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 for modeling extreme bimodal data. In this paper, we propose an extension of the GEV distribution that incorporates an additional parameter. The additional parameter introduces bimodality and aries tail weight, i.e., this proposed extension is more flexible than the GEV distribution. Inference for the proposed distribution was 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.

在极值理论中，对于足够大的块大小，极大值分布近似于广义极值 (GEV) 分布。GEV 分布是一族连续概率分布，在水文、工程、科学、生态学和金融等多个领域具有广泛的适用性。但是，GEV 分布不适用于对极端双峰数据建模。在本文中，我们提出了 GEV 分布的扩展，其中包含一个附加参数。附加参数引入了双峰性和 aries 尾重，即，这个提议的扩展比 GEV 分布更灵活。拟议分布的推断是在似然范式下进行的。进行蒙特卡罗实验以评估这些估计器在有限样本中的性能，并对结果进行讨论。最后，将提议的分布应用于环境数据集，说明它们在极值理论中具有挑战性的情况下的能力。