On the Reliability for Some Bivariate Dependent Beta and Kumaraswamy Distributions: A Brief Survey

Abstract In the area of stress-strength models, there has been a large amount of work regarding the estimation of the reliability {R=\Pr(X<Y)} . The algebraic form for {R=\Pr(X<Y)} has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, forms of R are considered when {(X,Y)} follow bivariate distributions with dependence between X and Y . In particular, explicit expressions for R are derived when the joint distribution are dependent bivariate beta and bivariate Kumaraswamy. The calculations involve the use of special functions.