A novel data analysis procedure is described, based on a variational solution of the Schrodinger equation, that can be used to analyze gas electron diffraction (GED) data obtained from molecular ensembles in nonequilibrium (non-Boltzmann) vibrational distributions. The method replaces the conventional expression used in GED studies, which is restricted to molecules with small-amplitude vibrations in equilibrium distributions, and is important in time-resolved (stroboscopic) GED, a new tool developed to study the nuclear dynamics of laser-excited molecules. As an example, the new formalism has been used to investigate the structural and vibrational kinetics of C equivalent to S, using stroboscopic GED data recorded during the first 120 ns following the 193 nm photodissociation of CS2. Temporal changes of vibrational population are observed, which can be rationalized by collision-induced electronic-to-vibrational energy transfer from excited S(D-1) atoms to ground state C equivalent to S and CS2. The time-evolution of the energy transfer is modeled by determining the vibrational distributions and mean internuclear distances (r(a,g)) of C equivalent to S as functions of delay time. Inverted (non-Boltzmann) distributions are observed, and the refined parameters of model distributions are presented.