Journal of Data Science

Abstract: This paper aims to generate multivariate random vector with prescribed correlation matrix by Johnson system. The probability weighted moment (PWM) is employed to assess the parameters of Johnson system. By equat ing the first four PWMs of Johnson system with those of the target distri bution, a system of equations solved for the parameters is established. With suitable initial values, solutions to the equations are obtained by the New ton iteration procedure. To allow for the generation of random vector with prescribed correlation matrix, approaches to accommodate the dependency are put forward. For the four transformation models of Johnson system, nine cases are addressed. Analytical formulae are derived to determine the equivalent correlation coefficient in the standard normal space for six cases, the rest three ones are handled by an interpolation method. Finally, several numerical examples are given out to check the proposed method.