Multivariate count data arise naturally in practice. In analysing such data, it is critical to define a model that can accurately capture the underlying dependence structure between the counts. To this end, this paper develops a multivariate model wherein correlated Poisson margins are generated by a comonotonic shock vector. The proposed model allows for greater flexibility in the dependence structure than that of the classical construction, which relies on the convolution of vectors of common Poisson shock variables. Several probabilistic properties of the multivariate comonotonic shock Poisson model are established, and various estimation strategies are discussed in detail. The model is further studied through simulations, and its utility is highlighted using a real data application.

中文翻译：

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基于共调冲击的多元泊松模型

多变量计数数据在实践中自然产生。在分析此类数据时，定义一个模型以准确捕获计数之间的底层依赖结构至关重要。为此，本文开发了一个多元模型，其中相关的泊松边际由共调冲击向量生成。与经典构造相比，所提出的模型在依赖结构方面具有更大的灵活性，后者依赖于公共泊松冲击变量向量的卷积。建立了多元共调冲击泊松模型的几个概率特性，并详细讨论了各种估计策略。通过模拟进一步研究该模型，并使用实际数据应用程序突出显示其效用。