  We analyze the effect of electron-phonon coupling on the full counting
statistics of a molecular junction beyond the lowest order perturbation theory.
Our approach allows to take into account analytically the feedback between the
non-equilibrium phonon and electronic distributions in the quantum regime. We
show that even for junctions with high transmission and relatively weak
electron-phonon coupling this feedback gives rise to increasingly higher
nonlinearities in the voltage dependence of the cumulants of the transmitted
charges distribution.
