Software for Extreme Value Theory

This web page was originally written by Alec Stephenson, and has now been passed on to this location, and is now maintained by Eric Gilleland; who can be contacted for any corrections, changes or updates. This page is intended as a brief guide to the various software for implementing extreme value theory with links to the various packages. See also Stephenson and Gilleland (2005) for information about some of the packages.

Software in R

R is a language and environment for statistical computing and graphics. Detailed information about R and the R project is available from http://www.r-project.org/. R is one of the best statistical environments available. It is also free (effectively). The latest version of R (2.7.0) can be downloaded via the R project web site. The R project is an Open Source project. The code you are using (whether written in the R language itself or in other languages through an R interface) is always available for you to look at. If you do not trust the routines, or want to know exactly what is going on, read the code!

All R packages can be downloaded and installed from the R prompt using the install.packages function. See the R help file for install.packages for installation instructions. That is, from the R prompt, type:

[R prompt]> ?install.packages

Once a package has been installed, it can be loaded using the library function. Again, see the help file for library for help and more information on doing this.

1. The evd Package (Version 2.1)
2. The evdbayes Package (Version 1.0)
3. The evir Package (Version 1)
4. The ismev Package (Version 1)
5. The extRemes Package (Version 1.0)
6. The fExtremes Package (Version 191)

The evd Package (Version 2.2-3)

evd (extreme value distributions) is and add-on package for the R system. It extends simulation, distribution, quantile and density functions to univariate and multivariate parametric extreme value distributions, and provides fitting functions which calculate maximum likelihood estimates for univariate and bivariate models, and for univariate and bivariate threshold models.

The evdbayes Package (Version 1.0-6)

evdbayes is and add-on package for the R system. It provides functions for the bayesian analysis of extreme value models, using MCMC methods.

The evir Package (Version 1.5)

evir is and add-on package for the R system. It is an R port (conversion) of Version 3 of Alexander McNeil's S library EVIS (Extreme Values in S). It contains functions for extreme value theory, which may be divided into the following groups; exploratory data analysis, block maxima, peaks over thresholds (univariate and bivariate), point processes, gev/gpd distributions.

The ismev Package (Version 1.3)

ismev is and add-on package for the R system. It is an R port of S functions written by Stuart Coles to support (univariate) extreme value modelling (or modeling, if you're on the other side of the pond), including the computations carried out in Coles (2001). The functions may be divided into the following groups; maxima/minima, order statistics, peaks over thresholds and point processes. Coles (2001) is the only book currently available that provides an (excellent) introduction to the topic at a relatively simple statistical level.

The extRemes Package (Version 1.57)

extRemes is and add-on package for the R system, written by Eric Gilleland, Rick Katz and Greg Young, and maintained by Eric Gilleland. It provides a windows GUI for the ismev package, allowing easy use of the tools that the ismev package provides, in addition to a few extra useful functions. See the extRemes web site for details.

The fExtremes Package (Version 260.72)

fExtremes is and add-on package for the R system, maintained and primarily written by Diethelm Wuertz. The package contains functions for the exploratory data analysis of extreme values for insurance, economic and financial applications. It also brings together many of the elements of the packages evd, evir and ismev. The fExtremes package comprises part of the Rmetrics software collection. See the Rmetrics web site for details.

Software in S

S is a language which is similar to R. Technically, S is a language and S-PLUS is an environment under which this language is used. In practice, no other environment uses (or is allowed to use) S, so the two terms are often used interchangeably. S-PLUS is a commercial product which can be purchased from Insightful. More details can be found on Insightful's web site.

1. The EVIS Library (Version 4)
2. Stuart Coles' S Routines
3. The S+Finmetrics Module

The EVIS Library (Version 4)

The S-PLUS library EVIS (Extreme Values in S-PLUS) was written and is maintained by Alexander McNeil. The library can by downloaded from his web site. The latest version includes the function gpdbiv which implements a bivariate model for joint exceedances of a pair of thresholds. For those who do not have access to S-PLUS the R package evir is an R port of Version 3 of EVIS.

Stuart Coles' S Routines

Stuart Coles has written a comprehensive set of functions in the S language to support (univariate) extreme value modelling. The functions are used extensively in Coles (2001). Stuart can provide a file containing the functions which can then be read in with source(). It is best to ensure the working directory is empty before the file is read in, otherwise objects in the directory with the same name as objects defined in the file will be lost.

The S+Finmetrics Module

S+Finmetrics is an S-Plus module (meaning that you have to spend even more money to obtain it), which can be purchased from Insightful. It contains a number of functions associated with extreme value theory. From what I can determine, these functions appear to be (based on) Version 4 of the EVIS library by Alexander McNeil and functions written by Rene Carmona for the book Carmona(2004). It appears that the latter functions can still be dowloaded from a fairly obscure link on the authors web site.

Other Various Software

1. Xtremes (Version 3.0)
2. Stable Distributions
3. EVIM -- Extreme Value Analysis in MATLAB

Xtremes (Version 3.0)

Xtremes is a statistical software system that accompanies the book by Reiss and Thomas (2001). It possesses a graphical user interface and provides a large number of statistical procedures and diagnostic tools. This includes procedures specifically targeted to applications in finance and hydrology. A professional version of Xtremes, which allows data sets of any size to be analysed, can be purchased from RiskTex. See the Xtremes web site for details.

Stable Distributions

John Nolan has written two programs for Windows. STABLE (Version 3.13) calculates density, distribution and quantile functions for stable distributions, and includes simulation and maximum likelihood fitting procedures. MVSTABLE (Version 2.0) includes similar routines for multivariate stable distributions. STABLE is also included in the Xtremes system.

The R package stable was written by Philippe Lambert and Jim Lindsey and is maintained by Jim Lindsey. It calculates density, distribution, quantile and hazard functions and allows generalized regression models for the parameters of the stable distribution.

EVIM

EVIM -- Extreme Value Analysis in MATLAB is created by Ramazan Gençay (University of Windsor), Faruk Selçuk (Bilkent University) and Abdurrahman Ulugülyagci (Bilkent University). A complete pdf document on EVIM.

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References

Carmona, R. A. (2004) Statistical Analysis of Financial Data in S-Plus. New York: Springer.

Coles, S. G. (2001) An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.

Reiss, R.-D. and M. Thomas (2001) Statistical Analysis of Extreme Values. Berlin: Birkhauser.

Stephenson, A. and E. Gilleland, 2005. Software for the Analysis of Extreme Events: The Current State and Future Directions, Extremes 8:87--109.

For corrections, updates, additions, or other comments about this page, please contact Eric Gilleland.