Flexible Three-Parameter Distribution for Matching Arbitrary First Three Moments and Its Application to Structural Reliability Analysis

Determining the probability distribution of random variables plays a key role in structural reliability analysis. Existing three-parameter distributions based on third-moment normal transformations are widely used due to their simplicity and flexibility. However, their applicability is limited to specific combinations of the first three moments of random variables, which limits their practical use in engineering. To address this limitation, this study proposes a novel three-parameter distribution derived from a modified exponential third-moment normal transformation, which is capable of fitting arbitrary first three moments. The parameters of the proposed distribution are explicitly defined by these moments. Unlike the existing three-parameter distributions, it naturally reduces to the standard normal distribution when the skewness is zero. Moreover, it remains valid over the entire support region of random variables under varying skewness conditions. The flexibility and robustness of the proposed distribution are demonstrated through accurate approximations of several well-known theoretical distributions and real-world datasets. In addition, four numerical examples further demonstrate its applicability and high accuracy in structural reliability analysis.