This thesis concerns statistical analysis for upper tails of distribution functions.
Firstly, we derive asymptotic distributions of exceedances under general monotone transformations and analyze the pertaining domains of attraction. It turns out that all possible limiting distributions satisfy a certain form of a generalized pot-stability.
We give a complete characterization of all strictly increasing, continuous limiting distributions. Further, we deduce the class of all limiting distributions under power-normalization and characterize the pertaining domains of attraction. The limiting distributions
are identified as generalized log-Pareto and negative generalized log-Pareto distributions as well as a certain class of discrete distributions. Moreover, we introduce and study an extended class of generalized log-Pareto distributions and provide a hybrid Maximum-Likelihood estimator. These distributions can serve as a parametric
asymptotic model for super-heavy tailed distributions.In the second part of this thesis statistical inference for the upper tail of the cnditional distribution of a response variable Y given a covariate X = x within the framework of asymptotic distributions is considered as well. We propose to base the inference on the conditional distribution of the point process of exceedances given the point process of covariates. The results are valid within a model where the response
variables are conditionally independent given the covariates.
Both parts of the thesis are linked to each other by the fact that that a Pareto modeling of the conditional distribution leads to super-heavy upper tailed unconditional distributions.