Abstract
Copula method plays an essential rule to study the dependence between data variables especially in bivariate distribution. It is noted that some bivariate models are constructed with uncomplete information of distributions. Copula improves the reliability of applications such as flood peak. Weibull distribution is a popular used in engineering, theory, medical and survival analysis. Despite its spread, it is known that the Weibull distribution could not implement the data set with non-monotone failure rate. In such case, many papers have suggested a modification and generalization of Weibull model. One of generalization is made through the baseline distribution by adding more shape parameters. The main purpose of our paper is to present some new bivariate Weibull models with respect to G cumulative distributions of baseline distribution. This approach converges the power series of probability distribution. We use the copula function to construct the bivariate Weibull distribution. The proposed models provide high flexibility and can be used effectively for modeling dataset with a different structure. We provide special cases in details namely; bivariate Weibull-exponential, bivariate Weibull-Rayleigh and bivariate Weibull Chi-square. We use Gaussian copula function to merge the dependent distributions, this copula is popular used in various applications like econometrics and finance. We discuss some structural properties of the proposed models. In order to estimate the model parameters, we discuss parametric methods via maximum likelihood estimation and modified maximum likelihood methods. In addition, we use the moment methods as semi-parametric methods for parameters estimations. Finally, Simulations are studied to illustrate methods of inference discussed and study the performance of new distributions. (C) 2018 The Authors. Published by IASE.