Modeling of truncated probability distributions

A method for modeling truncated probability distributions based on the transformation of some basic distribution is developed. One of the parameters of the simulated distributions is a quantile of arbitrary order. The cases of the initial multiplication of the basic density function by linear and quadratic factors are considered. In the case of the basic normal law with linear multipliers, expressions for the density and the first moments are generally presented. Using different base distributions and varying parameters leads to a wide class of new distributions. The results of the work can be useful in the processing of statistics with a non-standard structure.