**Abstract**

In this paper, we investigate algorithms stability for calculation of multidimensional integrals using the statistical modeling methods. We considered issues of the algorithms optimization and we give sufficient conditions for the stability. We apply our approach to both calculation of integral from the regression function and the moments integral calculation. In all our numerical experiences, we used the mt19937 pseudorandom number generator.

**Keywords:** statistical modeling, pseudorandom numbers, optimal density, integral estimation, Monte Carlo methods
