On Weibull–Burr impounded bivariate distribution

Abstract

In this work, we utilise a recently developed method of constructing a bivariate distributional model to generate a new bivariate distribution with Weibull and Burr type XII distributions as its marginals. Some general characteristics of this newly generated distribution together with some characterization results are further derived. The maximum likelihood method of estimation is applied for the estimation of the parameters of the constructed distribution. The closeness of the maximum likelihood estimators with the true values of the parameters have been illustrated through a simulation study. We have identified the generated model as a suitable model for a real life bivariate data set reported in the literature. We have also used another bivariate data set on geoelectrical variables X and Y in which X represents the aquifer thickness and Y represents the coefficient of anisotropy to illustrate the results described in this paper for bivariate distributional modelling.