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