On the Ristic—Balakrishnan distribution: Bivariate extension and characterizations
Over the last few decades, a significant development has been made toward 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 and Balakrishnan developed a special class of univariate distributions. We call this family of distribution the RB-G family of distributions. The RB-G family has the same parameters of the baseline distribution plus an additional positive shape parameter a. Several RB-G distributions 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 toward cases with various shapes. In this article we focus our attention on the characterizations of this family and discuss some structural properties of the bivariate RB-G family of distributions that are not discussed in detail by Ristic and Balakrishnan.
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- Glänzel, W. 1987. A characterization theorem based on truncated moments and its application to some distribution families. In Mathematical statistics and probability theory 1986, ed. B. Tatzmannsdorf, Vol. B, 75–84. Dordrecht, The Netherlands: Reidel.Google Scholar
- Kotz, S., N. Balakrishnan, and N. L. Johnson. 2000. Continuous multivariate distributions, volume 1, Models and applications, 2nd ed. New York, NY: John Wiley. Ramos, H. M., J. Ollero, and M. A. Sordo. 2000. A sufficient condition for generalized Lorenz order. Journal of Economic Theory 90:286–92.MathSciNetCrossRefGoogle Scholar