AI 中文总结
本文针对存在内点时极端值建模的阈值选择难题，提出含内点、极端值及尾部比例的鲁棒建模框架，经模拟与实际数据验证，其阈值估计与极端值推断精度优于现有经典方法。
AI 中文摘要
极端值理论为稀有极端事件建模提供了基础框架，但阈值选择始终是一个持续存在的挑战，尤其在存在内点（如瞬时故障或早期故障）的情况下。这类观测值常见于可靠性研究、环境数据等应用场景，其中靠近原点或处于原点的观测集群会严重扭曲经典阈值选择程序和尾部推断。本文提出一种鲁棒建模框架，可同时考虑内点、极端值及尾部比例，采用最大似然法进行参数估计。将所提方法与经典数值及图形诊断工具（包括平均超出量图、参数稳定性图、Hill图、Pickands图）及现有极端值混合模型进行对比，建立了所提模型的理论性质，并通过大量蒙特卡洛模拟和实际数据应用评估其性能。结果表明，与现有经典方法相比，所提方法在存在内点时能提供更准确的阈值估计和更可靠的极端值推断，解决了现有方法的关键局限。
英文摘要
Extreme value theory provides a fundamental framework for modeling rare and extreme events; however, threshold selection remains a persistent challenge, particularly in the presence of inliers such as instantaneous or early failures. Such observations commonly arise in applications including reliability studies and environmental data, where clusters of observations near the origin or at the origin can substantially distort classical threshold selection procedures and tail inference. In this paper, we propose a robust modeling framework that accounts for inliers, extremes, and the tail proportion. Parameter estimation is carried out using maximum likelihood. The proposed methodology is compared with classical numerical and graphical diagnostic tools, including the mean excess plot, parameter stability plot, Hill plot, and Pickands plot, as well as existing extreme value mixture models. The theoretical properties of the proposed model are established, and its performance is evaluated through extensive Monte Carlo simulations and real-data applications. The results demonstrate that the proposed methodology provides more accurate threshold estimation and more reliable extreme-value inference in the presence of inliers compared with existing classical approaches. Overall, the proposed methodology provides more accurate threshold estimation and tail inference in the presence of inliers, addressing key limitations of existing methods.
