Bivariate Omega Distribution and its Dependence Properties for Modeling Time of Vision Loss in Diabetic Retinopathy Study

A three-parameter Omega probability distribution has been used recently to analyze the failure time data. In a practical situation, the Omega probability distribution was applied very effectively in modeling bathtub-shaped hazard curves. In this paper, the bivariate Omega (BOM) distribution whose marginal are Omega distributions is introduced. This new bivariate model is a Marshall-Olkin type and has natural interpretations for illustrated the shock and competing risks models. Some probabilistic properties of the bivariate Omega distribution are derived and studied. The dependence properties for bivariate Omega distribution are proposed using the Marshall-Olkin copula. Parameters estimators are investigated using the maximum likelihood method. Two data sets are illustrated to show the usefulness of the new model for fitting such data.