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

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 4-year period.

Keywords:

• Laplace distribution
• goodness-of-fit tests
• Monte Carlo simulations
• power comparison
• double exponential
• symmetric distributions
• heavy-tailed distributions

AMS:

• Primary 62F03

Acknowledgments

This research includes computations performed using the computational cluster Katana supported by Research Technology Services at UNSW Sydney. Three anonymous referees have helped us greatly improve the paper. We are particularly grateful to one of the referees who spent a considerable amount of time improving its writing. We also thank the referees, the anonymous Associate Editor and the Editor in Chief for their patience.

Disclosure statement

No potential conflict of interest was reported by the authors.