  We use a three-dimensional molecular dynamics simulation to study the single
particle distribution function of a dilute granular gas driven by a vertically
oscillating plate at high accelerations ($15g - 90g$). We find that the density
and the temperature fields are essentially time-invariant above a height of
about 35 particle diameters, where typically 20% of the grains are contained.
These grains form the nonequilibrium steady state granular gas with a Knudsen
number unity or greater. In the steady state region, the distribution function
of horizontal velocities (scaled by the local horizontal temperature) is found
to be nearly independent of height, even though the hydrodynamic fields vary
with height. The high energy tails of the distribution functions are described
by a stretched exponential $\sim \exp(-{\cal B}c_x^{\alpha})$, where $\alpha$
depends on the normal coefficient of restitution $e$ ($1.2 < \alpha < 1.6$),
but $\alpha$ does not vary for a wide range of the friction parameter. We find
that the distribution function of a {\it frictionless} inelastic hard sphere
model can be made similar to that of a frictional model by adjusting $e$.
However, there is no single value of $e$ that mimics the frictional model over
a range of heights.
