  We investigate the viability of Galactic corona models of gamma-ray bursts by
calculating the spatial distribution expected for a population of high-velocity
neutron stars born in the Galactic disk and moving in a gravitational potential
that includes the Galactic bulge, disk, and a dark matter halo. We consider
models in which the bursts radiate isotropically and in which the radiation is
beamed. We place constraints on the models by comparing the resulting
brightness and angular distributions with the data in the BATSE 3B catalog. We
find that, if the burst sources radiate isotropically, the Galactic corona
model can reproduce the BATSE peak flux and angular distributions for neutron
star kick velocities > 800 km s$^{-1}$, source turn-on ages > 20 Myrs, and
BATSE sampling distances 130 kpc < d_{max} < 350 kpc. If the radiation is
beamed, no turn-on age is required and agreement with the BATSE data can be
found provided that the width of the beam is less than 20 deg.
