Bivariate Epanechnikov-Weibull distribution based on Sarmanov copula: properties, simulation, and uncertainty measures with applications

The modeling of bivariate data in statistics often requires constructing families of bivariate distributions with predefined marginals. In this study, we introduced a novel bivariate distribution, denoted as EP-WD-SAR, which combines the Sarmanov (SAR) copula with the Epanechnikov-Weibull marginal distribution (EP-WD). We analyzed its statistical properties, including product moments, correlation coefficient, moment-generating function, conditional distribution, and concomitants of order statistics. Additionally, we evaluated key reliability and information measures such as the hazard function, reversed hazard function, bivariate extropy, bivariate weighted extropy, and bivariate cumulative residual extropy. Parameter estimation was performed using maximum likelihood, asymptotic confidence intervals, and Bayesian methods. Finally, we demonstrated the advantages of the EP-WD-SAR model over existing alternatives, including the bivariate Weibull-SAR, bivariate Epanechnikov-exponential-SAR, bivariate exponential-SAR, and bivariate Chen-SAR distributions through applications to real data sets.