About the Software

The EXTREMES software gathers different tools dedicated to extreme values study. More precisely, it focuses on extreme quantiles estimation and model selection for distribution tails. It is written in C++ with a graphical user interface developped with the library QT. This solution matches rapid execution and user-friendliness. Avaible functions can be grouped in three classes:

  1. Usual statistical functions :

  2. These functions are not dedicated to extreme value study: sample simulation, ploting distribution related functions, parameter estimation, non parametric estimation of density, parametric estimation of quantiles, Anderson-Darling or Cramer-von Mises test.

  3. Usual functions for extreme value analysis :

  4. These are well known functions for estimation and test in extreme value analysis context.
    • Checking excess exponentiality. The goal is to check if the data distribution is in the Gumbel maximum domain of attraction and if the number of excesses is well choosen. Exponentiality of the excesses is graphically checked drawing a qq-plot. A test is also proposed.
    • Estimation of Generalized Pareto Distribution parameters.
    • Extreme quantiles estimation using POT method and the previous estimates.

  5. New procedures :

    • The GPD test is a goodness-of-fit test for the distribution tail of usual global models belonging to all the maximum domains of attraction (Gumbel, Weibull and Fréchet). We compare the parametric estimate using the global model and the POT method estimate of an extreme quantile. For the POT estimation, different estimates exist (Hill, DEH ...) leading to different tests.
    • The ET test is a particular case of the GPD test for which we suppose the data distribution is in the Gumbel maximum domain of attraction. To compute the POT estimate, we then use an exponential approximation of the distribution tail.
    • Bayesian regularisation procedure is a method to improve the extremal fit of previous models using an expert opinion on distribution tail.

    When one wants to know the data distribution both in central (most likely) and extremal ranges, an usual model can be looked for. Central fit is checked by usual tests like Anderson-Darling or Cramer-von Mises. Then the GPD (or ET) test allows to check extremal fit of these models. If no distribution is accepted both by central and extremal tests, the bayesian regularisation procedure can improve the extremal fit of a central adapted model.

      More details in french...

About the Team

EXTREMES is the result of several years of research in the MISTIS team at INRIA Rhône-Alpes.

This project-team aims at developing statistical methods for dealing with complex systems, complex models and complex data. Our applications consist mainly of image processing and spatial data problems with some applications in biology and medicine. Our approach is based on the statement that complexity can be handled by working up from simple local assumptions in a coherent way, defining a structured model.This is the key to modelling, computation, inference and interpretation. The methods we consider involve mixture models, Markovian models, and more generally hidden structure models on one hand, and semi and non-parametric methods on the other.

More information is available on the web site of MISTIS : http://mistis.inrialpes.fr.


Programming :
     Sophie CHOPART
     Jérome ECARNOT
Theoretical aspects :
     Jean DIEBOLT, Université de Marne la Vallée, 5 bd. Descartes, 77454 Marne la Vallée Cedex 2 (mail)
     Stéphane GIRARD, MISTIS, INRIA Rhône-Alpes, 655 av. de l’Europe, 38330 Montbonnot Saint Martin (page web)
     Myriam GARRIDO, Unité épidémiologie animale, Centre INRA de Clermont-Ferrand Theix, 63122 Saint-Genes-Champanelle (mail)
Industrial partner :
     Dominique LAGRANGE, EDF R&D/MRI, 6 quai Watier, BP 49, 78401 Chatou Cedex (mail)


  • Embrechts P., Klüppelberg C., Mikosh T., Modelling extremal events - Springer-Verlag,Applications of mathematics, 1997.
  • Garrido M., Modélisation des évènements rares et estimations des quantiles extrêmes, Méthode de sélection de modèles pour les queues de distribution, Thèse de doctorat, Université Grenoble 1, 2002.
  • De Haan L., Rootzen H., On the estimation of high quantiles - Journal of Statistical Planning and Inference, vol. 35, p1-13, 1993.
  • Dekkers A.L.M., Einmahl J.H.J. et de Haan L., A moment estimator for the index of an extreme-value distribution - The Annals of Statistics, vol. 17, p1833-1855, 1989.
  • Beirlant J., Dierckx G. et Guillou A., Estimation of the extreme value index and regression on generalized quantile plots, Bernouilli, vol. 11 , p949-970, 2005.
  • Diebolt J., Ecarnot J., Garrido M., Girard S., Lagrange D., Le logiciel Extremes, un outil pour l'étude des queues de distribution, La revue de Modulad, 30, 53-60, 2003.
  • J. Diebolt, M. Garrido, S. Girard "A goodness-of-fit test for the distribution tail" In M. Ahsanulah and S. Kirmani, editors, Extreme value distributions, p. 95-109, Nova Science, New-York, 2007.


Documentation is available on the use of EXTREMES : Documentation (in french).


EXTREMES is distributed under the licence CeciLL-B (http://cecill.info/ ).


For downloading the registration software, please complete the form. After submitting your data, you will be able to download EXTREMES.

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If you have problems, questions or comments on the download or on the software, you can send an email to this address : extremes-help@lists.gforge.inria.fr

Last modification : 07/05/2009



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