On the Ristic-Balakrishnan distribution: bivariate extension and characterizations

Over the last few decades, a significant development has been made towards the augmentation of some well-known lifetime distributions by various strategies. These newly developed models have enjoyed a considerable amount of success in modeling various real life phenomena. Motivated by this, Ristic & Balakrishnan (2012) developed a special class of univariate distributions (see Ristic- Balakrishnan (2012)). Henceforth we call this family of distribution as RB-G family of distributions. The RB-G family has the same parameters of the G distribution plus an additional positive shape parameter a. Several RB-G distribution can be obtained from a specified G distribution. For a = 1, the baseline G distribution is a basic exemplar of the RB-G family with a continuous crossover towards cases with various shapes. In this article we focus our attention on the characterization of this family and discuss some structural properties of the bivariate RB-G family of distributions which are not discussed in detail in Ristic and Balakrishnan (2012).