  In this paper we present the results from an empirical power comparison of 40
goodness-of-fit tests for the univariate Laplace distribution, carried out
using Monte Carlo simulations with sample sizes $n = 20, 50, 100, 200$,
significance levels $\alpha = 0.01, 0.05, 0.10$, and 400 alternatives
consisting of asymmetric and symmetric light/heavy-tailed distributions taken
as special cases from 11 models. In addition to the unmatched scope of our
study, an interesting contribution is the proposal of an innovative design for
the selection of alternatives. The 400 alternatives consist of 20 specific
cases of 20 submodels drawn from the main 11 models. For each submodel, the 20
specific cases corresponded to parameter values chosen to cover the full power
range. An analysis of the results leads to a recommendation of the best tests
for five different groupings of the alternative distributions. A real-data
example is also presented, where an appropriate test for the goodness-of-fit of
the univariate Laplace distribution is applied to weekly log-returns of Amazon
stock over a recent four-year period.
