The q-Gaussians, also known as "Tsallis functions", are probability distributions derived from the Tsallis statistics . The q-Gaussians are based on a generalized form of the exponential function (see discussion in , characterized by a continuous parameter q in the range 1 < q < 3. As given by , the q-Gaussian is based on function 𝑓(𝑥) = 𝐶𝑒 𝑞 (-𝛽𝑥 2 ) , where 𝑒 𝑞 (. ) is the q-exponential function and 𝐶 a constant. The q-exponential has expression: