A General Method of Construction of a Bivariate Lifetime Distribution with a Singular Component

Bivariate Lifetime Distribution

Abstract

Marshall-Olkin bivariate exponential distribution is the most popular bivariate distribution with a singular component. Since then several other bivariate distributions with a singular component have been introduced in the literature. It is observed that there are mainly two main approaches to construct a bivariate distribution with a singular component. In this paper we have proposed a general method to construct a bivariate distribution with a singular component. All the existing bivariate distributions with a singular component can be obtained using this method. Moreover, more flexible bivariate distributions with a singular component also can be constructed using this method. It is a very simple procedure based on mixing. Using this approach, we have considered one special case, namely bivariate Weibull distribution, in detail. We have derived several properties of the proposed bivariate Weibull distribution and it seems to be more flexible than the popular Marshall-Olkin bivariate Weibull distribution. Maximum likelihood estimators can be obtained quite conveniently in this case. It can be used to model dependent competing risks data and it can be generalized to the multivariate set up also.