Characteristic Function of the Tsallis q-Gaussian and Its Applications in Measurement and Metrology

The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian and commonly used in various fields, including non-extensive statistical mechanics, financial markets image processing. It belongs to $q$-distribution family, which characterized by non-additive entropy. Due their versatility practicality, $q$-Gaussians are natural choice for modeling input quantities measurement models. This paper presents characteristic function linear combination independent random variables proposes numerical method its inversion. proposed technique makes it possible determine exact probability output quantity models, with modeled as variables. provides an alternative computational procedure Monte Carlo uncertainty analysis through propagation distributions.