The functions for working with the basic statistical distributions implemented in the R language are considered. Those include the Cauchy, Weibull, normal, log-normal, logistic, exponential, uniform, gamma distributions, the central and noncentral beta, chi-squared, Fisher's F-distribution, Student's t-distribution, as well as the discrete binomial and negative binomial distributions, geometric, hypergeometric and Poisson distributions. There are functions for calculating theoretical moments of distributions, which allow to evaluate the degree of conformity of the real distribution to the modeled one.