The results in Fig. indicate that the pure third order cumulant spectrum for this mildly non-Gaussian system already exhibits negative contributions to the spectral lineshape. For the underlying non-Gaussian statistics of the energy gap, a prefactor of Φ = 0.43 is predicted for this system. When applying the dampening factor to the spectral lineshape we indeed successfully remove the unphysical negative absorbance from the onset of the spectrum at 2.8 eV.