Probability Chains with Polynomial Growth as a Model of Resource Distribution

The article is devoted to the method of discrete probability chains for constructing the forecast of changes in socio-economic data. Initial data about the distribution of the resource among several participants are presented in the form of the probabilistic vector, and its changing over time is described by a discrete dynamical system which is specified by a certain function. Chains with linear and logarithmic-linear growth have been well studied. In this paper, we consider the probabilistic chains in which the right-hand side is given by polynomials of a certain type. The results of the construction are applied to the research of the dynamics of the distribution of the national income of Canada, Great Britain, and the United States. The accuracy of the results obtained is estimated by using the correlation coefficient, and the dynamics of the process modeled is estimated by using Shannon’s entropy.