By assuming that the underlying distribution belongs to the domain of attraction of an extreme value distribution, one can extrapolate the data to a far tail region so that a rare event can be predicted. However, when the distribution is in the domain of attraction of a Gumbel distribution, the...

Consider n i.i.d. random vectors on R2, with unknown, common distribution function F. Under a sharpening of the extreme value condition on F, we derive a weighted approximation of the corresponding tail copula process. Then we construct a test to check whether the extreme value condition holds...

In certain cases partial sums of i.i.d. random variables with finite variance are better approximated by asequence of stable distributions with indices alpha n - 2 than by a normal distribution. We discusswhen this happens and how much the convergence rate can be improved by using penultimate...

Recently there has been an increasing interest in applying elliptical distributions to risk management. Under weak conditions, Hult and Lindskog (2002) showed that a random vector with an elliptical distribution is in the domain of attraction of a multivariate extreme value distribution. In this...