A Bimodal Model for Extremes Data

Abstract

In extreme values theory, for a sufficiently large block size, the maxima distribution is approximated by the generalized extreme value (GEV) distribution. The GEV distribution is a family of continuous probability distributions, which has wide applicability in several areas including hydrology, engineering, science, ecology and finance. However, the GEV distribution is not suitable to model extreme bimodal data. In this paper, we propose an extension of the GEV distribution that incorporate an additional parameter. The additional parameter introduces bimodality and to vary tail weight, i.e., this proposed extension is more flexible than the GEV distribution. Inference for the proposed distribution were performed under the likelihood paradigm. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. Finally, the proposed distribution is applied to environmental data sets, illustrating their capabilities in challenging cases in extreme value theory.