The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets, and image processing. It belongs to the $q$-distribution family, which is characterized by a non-additive entropy. Due to their versatility and practicality, $q$-Gaussians are a natural choice for modeling input quantities in measurement models. This paper presents the characteristic function of a linear combination of independent $q$-Gaussian random variables and proposes a numerical method for its inversion. The proposed technique enables the assessment of the probability distribution of output quantities in linear measurement models and the conduct of uncertainty analysis in metrology.

翻译：Tsallis $q$-高斯分布是标准高斯分布的一种强大推广，广泛应用于非广延统计力学、金融市场和图像处理等领域。它属于$q$-分布族，其特征是非加性熵。由于$q$-高斯分布具有通用性和实用性，它成为测量模型中输入量建模的自然选择。本文给出了独立$q$-高斯随机变量线性组合的特征函数，并提出了一种数值求逆方法。所提出的技术能够评估线性测量模型中输出量的概率分布，并在计量学中进行不确定性分析。