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.
翻译:在本文中,我们介绍了对40次单一象牙状拉帕特分布试验的实证功率比较的结果,这种试验是利用蒙泰卡洛模拟模型进行的,样品大小为20、50、100、200美元,重要等级为=20、50、100、200美元,重要等级为$alpha=0.01、0.05、0.10美元,以及从11种模型中作为特殊案例的400种替代品,包括不对称和对称光/重尾发散;除了研究范围不相称外,一项令人感兴趣的贡献是提出选择替代品的创新设计提案;400种替代品包括20个具体案例,从主要11种模型中抽取的20个子模型;对于每个子模型,20个具体案例对应选定的参数值以覆盖全部功率范围;对结果的分析导致建议对替代分布的5个不同组进行最佳试验;还介绍了一个真实数据实例,对最近4年亚马孙鱼群每周的日志回报进行了适当的测试,以利得体样。