  When assessing the impact of extreme events, it is often not just a single
component, but the combined behaviour of several components which is important.
Statistical modelling using multivariate generalized Pareto (GP) distributions
constitutes the multivariate analogue of univariate peaks over thresholds
modelling, which is widely used in finance and engineering. We develop general
methods for construction of multivariate GP distributions and use them to
create a variety of new statistical models. A censored likelihood procedure is
proposed to make inference on these models, together with a threshold selection
procedure, goodness-of-fit diagnostics, and a computationally tractable
strategy for model selection. The models are fitted to returns of stock prices
of four UK-based banks and to rainfall data in the context of landslide risk
estimation. Supplementary materials and codes are available online.
