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This paper develops a polynomial normal transformation model, whereby variousnon-normal probability distributions can be simulated by the standard normaldistribution. Two methods are presented to determine the coefficients ofpolynomial model: (1) probability weighted moment (PWM) matching (2) percentilematching. Compared to the existing raw moment or L-moment matching, theproposed methods are more computationally convenient, and can be used toestimate the coefficients of polynomial model with a higher degree.Furthermore, for two correlated random variables, a polynomial equation isderived to estimate the equivalent correlation coefficient in standard normalspace, and random vector with non-normal marginal distributions and prescribedcorrelation matrix can be generated. Finally, numerical examples are worked todemonstrate the proposed method.

Generating correlated random vector by polynomial normal transformation