A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal distribution function. This paper is concerned with two topics. First, the paper presents a number of extensions of the skew-normal copula. Notably these include a case in which the standardized marginal distributions are Student’s t, with different degrees of freedom allowed for each margin. In this case the skewing function need not be the distribution function for Student’s t, but can depend on certain of the special functions. Secondly, several multivariate versions of the skew-normal copula model are presented. The paper contains several illustrative examples.

中文翻译：

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偏态正态分布和偏态学生分布的Copulaesque版本

最近的论文提出了偏态正态分布的扩展，即正态分布。在此模型下，标准边际分布是标准正态分布。copula本身依赖于基于正态分布函数的熟悉的偏斜构造。本文涉及两个主题。首先，本文介绍了偏态法线对数的一些扩展。值得注意的是，这些情况包括标准化边际分布为学生t的情况，每个边际允许不同的自由度。在这种情况下，偏斜函数不必是学生t的分布函数，而可以取决于某些特殊函数。其次，提出了偏态正态copula模型的多个多元版本。本文包含几个说明性示例。