Statistical tools for extreme value analysis

Statistical tools for extreme value analysis

Stephen Chan Manchester University

Both academics and pratictioners widely apply Extreme Value Analysis (EVA) in their applied research work. Some examples of field applications: coastal engineers, structural engineers, geological engineers, investment banks, risk management, hydrologists and seismologists. More specifically the modelling of extreme events in environmental science has particularly intensified through disaster planning purposes for flood, wind, mudslides, fire, tornado, extreme temperatures and droughts.

EVA is a branch of statistics, which deals with the extreme deviations from the median of the probability distribution. Two distributions are commonly associated with the analysis of extreme value: the generalized extreme value (GEV) distribution and the generalized Pareto distribution (GPD).

Many software packages, particularly in the open source environment, are available to assist academics and industrial partners to perform analysis on extreme values. The main functions in these packages allow us to perform estimation of univariate, bivariate and multivariate extreme value theory. They include the following methods: block maxima, threshold model, estimation methods and non–stationary regression). Graphical techniques to analyse extreme value data are also available.

Statistical tools for extreme value analysis: a review of software packages

I propose a compiled review of the currently available software packages for extreme value analysis. This may not be a comprehensive list but it contains the most commonly used packages.

The development of software for statistical extremes has been rapid, particularly in the open source environment of R. R contains the most utilities and tools for modelling extreme values and is freely available without proprietary licensing requirements, causing R to be extremely popular for many academic statisticians.

This review list will greatly simplify the process of finding and understanding available software for EVA.

For more information on the use of statistical tools in risk management

For more information about statistical methods and their applications in finance (especially risk management with Value at Risk), you can read our contribution Estimation methods for Value at Risk with Professor Saralees Nadarajah (Manchester University) published in the Wiley handbook Extreme Events in Finance.

Stephen Chan
Manchester University

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