Gumbel distribution with heavy tails and applications to environmental data.

Abstract In this paper, we introduce a new extension to the extreme value type-1 (Gumbel) distribution, by constructing a slash type distribution. The result is a distribution with greater kurtosis than the Gumbel distribution. Properties of the distribution such as moments, moment generating function and kurtosis and asymmetry coefficients for the distribution are studied. Maximum likelihood estimation and moments estimators are applied and a simulation study is presented to illustrate parameter recovery. Results of applications to two real data sets, one from a wind velocity study and the other from snow accumulation indicate that the new model seems to perform better in the presence of atypical observations. Highlights • An extension of the Gumbel model is presented. • This extension allows to obtain a bigger range to the kurtosis coefficient. • Euler's constant and the zeta and polygamma functions are related. • The parameter estimation was approached using the method of moments and the MLE. • Simulations and two real data sets show the good performance of this new model. [ABSTRACT FROM AUTHOR]