Inverse cumulative distribution of a generalized q-exponential, N _≥ (x) = Mexp_q( − β_qx^γ). γ = 1 is a q-exponential, γ = 2 is a q-Gaussian, M is the size of the sample. Values of the parameters for this particular instance are q = 1.5, β_q = 0.1 and M = 10⁴. The transition point (x ^∗ )^γ given by Eq. (8) is indicated. Dashed curve (red online) is an ordinary (q = 1) exponential with β₁ = 0.1 and M = 10⁴. Evidently, the tail behavior is entirely different from both curves.