The well-known Marshall–Olkin model is known for its extension of exponential distribution preserving lack of memory property. Based on shock models, a new generalization of the bivariate Marshall–Olkin exponential distribution is given. The proposed model allows wider range tail dependence which is appealing in modeling risky events. Moreover, a stochastic comparison according to this shock model and also some properties, such as association measures, tail dependence and Kendall distribution, are presented. The new shock model is analytically quite tractable, and it can be used quite effectively, to analyze discrete–continuous data. This has been shown on real data. Finally, we propose the multivariate extension of the Marshall–Olkin model that has some intersection with the well-known multivariate Archimax copulas.

中文翻译：

---

双变量马歇尔-奥尔金指数冲击模型

著名的 Marshall-Olkin 模型以其保留缺乏记忆特性的指数分布扩展而闻名。基于冲击模型，给出了双变量 Marshall-Olkin 指数分布的新推广。所提出的模型允许更广泛的尾部依赖，这在建模风险事件时很有吸引力。此外，还提出了根据该冲击模型的随机比较以及一些属性，例如关联度量、尾部依赖性和 Kendall 分布。新的冲击模型在分析上非常易于处理，并且可以非常有效地用于分析离散-连续数据。这已在实际数据中显示出来。最后，我们提出了 Marshall-Olkin 模型的多元扩展，它与著名的多元 Archimax copulas 有一些交集。