Linking representations for multivariate extremes via a limit set

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