Evaluating correlation coefficient for Nataf transformation

• Two methods are presented to handle the correlation for Nataf transformation.
• A Monte Carlo simulation for validation is put forward.
• An interpolation method is presented to evaluate the correlation coefficient.

In this paper, a novel approach is proposed to calculate the equivalent correlation coefficient ρz in the standard normal space for two correlated random variables with desired correlation coefficient ρx. According to Weierstrass approximation theorem, ρx is expressed as a polynomial function of ρz. For a given ρx, the associated ρz is evaluated by solving the polynomial equation. Especially, when one random variable is normal, ρx is proved to be a linear function of ρz. In order to check the proposed method, a Monte Carlo simulation method is put forward. Finally, three numerical examples are worked to demonstrate the proposed method.