Bivariate Weibull-G Family Based on Copula Function: Properties, Bayesian and non-Bayesian Estimation and Applications

Abstract

This paper aims to obtain a new flexible bivariate generalized family of distributions based on FGM copula, which is called bivariate FGM Weibull-G family. Some of its statistical properties are studied as marginal distributions, product moments, and moment generating functions. Some dependence measures as Kendall’s tau and median regression model are discussed. After introducing the general class, four special sub models of the new family are introduced by taking the baseline distributions as Pareto, inverted Topp-Leone, exponential, and Rayleigh distributions. Maximum likelihood and Bayesian approaches are used to estimate the model unknown parameters. Further, percentile bootstrap confidence interval and bootstrap-t confidence interval are estimated for the model’s parameters. A Monte-Carlo simulation study is carried out of the maximum likelihood and Bayesian estimators. Finally, we illustrate the importance of the proposed bivariate family using two real data sets in medical field.