On dependence of the weighted Marshall-Olkin bivariate exponential model in the presence of the copula function

In this paper‎, ‎we develop a version of the weighted Marshall-Olkin bivariate exponential model by incorporating a new parameter‎. ‎This parameter describes the dependence structure between margins via a copula function‎. ‎We choose the inference for margins method to estimate the model parameters along with the copula parameter‎, ‎as this method offers more advantages than the maximum likelihood estimation method‎. ‎Additionally‎, ‎we conduct a comprehensive simulation study to investigate the behavior of the copula parameter estimator and the remaining parameters‎. ‎Finally‎, ‎an analysis of a real dataset on automobile insurance reveals that the Clayton copula characterizes the dependence structure within the Archimedean copula family