In this paper, we introduce two families of general bivariate distributions. We refer to these families as general bivariate exponential family and general bivariate inverse exponential family. Many bivariate distributions in the literature are members of the proposed families. Some properties of the proposed families are discussed, as well as a characterization associated with the stress-strength reliability parameter, R , is presented. Concerning R , the maximum likelihood estimators and a simple estimator with an explicit form depending on some marginal distributions are obtained in case of complete sampling. When the stress is censored at the strength, an explicit estimator of R is also obtained. The results obtained can be applied to a variety of bivariate distributions in the literature. A numerical illustration is applied on some well-known distributions. Finally a real data example is presented to fit one of the proposed models.

中文翻译：

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具有应力强度可靠性应用的双变量一般指数模型

在本文中，我们介绍了两个一般二元分布族。我们将这些族称为一般二元指数族和一般二元逆指数族。文献中的许多双变量分布都是提议的家族的成员。讨论了所提议系列的一些特性，并介绍了与应力强度可靠性参数 R 相关的特征。关于 R ，在完全抽样的情况下获得最大似然估计量和具有依赖于某些边际分布的显式形式的简单估计量。在强度处审查应力时，还可以获得 R 的显式估计量。获得的结果可以应用于文献中的各种双变量分布。数值说明应用于一些众所周知的分布。最后，给出了一个真实的数据示例来拟合所提出的模型之一。