Abstract
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.
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Safety, Risk, Reliability and Quality,Statistics and Probability
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