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

TL;DR

This study empirically compares the power of 40 goodness-of-fit tests for the univariate Laplace distribution using extensive simulations across various sample sizes, significance levels, and alternative distributions, providing practical recommendations.

Contribution

It introduces an innovative design for selecting alternatives and offers comprehensive power comparisons, enhancing the understanding of test performances for the Laplace distribution.

Findings

Identifies the most powerful tests for different distribution groups

Provides practical recommendations for test selection in real-world data

Demonstrates the application of tests on Amazon stock returns

Abstract

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.