A Simulation Analysis of the Power of Several Tests for Detecting Heavy-Tailed Distributions

Abstract

This article presents estimates of the power of five tests for detecting heavy-tailed distributions with the null hypothesis of normality and alternative hypotheses of each of eleven members of the symmetric stable Paretian distribution. The findings indicate that for small samples and low values of the characteristic exponent, the ratio of the standard deviation to mean deviation would be the most appropriate test. With larger sample sizes and/or larger values of the characteristic exponent, Kurtosis and the ratio of one-half the range to the mean deviation from the sample median appear to be the best tests.