Testing for lower tail dependence in extreme value models

Abstract

ABSTRACTThis paper proposes some tests for lower tail dependence in extreme value models. Let be a random vector which follows in its lower tail a bivariate extreme value distribution with unit Frechet margins. We show that the conditional distribution function (df) of X+Y, given that X+Y <c, has a limiting df uniform on , i.e. , as if and only if X, Y have a lower tail dependence. We recommend using Fisher's κ, Chi-square goodness-of-fit, Kolmogorov–Smirnov, Cramer–von Mises and Anderson–Darling tests for lower tail dependence. Simulations show that, except the Fisher's κ test, all tests have good performance in terms of the size and power. Finally, by using two real datasets, we illustrate the application of the proposed statistics in testing for lower tail dependence.