Reliability for some bivariate beta distributions

By Saralees Nadarajah. 2005

76 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/59d00c8e23279941ef07cb33e625f8814bfb10da

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Classical and Bayesian estimation of P(Y < X) for Kumaraswamy's distribution (2014, background): “Constantine and Karson [25] and Nadarajah [26] considered the estimation of P(Y X) when X and Y are assumed as independent and dependent gamma random variables.”
A copula-based approach to account for dependence in stress-strength models (2013, background): “…of strength and stress, e.g. bivariate normal (Gupta and Subramanian, 1998), bivariate Pareto (Hanagal, 1997; Jeevanand, 1997), bivariate exponential (Nadarajah and Kotz, 2005), bivariate beta (Nadarajah, 2005), bivariate gamma (Nadarajah, 2004) and bivariate log-normal (Gupta et al., 2012).”