The copulas of random vectors with standard uniform univariate margins truncated from the right are considered and a general formula for such right-truncated conditional copulas is derived. This formula is analytical for copulas that can be inverted analytically as functions of each single argument. This is the case for Archimedean and related copulas. The resulting right-truncated Archimedean copulas are not only analytically tractable but can also be characterized as tilted Archimedean copulas, one of the main contributions of this work. This characterization now allows one to not only immediately obtain a limiting Clayton copula for a general vector of truncation points converging to zero (an extension of a result known in the special case of equal truncation points), but to work with an exact model instead of an approximate limiting model in the first place. As tilted Archimedean copulas have been studied in the literature, the characterization allows one to obtain various analytical and stochastic properties of right-truncated Archimedean copulas. Further contributions include the characterization of right-truncated Archimax copulas with logistic stable tail dependence functions as tilted outer power Archimedean copulas, and an analytical form of right-truncated nested Archimedean copulas.

考虑从右边被截断的具有标准均匀单变量边距的随机向量的copulas，并推导此类右截断的条件copulas的一般公式。此公式是对copula的解析，可以将其作为每个单个参数的函数进行解析地反转。阿基米德和相关系的情况就是这样。由此产生的右截短的阿基米德系脉不仅在分析上易于处理，而且还可以表征为倾斜的阿基米德系脉，这是这项工作的主要贡献之一。现在，这种表征不仅可以让人们立即获得收敛于零的一般截断点矢量的极限Clayton copula（在相等截断点的特殊情况下，已知结果的扩展），但首先要使用精确模型而不是近似限制模型。在文献中已经研究了倾斜的阿基米德系copulas时，这种表征使人们可以获得右截短的阿基米德系copulas的各种分析和随机性质。进一步的贡献包括具有逻辑稳定尾部依赖功能的右截断的Archimax copula的表征，如倾斜的外力Archimedean copulas，以及右截短的嵌套Archimedean copula的分析形式。