In the case of the q-Gaussian function, the physics of the q-parameter is in its ability to evaluate the power law of the wings, as previously discussed. Moreover, as recently shown in ijSciences, 2024, properly fitted q-Gaussian functions can be also proposed for the Kubo lineshapes, which are the Fourier transforms of Kubo stochastic time-correlation functions. In this manner a q-Gaussian function, with its simple analytic expression, can be used as a substitute of Kubo lineshape, which is requiring a numerical Fourier transform calculation. The value of the q-parameter turns out to the related to the time scales of dynamics (fast q=2, mid q=1.4, and slow q=1). Then, besides its ability of evaluating the power law of wings, the q-Gaussian is also providing an estimation of the process modulation.