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

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.