q-Gaussian Tsallis functions are probability distributions based on a generalized form of the exponential function, characterized by a continuous parameter q-index . The q-Gaussian function is given as 𝑓(𝑥) = 𝐶𝑒 𝑞 (-𝛽𝑥 2 ) , where 𝑒 𝑞 (. ) is the q-exponential function and 𝐶 a constant. We assume the exponent as 𝛽 = 1 (2𝜎 2 ) ⁄ , with variance σ. The q-exponential has expression: 𝑒𝑥𝑝 𝑞 (𝑢) = [1 + (1 -𝑞)𝑢] 1 (1-𝑞) ⁄ . In the range 1 < q < 2, the shape of q-Gaussian function is intermediate between the Gaussian and the Lorentzian profile. For q equal to 2, the q-Gaussian is the Cauchy-Lorentzian distribution . When q is close to 1, we have the usual Gaussian form (for q=1.01, q-Gaussian and Gaussian are numerically indistinguishable).