Normal Transformation for Correlated Random Variables based on L-moments and its Application in Reliability Engineering

Abstract In this paper, a new method for normal transformation is proposed to transform correlated non-normal random variables into independent standard normal ones based on their first four linear moments (L-moments), standard deviations and correlation matrix. The complete monotonic expressions of the equivalent correlation coefficient are proposed and the applicable range of the original correlation coefficient to ensure the transformation's executability is identified. Numerical studies demonstrate that the admissible range of the normal transformation for correlated random variables based on L-moments is larger in scope than that based on ordinary central moments (C-moments), and the proposed method is effective for normal transformations and sufficiently accurate for reliability engineering practices.