Bivariate odd Weibull-G family of distributions: properties, Bayesian and non-Bayesian estimation with bootstrap confidence intervals and application

Abstract

ABSTRACT The aim of our paper is to introduce a new flexible bivariate generalized family of distributions based on Marshall and Olkin shock model, in the so-called the bivariate odd Weibull-G family. The proposed family is constructed from three independent odd Weibull-G families using a minimization process. Creating a bivariate distribution using shock model technique is nothing new, but here, we used only this technique to propose a flexible bivariate family, which has not been considered in the statistical literature yet. Some of its statistical properties are studied. After introducing the general class, one special model of the new family is discussed in detail. Maximum likelihood and Bayesian approaches are used to estimate the model parameters. Further, percentile bootstrap confidence interval and bootstrap-t confidence interval are estimated for the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of the maximum likelihood and Bayesian estimators. Finally, we illustrate the importance of the proposed bivariate family by means of real data set.