**Ulf Cormann**

University of Siegen

**February 25, 2009**

**ML - Directors Conference Room**

**12:00pm (Bring your lunch)**

### When the POT-approach Fails: Super Heavy Tailed Distributions and Covariate Information

We consider the case that the conditional distribution of a random variable *Y* given *X = x* is in the domain of attraction of a generalized Pareto distribution (GPD), which parameters depend on *x*. In many cases this entails that the distribution of *Y* is not in the domain of attraction of any GPD anymore. We distinguish two cases whether the covariate variable *X* can be observed or not.
Considering the first case we propose a conditional point process model to estimate the tail of the conditional distribution via Maximum-Likelihood. In the second case we derive limiting distribution of exceedances from super-heavy tailed distributions using nonlinear transformations.

Finally some open questions are addressed concerning threshold selection in the first case and discriminating between heavy and super-heavy tailed distributions in the second case.