ABSTRACT
This chapter has theorems and more advanced examples on dependence properties and tail behavior of copula families, such as multivariate Gaussian, Archimedean, elliptical, extreme value, mixture of max-id, vine, and factor. Also there are general results on copulas and dependence properties: absolutely and singular components of continuous distributions, tail heaviness, regular variation, dependence orderings, relations of dependence concepts, tail dependence and tail order functions, and Laplace transforms. This chapter is intended as a reference for results to determine dependence and tail properties of multivariate distributions which are constructed from a combination of methods in Chapter 3. For a theorem, a proof is given if (i) the proof is simpler than the original proof, (b) if the theorem is a variation of previously published results, or (c) the proof is short and provides some insight such as illustrating a useful technique.
