The Bivariate Inverted Topp–Leone Distribution: Distributional Properties and Statistical Inference

In this article, we propose a new bivariate generalization of the inverted Topp–Leone distribution. First, we express its joint cumulative distribution and survival functions in series forms using special functions, which yields the bivariate hazard rate, reversed hazard rate, and the exact distributions of min{X,Y}. We then establish several essential properties, such as marginal and conditional distributions, joint moments, entropy, and the Fisher information matrix. After proving that the distribution exhibits positive likelihood ratio dependence, we derive the exact distributions for the transformations X+Y, X/(X+Y), and XY when X and Y follow an inverted bivariate Topp–Leone distribution. Finally, we round out the statistical framework by presenting parameter estimation techniques, a simulation study, and Bayesian inference.