[ABE-L] Seminário - IME-USP - Modelos de Regressão e Aplicações - A comparative review of generalizations of the Gumbel extreme value distribution with an application to wind speed data

[Silvia Ferrari]

*Seminário - Projeto Temático: Modelos de Regressão e Aplicações*

*Título*: A comparative review of generalizations of the Gumbel extreme
value distribution with an application to wind speed data

*Palestrante*: Eliane C. Pinheiro – Pós-doutorado, Estatística, IME-USP

*Quando*: 13 de novembro, sexta-feira, às 11h.

*Onde*: Auditório Jacy Monteiro, Bloco B, piso térreo - IME-USP

*Resumo*. The generalized extreme value distribution and its particular
case, the Gumbel extreme value distribution, are widely applied for extreme
value analysis. The Gumbel distribution has certain drawbacks because it is
a non-heavy-tailed distribution and is characterized by constant skewness
and kurtosis. The generalized extreme value distribution is frequently used
in this context because it encompasses the three possible limiting
distributions for a normalized maximum of infinite samples of independent
and identically distributed observations. However, the generalized extreme
value distribution might not be a suitable model when each observed maximum
does not come from a large number of observations. Hence, other forms of
generalizations of the Gumbel distribution might be preferable. Our goal is
to collect in the present literature the distributions that contain the
Gumbel distribution embedded in them and to identify those that have
flexible skewness and kurtosis, are heavy-tailed and could be competitive
with the generalized extreme value distribution. The generalizations of the
Gumbel distribution are described and compared using an application to a
wind speed data set and Monte Carlo simulations. We show that some
distributions suffer from overparameterization and coincide with other
generalized Gumbel distributions with a smaller number of parameters, i.e.,
are non-identifiable. Our study suggests that the generalized extreme value
distribution and a mixture of two extreme value distributions should be
considered in practical applications.

Joint work with Silvia L. P. Ferrari.
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