We introduce two ratio-based robust test statistics, max-robust-sum (MRS) and sum-robust-sum (SRS), designed to enhance the robustness of outlier detection in samples with exponential or Pareto tails. We also reintroduce the inward sequential testing method -- formerly relegated since the introduction of outward testing -- and show that MRS and SRS tests reduce susceptibility of the inward approach to masking, making the inward test as powerful as, and potentially less error-prone than, outward tests. Moreover, inward testing does not require the complicated type I error control of outward tests. A comprehensive comparison of the test statistics is done, considering performance of the proposed tests in both block and sequential tests, and contrasting their performance with classical test statistics across various data scenarios. In five case studies -- financial crashes, nuclear power generation accidents, stock market returns, epidemic fatalities, and city sizes -- significant outliers are detected and related to the concept of `Dragon King' events, defined as meaningful outliers that arise from a unique generating mechanism.

翻译：本文引入了两种基于比率的稳健检验统计量——最大稳健和（MRS）与总和稳健和（SRS），旨在增强具有指数或帕累托尾样本中离群值检测的稳健性。同时，我们重新引入了内序逐步检验方法（该方法自外序检验提出后长期被忽视），并证明MRS与SRS检验能有效降低内序方法对掩蔽效应的敏感性，使其检验效能与外序检验相当，且可能更不易出错。此外，内序检验无需外序检验中复杂的I类误差控制。研究对检验统计量进行了全面比较，考察了所提检验在分块检验与序贯检验中的性能，并在多种数据情境下将其与经典检验统计量进行对比。通过五个案例研究——金融危机、核电事故、股市收益、疫情死亡人数与城市规模——我们检测到显著离群值，并将其与“龙之王”事件概念相关联；该概念特指由独特生成机制产生的、具有实际意义的离群值。