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

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 , and 400 alternatives consisting of asymmetric and symm...

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Bibliographic Details
Published in:Journal of statistical computation and simulation 2022-12, Vol.92 (18), p.3743-3788
Main Authors: Desgagné, Alain, Lafaye de Micheaux, Pierre, Ouimet, Frédéric
Format: Article
Language:English
Subjects:
double exponential
Empirical analysis
Goodness of fit
goodness-of-fit tests
heavy-tailed distributions
Laplace distribution
Mathematics
Monte Carlo simulations
power comparison
Primary 62F03
Statistical tests
Statistics
symmetric distributions
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Summary: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 , 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.
ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2022.2082428