Extreme values of real phenomena are events that occur with low frequency,
but can have a large impact on real life. These are, in many practical
problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991).
To study these events is of fundamental importance. For this purpose,
probabilistic models and statistical methods are in high demand. There are
several approaches to modelling multivariate extremes as described in Falk et
al. (2011), linked to some extent. We describe an approach for deriving
multivariate extreme value models and we illustrate the main features of some
flexible extremal dependence models. We compare them by showing their utility
with a real data application, in particular analyzing the extremal dependence
among several pollutants recorded in the city of Leeds, UK.Comment: To appear in Extreme Value Modelling and Risk Analysis: Methods and
Applications. Eds. D. Dey and J. Yan. Chapman & Hall/CRC Pres
