Considering discrete models, the univariate framework has been studied in depth compared to the multivariate one. This paper first proposes two criteria to define a sensu stricto multivariate discrete distribution. It then introduces the class of splitting distributions that encompasses all usual multivariate discrete distributions (multinomial, negative multinomial, multivariate hypergeometric, multivariate neg- ative hypergeometric, etc . . . ) and contains several new. Many advantages derive from the compound aspect of split- ting distributions. It simplifies the study of their characteris- tics, inferences, interpretations and extensions to regression models. Moreover, splitting models can be estimated only by combining existing methods, as illustrated on three datasets with reproducible studies.

中文翻译：

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多元计数数据的拆分模型

考虑到离散模型，与多变量框架相比，已经深入研究了单变量框架。本文首先提出了两个标准来定义严格的多元离散分布。然后介绍了包含所有常见多元离散分布（多项式、负多项式、多元超几何、多元负超几何等）的分裂分布类别，并包含几个新的。许多优点来自分裂分布的复合方面。它简化了对回归模型的特征、推论、解释和扩展的研究。此外，只能通过结合现有方法来估计拆分模型，如具有可重复研究的三个数据集所示。