A method of constructing consistent and effective algorithms for robust parametric generators of random variables intended for solving problems of statistical simulation and constructing bootstrap procedures is considered. The consistency and efficiency of the standard and robust generators are analyzed in the presence of asymmetric and symmetric outliers. It is shown on real examples that the standard parametric generators of random variables are inconsistent for heterogeneous samples, and their use can significantly and unpredictably distort simulation results and decision-making procedures. It is demonstrated that in the presence of outliers, the efficiency of the robust generators can considerably exceed that of the standard parametric random variable generators, especially in the presence of asymmetric outliers