  On the elementary level, electronic current consists of individual electron
tunnelling events that are separated by random time intervals. The waiting time
distribution is a probability to observe the electron transfer in the detector
electrode at time $t+\tau$ given that an electron was detected in the same
electrode at earlier time $t$. We study waiting time distribution for quantum
transport in a vibrating molecular junction. By treating the electron-vibration
interaction exactly and molecule-electrode coupling perturbatively, we obtain
master equation and compute the distribution of waiting times for electron
transport. The details of waiting time distributions are used to elucidate
microscopic mechanism of electron transport and the role of electron-vibration
interactions. We find that as nonequilibrium develops in molecular junction,
the skewness and dispersion of the waiting time distribution experience
stepwise drops with the increase of the electric current. These steps are
associated with the excitations of vibrational states by tunnelling electrons.
In the strong electron-vibration coupling regime, the dispersion decrease
dominates over all other changes in the waiting time distribution as the
molecular junction departs far away from the equilibrium.
