Nadarajah, Saralees Reliability for some bivariate gamma distributions. (English) Zbl 1094.62132 Math. Probl. Eng. 2005, No. 2, 151-163 (2005). Summary: In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability \(R=\text{Pr} (X<Y)\). The algebraic form for \(R=\text{Pr}(X<Y)\) 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. 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 gamma. The calculations involve the use of special functions. Cited in 18 Documents MSC: 62N05 Reliability and life testing 62H10 Multivariate distribution of statistics PDFBibTeX XMLCite \textit{S. Nadarajah}, Math. Probl. Eng. 2005, No. 2, 151--163 (2005; Zbl 1094.62132) Full Text: DOI EuDML