AMS classifications: 62G20, 62G32;

Extreme rainfall events and the clustering of extreme values provide fundamental information which can be used for the risk assessment of extreme floods. Event probability can be estimated using the extreme value index (γ) which describes the behavior of the upper tail and measures the degree...

Despite its wide use, the Hill estimator and its plot remain to be difficult to use in Extreme Value Theory (EVT) due to substantial sampling variations in extreme sample quantiles. In this paper, we propose a new plot we call the eigenvalue plot which can be seen as a generalization of the Hill...

The theory of stable probability distributions and their domains of attraction is derived in a direct way(avoiding the usual route via infinitely divisible distributions) using Fourier transforms. Regularly varyingfunctions play an important role in the exposition.