  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).
