Reliability for some bivariate beta distributions
Saralees Nadarajah
Source abstract
In the area of stress‐strength models there has been a large amount of work as regards 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, we consider forms of R when ( X , Y ) follows a bivariate distribution with dependence between X and Y . In particular, we derive explicit expressions for R when the joint distribution is bivariate beta. The calculations involve the use of special functions.
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