Testing for Heavy Tails using Empirical Distribution Shape: The Tail Ratio Test

We look at goodness-of-fit tests for heavy tailed distributions. As these distributions are found in numerous fields, adequate goodness-offit testing helps to correctly model them. We inspect the power of four different tests to find the best one: the Kolmogorov-Smirnov test, the Anderson-Darling test, the Estimated Score test and the Tail Ratio test. The latter is developed in this paper. We use simulation to find critical values of these tests and use simulation once again to find their power. Our results show that the Tail Ratio test has the highest power of the four tests.