A New Bivariate Distribution With Applications on Dependent Competing Risks Data

Abstract

A new bivariate distribution is proposed in this paper using the univariate modified Weibull extension distribution. The proposed distribution is referred to as the bivariate Modified Weibull Extension (BMWE) distribution. The BMWE distribution is of Marshall-Olkin type. We discuss some of the statistical properties of the BMWE  distribution.  Applications of this distribution to dependent competing risks data are discussed.  The maximum likelihood estimators (MLE) of the model parameters using both bivariate data and dependent competing risks data are discussed. These MLE's cannot be obtained in closed form. Therefore, numerical optimization methods are  applied. A simulation study is carried out to investigate the performance of the estimation technique. Two real data sets;  one bivariate data set and another dependent competing risks data set, are analyzed using the proposed distribution for illustrative and comparison purposes.