  We analyze the deviations from Maxwell-Boltzmann statistics found in recent
experiments studying velocity distributions in two-dimensional granular gases
driven into a non-equilibrium stationary state by a strong vertical vibration.
We show that in its simplest version, the ``stochastic thermostat'' model of
heated inelastic hard spheres, contrary to what has been hitherto stated, is
incompatible with the experimental data, although predicting a reminiscent high
velocity stretched exponential behavior with an exponent 3/2. The experimental
observations lead to refine a recently proposed random restitution coefficient
model. Very good agreement is then found with experimental velocity
distributions within this framework, which appears self-consistent and further
provides relevant probes to investigate the universality of the velocity
statistics.
