valued random variables, i.e. random variables which
have a finite number of values, with rational probabilities of values. By a discrete transformation of
finite-valued random variables we mean a random variable with finite number of values which are the values
of an arbitrary finite-valued function whose variables values are the values of the independent initial
random variables. The closure of a set of finite rational probabilistic distributions, i.e. distributions
consisting of a finite number of rational probabilities, is the set of finite rational probabilistic
distributions for all random variables obtained by discrete transformations of finite-valued random variables
whose probabilistic distributions belong to the initial set of probabilistic distributions. In the paper
the closures of all finite sets of finite rational probabilistic distributions are described. Moreover,
an effective procedure of checking if a given finite rational probabilistic distribution can be obtained
by discrete transformations from a given finite set of finite rational probabilistic distributions is
proposed.

Keywords:

finite-valued random variables, discrete transformation, closed class