Abstract Classic extreme value theory provides asymptotic distributions of block maxima (BM) Y or peaks over threshold (POT). However, as BM and POT are relatively small subsets of the values assumed by the parent process Z, alternative approaches have been proposed to make inferences on extremes by using intermediate values and non-asymptotic models. In this study, we investigate the finite sample theory of extremes based on order statistics, and present a set of results enabling the analysis of the properties of non-asymptotic distributions of BM in finite-size blocks of data under the assumption that the parent process Z has stationary temporal dependence. In particular, we suggest the beta-binomial distribution ( F β B ) as a suitable approximation of the marginal distribution of order statistics and BM under dependence, thus generalizing the theoretical results available under independence. We demonstrate the usefulness of the F β B distribution in three conceptual applications of hydrological interest. Firstly, we review the so-called Complete Time-series Analysis (CTA) framework, showing that the differences between FY and FZ are due to the inherent theoretical nature of the processes Y and Z and the different probabilistic failure scenarios described by FY and FZ. Secondly, we provide a theoretical rule to select the number of the largest maxima (LM) and over-threshold exceedances (OT) required to approximate the desired portion of the upper tail of FZ with specified accuracy. Finally, we discuss how the F β B distribution offers an interpretation and generalization of the so-called metastatistical extreme value (MEV) framework and its simplified version (SMEV), avoiding the use of high-dimensional joint distributions and preliminary data thresholding and declustering. All methodological results are validated by Monte Carlo simulations involving widely used stochastic processes with persistence. Real-world stream flow data are also analyzed as proof of concept.

中文翻译：

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井井有条：串行相关顺序统计的分布与极端水文应用

摘要 经典极值理论提供了块最大值 (BM) Y 或阈值峰值 (POT) 的渐近分布。然而，由于 BM 和 POT 是父进程 Z 假定值的相对较小的子集，因此已经提出了替代方法来通过使用中间值和非渐近模型对极端情况进行推断。在这项研究中，我们研究了基于阶统计的极值的有限样本理论，并提出了一组结果，可以在父进程的假设下分析有限大小数据块中 BM 的非渐近分布的性质Z 具有平稳的时间依赖性。特别是，我们建议β-二项式分布 (F β B ) 作为顺序统计和 BM 依赖下边际分布的合适近似值，从而概括了独立下可用的理论结果。我们证明了 F β B 分布在水文兴趣的三个概念应用中的有用性。首先，我们回顾了所谓的完整时间序列分析 (CTA) 框架，表明 FY 和 FZ 之间的差异是由于过程 Y 和 Z 的固有理论性质以及 FY 和 FZ 描述的不同概率故障场景. 其次，我们提供了一个理论规则来选择以指定精度逼近 FZ 上尾的所需部分所需的最大最大值 (LM) 和超阈值超出 (OT) 的数量。最后，我们讨论了 F β B 分布如何提供对所谓的转移统计极值 (MEV) 框架及其简化版本 (SMEV) 的解释和概括，避免使用高维联合分布和初步数据阈值化和去聚类。所有方法论结果均通过蒙特卡罗模拟验证，该模拟涉及广泛使用的具有持久性的随机过程。现实世界的流数据也被分析为概念证明。