A new test for tail index with application to Danish fire loss data

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.