The L\'evy distribution, alongside the Normal and Cauchy distributions, is one of the only three stable distributions whose density can be obtained in a closed form. However, there are only a few specific goodness-of-fit tests for the L\'evy distribution. In this paper, two novel classes of goodness-of-fit tests for the L\'evy distribution are proposed. Both tests are based on V-empirical Laplace transforms. New tests are scale free under the null hypothesis, which makes them suitable for testing the composite hypothesis. The finite sample and limiting properties of test statistics are obtained. In addition, a generalization of the recent Bhati-Kattumannil goodness-of-fit test to the L\'evy distribution is considered. For assessing the quality of novel and competitor tests, the local Bahadur efficiencies are computed, and a wide power study is conducted. Both criteria clearly demonstrate the quality of the new tests. The applicability of the novel tests is demonstrated with two real-data examples.

翻译：Lévy分布与正态分布、柯西分布并列为仅有的三种密度函数具有封闭形式的稳定分布。然而针对Lévy分布的专门拟合优度检验方法却十分有限。本文提出了两类新颖的Lévy分布拟合优度检验方法，两类检验均基于V-经验拉普拉斯变换。新检验在零假设下具有尺度不变性，适用于复合假设检验场景。我们推导了检验统计量的有限样本性质与极限性质，并进一步将近期提出的Bhati-Kattumannil拟合优度检验方法推广至Lévy分布。为评估新检验方法与竞争方法的性能，我们计算了局部Bahadur效率并开展了广泛的功效研究，两项指标均充分证明了新检验方法的优越性。通过两个实际数据案例展示了新检验方法的应用价值。