In this paper we introduce a novel statistical framework based on the first two quantile conditional moments that facilitates effective goodness-of-fit testing for one-sided L\'evy distributions. The scale-ratio framework introduced in this paper extends our previous results in which we have shown how to extract unique distribution features using conditional variance ratio for the generic class of {\alpha}-stable distributions. We show that the conditional moment-based goodness-of-fit statistics are a good alternative to other methods introduced in the literature tailored to the one-sided L\'evy distributions. The usefulness of our approach is verified using an empirical test power study. For completeness, we also derive the asymptotic distributions of the test statistics and show how to apply our framework to real data.

翻译：本文提出了一种基于前两个分位数条件矩的新型统计框架，可有效实现对单侧Lévy分布的拟合优度检验。本文引入的尺度比框架拓展了我们先前的研究成果——此前我们已证明如何利用条件方差比对广义α-稳定分布类提取分布特征。研究表明，基于条件矩的拟合优度统计量是文献中针对单侧Lévy分布设计的其他方法的有效替代方案。通过经验检验功效研究验证了本方法的实用性。为完整起见，我们还推导了检验统计量的渐近分布，并展示了如何将所提框架应用于实际数据。