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Comparative analysis of scalar upper tail indicators
Hydrological Sciences Journal ( IF 2.8 ) Pub Date : 2020-05-15
L.M. Wietzke, B. Merz, L. Gerlitz, H. Kreibich, B. Guse, A. Castellarin, S. Vorogushyn

Different upper tail indicators exist to characterize heavy tail phenomena, but no comparative study has been carried out so far. We evaluate the shape parameter (GEV), obesity index, Gini index and upper tail ratio (UTR) against a novel benchmark of tail heaviness – the surprise factor. Sensitivity analyses to sample size and changes in scale-to-location ratio are carried out in bootstrap experiments. The UTR replicates the surprise factor best but is most uncertain and only comparable between records of similar length. For samples with symmetric Lorenz curves, shape parameter, obesity and Gini indices provide consistent indications. For asymmetric Lorenz curves, however, the first two tend to overestimate, whereas Gini index tends to underestimate tail heaviness. We suggest the use of a combination of shape parameter, obesity and Gini index to characterize tail heaviness. These indicators should be supported with calculation of the Lorenz asymmetry coefficients and interpreted with caution.



中文翻译:

标量上尾指标比较分析

存在用于表征重尾现象的不同上尾指标,但是迄今为止尚未进行比较研究。我们根据新的尾巴重量基准(意外因素)评估形状参数(GEV),肥胖指数,基尼指数和上尾巴比(UTR)。在自举实验中进行了对样品大小和比例位置比变化的敏感性分析。UTR可以最好地复制意外因素,但不确定性最大,并且只能在长度相似的记录之间进行比较。对于具有对称Lorenz曲线的样本,形状参数,肥胖率和Gini指数提供一致的指示。但是,对于不对称的Lorenz曲线,前两个倾向于高估,而Gini指数则倾向于低估尾重。我们建议使用形状参数的组合,肥胖和基尼系数来表征尾巴的重量。这些指标应以洛伦兹不对称系数的计算为依据,并应谨慎解释。

更新日期:2020-05-15
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