Extended generalized extreme value distribution with applications in environmental data

Year 2016, Volume: 45 Issue: 6, 1847 - 1864, 01.12.2016

Fernando Nascimento Marcelo Bourguignon Jeremias Leão

Abstract

In probability theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within
extreme value theory, which has wide applicability in several areas including
hydrology, engineering, science, ecology and finance. In this paper, we propose three extensions of the GEV distribution that incorporate an additional
parameter. These extensions are more flexible than the GEV distribution, i.e.,
the additional parameter introduces skewness and to vary tail weight. In these
three cases, the GEV distribution is a particular case. The parameter estimation
of these new distributions is done under the Bayesian paradigm, considering
vague priors for the parameters. Simulation studies show the efficiency of the
proposed models. Applications to river quotas and rainfall show that the generalizations can produce more efficient results than is the standard case with GEV
distribution. 

Keywords

Extreme value theory, Generalized extreme value distribution, Generalized classes of distributions, Environmental and Economic data

References

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