Tail similarity

Abstract

Simple tail similarity measures are investigated in this paper so that the overarching tail similarity between two distributions is captured. We develop some theoretical results to support our novel measures, where the focus is on asymptotic approximations of our similarity measures for Fréchet-type tails. A simulation study is provided to validate the effectiveness of our proposed measures and demonstrate their great potential in capturing the intricate tail similarity. We conclude that our measure and the standard comparisons between the (first-order) extreme index estimates provide complementary information, and one should analyze them in tandem rather than in isolation. We also provide a simple rule of thumb, summarized as a sequential decision rule, for using the two sources of information to assess tail similarity.