(untitled) (REC 2026 - 11th International Workshop on Reliable Engineering Computing: Reliability Computations in a Data and Model-Driven World, 2026)
Modeling non-Gaussian dependent random variables remains challenging in structural reliability analysis. This study proposes a bivariate squared normal (BSN) distribution based on the squared normal transformation (SNT). The joint cumulative distribution function (JCDF) is constructed by decomposing the probability into marginal distributions and a dependence function, both modeled using SNT. A power transformation with an optimized parameter is introduced to align the kurtosis of the transformed variable with that of a squared normal reference distribution, improving accuracy for strongly non-Gaussian cases. The joint probability density function (JPDF) is obtained by applying a central difference scheme to the JCDF. Validation against typical bivariate distributions, including classical and copula-based models, shows that the BSN distribution achieves high JCDF accuracy and acceptable JPDF accuracy, demonstrating strong flexibility and robustness across diverse dependence structures.