The occurrence of extreme events like heavy precipitation or storms at a certain location often shows a clustering behaviour and is thus not described well by a Poisson process. We construct a general model for the inter-exceedance times in between such events which combines different candidate models for such behaviour. This allows us to distinguish data generating mechanisms leading to clusters of dependent events with exponential inter-exceedance times in between clusters from independent events with heavy-tailed inter-exceedance times, and even allows us to combine these two mechanisms for better descriptions of such occurrences. We propose a modification of the Cram\'er-von Mises distance for model fitting. An application to mid-latitude winter cyclones illustrates the usefulness of our work.

翻译：特定地点极端事件（如强降水或风暴）的发生常呈现聚类特征，因而无法用泊松过程准确描述。本文构建了一个描述此类事件间超越时间间隔的通用模型，该模型融合了多种解释该行为的候选模型。这使得我们能够区分两种数据生成机制：一种产生具有指数型超越时间间隔的依赖事件簇，另一种产生具有重尾型超越时间间隔的独立事件。该模型甚至允许结合这两种机制以更精确地描述此类事件的发生规律。我们提出了Cramér-von Mises距离的修正方法用于模型拟合。通过对中纬度冬季气旋的应用研究，验证了本工作的实用价值。