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 MATLAB. This solution matches rapid
execution and
user-friendliness. Avaible functions can be grouped in three
classes:

**1) Usual statistical functions.**

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.

**2) Usual functions for extreme value analysis.**

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.

**3) 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, Dekkers ...) 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.

**References**

[1] Diebolt, J., Ecarnot, J., Garrido, M., Girard, S., Lagrange, D.
(2003)
*Le logiciel Extremes, un outil pour l'étude des queues de
distribution*,
La revue de Modulad, 30, 53-60.