  We consider the accretion model for anomalous X-ray pulsars proposed recently
by Chatterjee, Hernquist and Narayan, in which the emission is powered by
accretion from a fossil disk formed by the fallback of material from a
supernova explosion. We demonstrate that this model is able to account for the
spin period, luminosity and age distributions of the observed population of
AXPs for reasonable and broad distributions of the free parameters of the
model, namely, the surface magnetic field of the neutron star, the mass of its
accretion disk and its initial spin period. In particular, this model is able
statistically to account for the puzzlingly narrow observed spin distribution
of the AXPs. We show also that if the establishment of fallback accretion disks
around isolated neutron stars is a universal phenomenon, then a fairly large
minority ($\sim 20%$) of these objects become X-ray bright AXPs or X-ray faint
systems spinning down by propeller action, while the rest become radio pulsars.
