The conventional use of the Generalized Extreme Value (GEV) distribution to model block maxima may be inappropriate when extremes are actually structured into multiple heterogeneous groups. In this work, we propose a novel approach for describing the behavior of extreme values in the presence of such heterogeneity. Rather than defaulting to the GEV distribution simply because it arises as a theoretical limit, we show that alternative block maxima-based models can also align with the extremal types theorem while providing improved flexibility in practice. Our formulation leads us to a mixture model that has a Bayesian nonparametric interpretation as a Dirichlet process mixture of GEV distributions. The use of an infinite number of components enables the characterization of every possible block behavior, while at the same time capturing similarities between observations based on their extremal behavior. By employing a Dirichlet process prior on the mixing measure, we can capture the complex structure of the data without the need to pre-specify the number of mixture components. The application of the proposed model is illustrated using both simulated and real-world data.

翻译：广义极值分布（GEV）传统上用于建模块极大值，但当极值实际上由多个异质性群体构成时，这种应用可能不合适。本文提出了一种新方法，用于描述存在异质性时极值的行为。我们并未简单默认采用作为理论极限的GEV分布，而是证明基于块极大值的替代模型同样能符合极值类型定理，并在实践中提供更好的灵活性。我们的建模方案最终形成了一个混合模型，该模型具有贝叶斯非参数解释，即GEV分布的狄利克雷过程混合。通过使用无限数量的混合分量，我们能够表征每一个可能的块行为，同时基于观测的极值行为捕捉其相似性。通过对混合测度施加狄利克雷过程先验，我们无需预先指定混合分量的数量即可捕捉数据的复杂结构。通过模拟数据和真实数据验证了所提模型的应用效果。