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 $q$-Gausian的分布是标准Gaussian分布的有力概括,通常用于各个领域,包括非广泛的统计力学、金融市场和图像处理,属于Q$分配家庭,其特点是非增加的酶,由于其多功能和实用性,$q美元-Gausians是测量模型中建模投入量的自然选择,本文介绍了独立的Gaussian随机变量的线性组合的特征,并提出了将其转换的数值方法,拟议技术使得能够评估线性测量模型中产出量的概率分布和计量学的不确定性分析。</s>