Power Families of Bivariate Proportional Hazard Models

Abstract

In this paper, we propose a general class of bivariate proportional hazard distributions, which is based on the family of asymmetric proportional hazard distributions and the bivariate Pareto copula. Distributional properties of the bivariate proportional hazard distribution are derived. We specialize the bivariate proportional hazard family of distributions to the normal case, and so we introduce the bivariate proportional hazard normal distribution. Parameter estimation by the maximum likelihood method of the bivariate proportional hazard normal distribution is then discussed. Finally, an application of the new bivariate distribution to real data is considered for illustrative purposes.

Keywords

• asymmetric distribution
• bivariate distribution
• copula
• two-stage estimation