City Research Online

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 Fr´echet-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 analyse them in tandem rather than in isolation. We also provide some very simple guiding principles of good practice when using the two sources of information; these are recommended to be complemented further by domain knowledge to validate and clarify the conclusions of our guiding principles, especially in situations when there is no clear-cut conclusion as it is often the case in real-life applications.

Publication Type:	Other (Preprint)
Additional Information:	Copyright, the authors, 2024.
Subjects:	H Social Sciences > HF Commerce Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments:	Bayes Business School Bayes Business School > Actuarial Science & Insurance
SWORD Depositor:	Symplectic Administrator

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