Bivariate cubic normal distribution for non-Gaussian problems

Abstract

Probabilistic models play critical role in various engineering fields. Numerous critical issues exist in probabilistic modeling, especially for non-Gaussian correlated random variables. However, conventional parameter-based bivariate distribution models are generally developed for specific types of random variables, limiting their flexibility and applicability. A flexible bivariate distribution model is proposed, in which the joint cumulative distribution function is derived with the probability equivalently expressed as the summation of three basic probabilities corresponding to simple functions. These three basic probabilities are calculated with the aid of 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 model accurately models both typical theoretical distributions and the JCDF of practical datasets, offering a significant improvement over existing models. Furthermore, the proposed BCN distribution has been 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.