Abstract
Lifetime distributions have various scientific applications which expose bivariate measurements in their data. The Weibull distribution has been used effectively in reliability, engineering, biomedical, social sciences, and other applications. The aim of this paper is to introduce new bivariate Weibull models concerning G cumulative distributions with two parameters. This construction is made with the Gaussian copula. The new models impose good flexibility for modeling different dataset structures. We propose a new class of baseline distributions in detail, namely the bivariate Weibull-Weibull, the bivariate Weibull-F, the bivariate Weibull-Gompertz, and the bivariate Weibull-Chen distributions. The structural properties of the new models are illustrated. The estimations for model parameters are obtained using parametric estimations, maximum likelihood estimation and modified maximum likelihood methods. Moreover, we use the moment methods as semi-parametric methods for parameter estimation. Finally, simulations are used to discuss whether the performance of the proposed distribution is satisfactory.