Study the modeling of bivariate Weibull Rayleigh distribution with Gaussian copula

Abstract

Dealing with lifetime distributions is interested in various scientific fields such as medical studies and social science. The aim of this paper to introduce Bivariate Weibull G distribution based on Rayleigh distribution. We use copula function to emerge the selected distributions. The proposed distribution could capture different shape behavior. We illustrate the joint distribution, the cumulative distribution and hazard functions of the proposed model. We construct the estimation equations via parametric estimation methods and discuss the goodness of fit test for copula function. Finally, the performance of bivariate Weibull Rayleigh distribution is discussed via simulation case study.