Bivariate cubic normal distribution for non-Gaussian problems

Probabilistic models play critical role in various engineering fields. Numerous critical issues exist in probabilistic modeling, especially for non-Gaussian correlated random variables. Traditional parameter-based bivariate distribution models are typically developed for specific types of random variables, which limits their flexibility and applicability. In this study, a flexible bivariate distribution model is proposed, in which the joint cumulative distribution function (JCDF) is derived by expressing the probability as the summation of three basic probabilities corresponding to simple functions. These probabilities are computed using a univariate cubic normal distribution, and thus the proposed model is named as bivariate cubic normal (BCN) distribution. The proposed BCN distribution has been applied in modeling several common bivariate distributions and actual engineering datasets. Results show that the BCN distribution accurately fits the JCDFs of both theoretical distributions and practical datasets, offering significant improvement over existing models. Furthermore, the proposed BCN distribution is utilized in seismic reliability assessment and the calculation of the mean recurrence interval and hazard curve of hurricane wind speed and storm size. Results demonstrate that the BCN distribution excels in modeling and matching capabilities, proving its accuracy and effectiveness in civil engineering applications.