An unresolved problem in statistical analysis of hydrological extremes (e.g., storms, floods) using POT model is identification of optimal threshold. There are various issues affecting performance of different methods available for threshold selection (TS). To overcome those issues, this study contributes a novel Mahalanobis distance‐based automatic TS method. It involves use of proposed transformation to map Generalized Pareto distributed random variable (depicting peaks over tentative thresholds) from the original space to standard exponential (Exp(1)) distributed random variable in a nondimensional space. Optimal threshold is identified as that which minimizes Mahalanobis distance between L‐moments of the transformed random variable and those of the population (i.e., Exp(1) distribution) in the nondimensional space. Its effectiveness is demonstrated over four existing automatic TS methods through Monte Carlo simulation experiments and case studies over rainfall and streamflow data sets chosen from India, United Kingdom, and Australia. The four methods include three based on goodness of fit (GoF) test statistics (of Anderson‐Darling and two nonparametric tests), and a recent one based on L‐moment ratio diagram whose potential is unexplored in hydrology. This study further provides insight into properties and effectiveness of the four TS methods, which is scanty in literature. Results indicate that there is inconsistency in performance of GoF test‐based methods across data sets exhibiting fat and thin tail behavior, owing to their theoretical assumptions and uncertainty associated with sampling distribution of test statistics. Issues affecting performance of L‐moment ratio diagram‐based TS method are also identified. The proposed method overcomes those issues and appears promising for hydrologic applications.

中文翻译：

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基于Mahalanobis距离的阈值模型中基于距离的自动阈值选择方法

使用POT模型对水文极端事件（例如暴风雨，洪水）进行统计分析时，尚未解决的问题是确定最佳阈值。存在影响可用于阈值选择（TS）的不同方法的性能的各种问题。为了克服这些问题，本研究提出了一种新颖的基于Mahalanobis距离的自动TS方法。它涉及使用建议的变换将原始空间中的广义Pareto分布随机变量（描绘出超过暂定阈值的峰）映射到无量纲空间中的标准指数（Exp（1））分布随机变量。最佳阈值被确定为使L之间的马氏距离最小化的阈值无量纲空间中变换后的随机变量和总体的矩（即Exp（1）分布）。通过蒙特卡洛模拟实验以及从印度，英国和澳大利亚选择的降雨和流量数据集的案例研究，通过四种现有的自动TS方法证明了其有效性。四种方法包括三种基于拟合优度（GoF）的检验统计数据（Anderson-Darling检验和两种非参数检验），以及一种基于L的最近检验矩比图，其潜力在水文学中尚待开发。这项研究进一步提供了对四种TS方法的性质和有效性的见解，这在文献中还很少。结果表明，由于GoF测试方法的理论假设和与测试统计数据的抽样分布相关的不确定性，因此在表现出胖尾行为和瘦尾行为的数据集中，基于GoF测试的方法的性能不一致。还确定了影响基于L矩比图的TS方法性能的问题。所提出的方法克服了这些问题，并且在水文应用中似乎很有希望。