Reliability for some bivariate exponential distributions

By Saralees Nadarajah, Samuel Kotz. 2006

73 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, 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 isbivariate exponential. The calculations involve the use of special functions. An application of the results is also provided.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7c8421e64d7710086768f1d225f2490dfef073a2

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In Statistics and Probability

1. Filippo Domma
2. Sabrina Giordano

Citations in the corpus

• 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).”