Goodness-of-fit tests for a heavy tailed distribution

Abstract

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