Abstract: Let X be a Kotz Type III elliptical random vector in IR, k ≥ 2, and let tn, n ≥ 1 be positive constants such that limn→∞ tn = ∞. In this article we obtain an asymptotic expansion of the tail probability P {X > tna},a ∈ IR. As an application we derive an approximation for the conditional excess distribution. Furthermore, we discuss the asymptotic dependence of Kotz Type III triangular ...

The authors examine the asymptotic behaviour of conditional threshold exceedance probabilities for an elliptically distributed pair (X,Y ) of random variables. More precisely, they investigate the limiting behaviour of the conditional distribution of Y given that X becomes extreme. They show that this behaviour differs between regularly and rapidly varying tails. Le comportement extrême des loi...

We introduce a mixture of generalized hyperbolic distributions as an alternative to the ubiquitous mixture of Gaussian distributions as well as their near relatives of which the mixture of multivariate t and skew-t distributions are predominant. The mathematical development of our mixture of generalized hyperbolic distributions model relies on its relationship with the generalized inverse Gauss...