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A Bayesian Inference Approach for Bivariate Weibull Distributions Derived from Roy and Morgenstern Methods

Bivariate lifetime distributions are of great importance in studies related to interdependent components, especially in engineering applications. In this paper, we introduce two bivariate lifetime assuming three- parameter Weibull marginal distributions. Some characteristics of the proposed distributions as the joint survival function, hazard rate function, cross factorial moment and stress-strength parameter are also derived. The inferences for the parameters or even functions of the parameters of the models are obtained under a Bayesian approach. An extensive numerical application using simulated data is carried out to evaluate the accuracy of the obtained estimators to illustrate the usefulness of the proposed methodology. To illustrate the usefulness of the proposed model, we also include an example with real data from which it is possible to see that the proposed model leads to good fits to the data.