A comprehensive empirical power comparison of univariate goodness-of-fit tests for the Laplace distribution

In this paper, we survey the 40 univariate Laplace goodness-of-fit tests currently available in the literature. We provide a brief description of each test, and we include an expression of their test statistic. An empirical power comparison of the 40 tests is carried out using Monte Carlo simulations, with the sample sizes $n = 20, 50, 100, 200$, the significance levels $\alpha = 0.01, 0.05, 0.10$, and 400 alternatives comprising a variety of asymmetric and symmetric light/heavy-tailed distributions. Aside from the unmatched size of our study, the main contribution is the proposal of an innovative design for the selection of alternatives. The 400 alternatives are evenly divided into 20 classes, each of them corresponding to 20 alternatives of a specific family of distributions with the appropriate parameter chosen to cover the whole range of power curves. An analysis of the results leads to a recommendation of the best tests for different types of alternatives. A real-data example is also presented, where the Laplace tests are applied to the weekly log returns of the AMZN stock over a recent five-year period. Complete tables for the empirical power results are provided in the appendices.