A New Bivariate Exponentiated Family of Distributions: Properties and Applications

The bivariate distributions are useful for the joint modeling of two random variables. In this paper, we have presented a bivariate version of the exponentiated family of distributions. Some desirable properties of the proposed bivariate family of distributions have been explored. These include the conditional distributions, the joint and conditional moments, dependence measures, reliability analysis, and maximum likelihood estimation of the parameters. A specific member of the proposed family has been explored for the power function baseline distribution giving rise to the bivariate exponentiated power function distribution. Some properties of the derived bivariate exponentiated power function distribution have been explored. The derived bivariate exponentiated power function distribution is fitted on some real data sets to see its suitability. It is found that the derived bivariate exponentiated power function distribution performs better than the competing distributions for modeling of the used data.