Power of One-Sample Location Tests Under Distributions with Equal Lévy Distance

Abstract

In this article, we study the power of one-sample location tests under classical distributions and two supermodels which include the normal distribution as a special case. The distributions of the supermodels are chosen in such a way that they have equal distance to the normal as the logistic, uniform, double exponential, and the Cauchy, respectively. As a measure of distance we use the Lévy metric. The tests considered are two parametric tests, the t-test and a trimmed t-test, and two nonparametric tests, the sign test and the Wilcoxon signed-rank tests. It turns out that the power of the tests, first of all, does not depend on the Lévy distance but on the special chosen supermodel.

Keywords:

• Lévy metric
• Location alternatives
• Measure of tailweight
• Monte Carlo simulation
• Non normality
• Nonparametric tests
• Parametric tests
• Power comparison
• Supermodel

Mathematics Subject Classification:

• G2F03
• G2G35