The class of \(\alpha\)-stable distributions is ubiquitous in many areas including signal processing, finance, biology, physics, and condition monitoring. In particular, it allows efficient noise modeling and incorporates distributional properties such as asymmetry and heavy-tails. Despite the popularity of this modeling choice, most statistical goodness-of-fit tests designed for \(\alpha\)-stable distributions are based on a generic distance measurement methods. To be efficient, those methods require large sample sizes and often do not efficiently discriminate distributions when the corresponding \(\alpha\)-stable parameters are close to each other. In this paper, we propose a novel goodness-of-fit method based on quantile (trimmed) conditional variances that is designed to overcome these deficiencies and outperforms many benchmark testing procedures. The effectiveness of the proposed approach is illustrated using extensive simulation study with focus set on the symmetric case. For completeness, an empirical example linked to plasma physics is provided.

类的\（\阿尔法\） -stable分布是在许多领域，包括信号处理，金融，生物，物理，和状态监测无处不在。特别是，它允许有效的噪声建模并结合分布特性，例如不对称和重尾。尽管这种建模选择很受欢迎，但大多数为\(\alpha\) 稳定分布设计的统计拟合优度测试都基于通用距离测量方法。为了提高效率，这些方法需要大样本量，并且当相应的\(\alpha\)-stable 参数彼此接近。在本文中，我们提出了一种基于分位数（修剪）条件方差的新型拟合优度方法，旨在克服这些缺陷并优于许多基准测试程序。所提出的方法的有效性通过广泛的模拟研究来说明，重点集中在对称情况上。为完整起见，提供了一个与等离子体物理学相关的经验示例。