The basis for the study was the absence in libraries of statistical functions with open code families of distributions of Pearson and Johnson. Typically, they are needed when building software for modeling and analysis of technical systems. Despite the fact that the distributions of Pearson and Johnson are known for a long time, their practical use is faced with computational difficulties. For the family of Pearson distributions, this is the absence of an expression in terms of known functions of the integral of the IV type of distribution, which makes it difficult to find the normalization coefficient. For the family of Johnson distributions the main drawback is the lack of analytic expressions for the distribution of SB for moments suitable for practical calculations. This makes it difficult to fit the experimental data to this type of distribution. The problem was solved on the basis of the proposed mixed family of Pearson and Johnson distributions, which included the Pearson distributions (except for IV and V types) and the Johnson SU distribution (their substitute). The author obtained the following results: 1. for the approximation of distributions and the calculation of probabilistic characteristics, it is proposed to use a mixed family of Pearson and Johnson distributions; 2. for the Johnson SU distribution, expressions are found for the relationship of the distribution parameters through moments; an efficient algorithm for calculating the distribution parameters; 3. relations are obtained for the probability of exceeding the threshold by a random variable from a mixed family, expressed in terms of known functions.