The conditional approach of Hill's estimator depends on a threshold choice. This may give different results in a statistical test when different thresholds are used. Motivated by the uniformly most powerful test, this article proposes a new test for heavy tail of various degrees. Simulation shows that the test is applicable and its power is superior to three existing methods in the literature. An example of the Danish fire loss data elucidates the inconsistent conclusion in existing statistical tests and demonstrates the consistent conclusion the proposed test leads to. A new and affirmative insight into the data is that the variance does not exist.

中文翻译：

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应用于丹麦火灾损失数据的尾部指数新测试

Hill 估计量的条件方法取决于阈值选择。当使用不同的阈值时，这可能会在统计测试中给出不同的结果。在统一最强测试的推动下，本文提出了不同程度的重尾测试。仿真表明，该测试是适用的，其功效优于文献中现有的三种方法。丹麦火灾损失数据的一个例子阐明了现有统计测试中不一致的结论，并证明了提议的测试得出的一致结论。对数据的一个新的、肯定的见解是差异不存在。