Monte Carlo Methods of high-dimensional Numerical Integration

In this paper,a way of producing random numbers with arbitrary distribution are present.These random numbers are verified by uniform and independence tests.And then,the resulting random numbers is used to Monte Carlo averaged-value method of computing high-dimensional numerical integration.We obtain a kind of rectifying averaged-value method of evaluating high-dimensional numerical integration.Moreover,its compounded-form is made.Finally,several numerical examples are given to show validities of these methods.