For testing whether a distribution function is heavy tailed, we study the Kolmogorov test, Berk-Jones test, score test and their integrated versions. A comparison is conducted via Bahadur efficiency and simulations. The score test and the integrated score test show the best performance. Although the Berk-Jones test is more powerful than the Kolmogorov-Smirnov test, this does not hold true for their integrated versions; this differs from results in \\citet{EinmahlMckeague2003}, which shows the difference of Berk-Jones test in testing distributions and tails.

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Keywords Bahadur efficiency, heavy tail, tail index
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Koning, A.J., & Peng, L.. (2005). Goodness-of-fit tests for a heavy tailed distribution (No. EI 2005-44). Report / Econometric Institute, Erasmus University Rotterdam. Retrieved from