The problem of estimating the tail index in heavy-tailed distributions is very important in a variety of applications. Three new graphical methods, the H(k ) plot, the K(k ) plot, and the Sum plot, are proposed for choosing the appropriate number of upper order statistics used in the estimation of the tail index. The Sum plot exhibits stable patterns and facilitates the choice of the correct number of upper order statistics involved in this estimation. Its theoretical properties are investigated. The performance of these procedures in finite samples are examined through a simulation study when the data are from a Pareto, an Inverted Gamma, and a Symmetric α-Stable distribution and are also applied to several real data sets. The results suggest that the Sum plot, together with the Hill estimator, overcomes many of the uncertainties present in some of the most common techniques used in the estimation of the tail index, such as the Hill, the Zipf, and the CD plots.
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机译：在各种应用中，估计重尾分布中的尾部索引问题非常重要。三种新的图形化方法， H （ k ）图， K （ k ）图和Sum图来选择合适的用于估计尾部索引的高阶统计量。 Sum图显示出稳定的模式，并有助于选择此估计中涉及的正确数量的高阶统计量。研究其理论性质。当数据来自帕累托，反伽马和对称α-稳定分布时，将通过模拟研究检查这些程序在有限样本中的性能，并将这些结果应用于多个实际数据集。结果表明，Sum图与Hill估计器共同克服了一些用于尾部指数估计的最常见技术（例如Hill，Zipf和CD图）中存在的许多不确定性。
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