Software for the analysis of extreme events: The current state and future directions

The last few years have seen a significant increase in publicly available software specifically targeted to the analysis of extreme values. This reflects the increase in the use of extreme value methodology by the general statistical community. The software that is available for the analysis of extremes has evolved in essentially independent units, with most forming extensions of larger software environments. An inevitable consequence is that these units are spread about the statistical landscape. Scientists seeking to apply extreme value methods must spend considerable time and effort in determining whether the currently available software can be usefully applied to a given problem. We attempt to simplify this process by reviewing the current state, and suggest future approaches for software development. These suggestions aim to provide a basis for an initiative leading to the successful creation and distribution of a flexible and extensible set of tools for extreme value practitioners and researchers alike. In particular, we propose a collaborative framework for which cooperation between developers is of fundamental importance.

[1]  J. Pickands Statistical Inference Using Extreme Order Statistics , 1975 .

[2]  C. Wild,et al.  Vector Generalized Additive Models , 1996 .

[3]  Richard L. Smith Maximum likelihood estimation in a class of nonregular cases , 1985 .

[4]  L. de Haan,et al.  A Spectral Representation for Max-stable Processes , 1984 .

[5]  Rolf-Dieter Reiss,et al.  Statistical analysis of extreme values : from insurance, finance, hydrology and other fields , 1998 .

[6]  Janet E. Heffernan,et al.  Dependence Measures for Extreme Value Analyses , 1999 .

[7]  S. Coles,et al.  Modelling Extreme Multivariate Events , 1991 .

[8]  E. J. Gumbel,et al.  Statistics of Extremes. , 1960 .

[9]  S. Coles,et al.  An Introduction to Statistical Modeling of Extreme Values , 2001 .

[10]  A. Ledford,et al.  Statistics for near independence in multivariate extreme values , 1996 .

[11]  René Carmona,et al.  Statistical Analysis of Financial Data in S-Plus , 2004 .

[12]  B. M. Hill,et al.  A Simple General Approach to Inference About the Tail of a Distribution , 1975 .

[13]  Jonathan A. Tawn,et al.  Bayesian Inference for Extremes: Accounting for the Three Extremal Types , 2004 .

[14]  Eric R. Ziegel Statistical Analysis of Financial Data in S–PLUS , 2005, Technometrics.

[15]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

[16]  Johan Segers,et al.  Inference for clusters of extreme values , 2003 .

[17]  L. Haan,et al.  A moment estimator for the index of an extreme-value distribution , 1989 .

[18]  Eric P. Smith,et al.  An Introduction to Statistical Modeling of Extreme Values , 2002, Technometrics.

[19]  Ramazan Gençay,et al.  EVIM: A Software Package for Extreme Value Analysis in MATLAB , 2001 .

[20]  J. R. Wallis,et al.  Estimation of the generalized extreme-value distribution by the method of probability-weighted moments , 1985 .

[21]  C. Klüppelberg,et al.  Modelling Extremal Events , 1997 .