Mathematics Colloquium: Tail Dependence of Multivariate Distributions
4:00 p.m., Neill Hall 5W
Abstract: The tail dependence of a multivariate distribution describes the limiting proportion of exceedence of some margins over a certain threshold given that the other margins have already exceeded that threshold, and can be used in the analysis of dependence among extremal events. The multivariate tail dependence is frequently studied via the method of copulas. In this talk, we discuss an alternative method to derive tractable formulas of tail dependence for the distributions whose copulas are not explicitly available. Our method depends only on the tail analysis and does not involve the method depends only on the tail analysis and does not involve the marginal transforms on the entire distributions. Combining with closure properties of total positivity, our method also enables us to establish the monotonicity of tail dependence with respect to heavy tail index. The bivariate elliptical distribution and bivariate Pareto distribution are discussed throughout to illustrate the results.