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 investigate a modification of the Cram\'er-von Mises distance for the purpose of model fitting. An application to mid-latitude winter cyclones illustrates the usefulness of our work.

翻译：极端事件（如强降水或风暴）在特定地点的发生通常呈现聚类行为，因此不能用泊松过程很好地描述。我们构建了此类事件间超阈时间间隔的通用模型，该模型整合了描述此类行为的不同候选模型。这使我们能够区分两类数据生成机制：一类是事件间存在指数型超阈时间间隔的相依事件簇，另一类是具有重尾超阈时间间隔的独立事件，甚至可将这两种机制结合以更精准地描述此类事件发生模式。我们研究了基于Cramér-von Mises距离的修正方法用于模型拟合。对中纬度冬季气旋的应用分析验证了本研究的实用价值。