The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously large. Various alternative dependence measures and representations have been proposed, with the most well-known being hidden regular variation and the conditional extreme value model. These varying depictions of extremal dependence arise through consideration of different parts of the multivariate domain, and particularly exploring what happens when extremes of one variable may grow at different rates to other variables. Thus far, these alternative representations have come from distinct sources and links between them are limited. In this work we elucidate many of the relevant connections through a geometrical approach. In particular, the shape of the limit set of scaled sample clouds in light-tailed margins is shown to provide a description of several different extremal dependence representations.

翻译：多变性极端的研究主要以多变性经常变数为主,尽管众所周知,这种办法并未充分区分其组成部分并不总是同时大的随机矢量。提出了各种替代依赖措施和表述,最著名的是隐蔽的经常变数和有条件的极端值模型。这些对极端依赖性的不同描述是通过考虑多变域的不同部分而产生的,特别是探索当一个变数的极端可能以不同速度与其他变数增长时会发生什么情况。迄今为止,这些变数来自不同的来源,它们之间的联系有限。在这项工作中,我们通过几何方法阐明了许多相关联系。特别是,在光序边际中,对按比例标定的样云的形状显示了几个不同的极端依赖性表示。