Modeling rainfall intensity distributions across aggregation scales (from sub-hourly to weekly) is essential for hydrological risk analysis and IDF curves. Aggregation naturally imposes mathematical constraints: return levels must be ordered by time scale, as daily accumulations necessarily exceed sub-daily ones. From a statistical perspective, each aggregation step should ideally not require additional parameters, yet parsimonious models describing the full distribution remain scarce, as most literature focuses on seasonal block maxima. In this study, we propose a parsimonious framework to model all rainfall intensities (low to large) across scales. We utilize the Extended Generalized Pareto Distribution (EGPD), which aligns with extreme value theory for both tails while remaining flexible for the bulk of the distribution. We establish a general result on the behavior of EGPD variables under various aggregation procedures. To overcome the difficulty of direct likelihood inference, we link the EGPD class to Poisson compound sums. This allows the use of the Panjer algorithm for efficient composite likelihood evaluation. Our approach ensures that return levels do not cross across scales and enables estimation for return periods below annual or seasonal levels. We demonstrate the method using sub-hourly series from six French stations with diverse climates. Only eight parameters are needed per station to capture scales from six minutes to three days. IDF curves above and below the annual scale are provided.

翻译：对跨聚合尺度（从亚小时到周尺度）的降雨强度分布进行建模对于水文风险分析和强度-持续时间-频率曲线至关重要。聚合过程天然地施加了数学约束：重现期水平必须按时间尺度排序，因为日累积量必然超过亚日累积量。从统计视角看，每个聚合步骤理想情况下不应需要额外参数，然而描述完整分布的简约模型仍然稀缺，因为大多数文献集中于季节性区块极值。在本研究中，我们提出一个简约框架来建模跨尺度的所有降雨强度（从低值到极值）。我们采用扩展广义帕累托分布，该分布在两端与极值理论保持一致，同时对分布主体部分保持灵活性。我们建立了关于扩展广义帕累托分布变量在不同聚合程序下行为的一般性结论。为克服直接似然推断的困难，我们将扩展广义帕累托分布类与泊松复合和相联系。这使得能够利用Panjer算法进行高效的复合似然评估。我们的方法确保重现期水平在跨尺度时不发生交叉，并能实现低于年或季节尺度的重现期估计。我们使用来自六个不同气候条件法国气象站的亚小时序列验证了该方法。每个站点仅需八个参数即可捕捉从六分钟到三天尺度的特征。研究同时提供了年尺度以上及以下的强度-持续时间-频率曲线。