Modeling of random numbers by an arbitrary distribution law

The groups of methods for modeling random numbers according to arbitrary distribution laws are considered, their disadvantages are given, the composition methods are highlighted as the most universal. The order of obtaining random numbers according to the original empirical law by replacing it with a weighted sum of normal distribution laws is developed. It is shown that at the initial stage the initial law is described by isosceles triangles graphically with their subsequent replacement by normal laws with specified parameters. An example of modeling a specific initial empirical distribution is given. On the basis of the developed block diagram of random numbers modeling and the corresponding program, the calculated histograms approximating the initial distribution are obtained. It is shown that with an increase in the number of triangles, a better description of the initial distribution is achieved with increasing accuracy.