  We combine the catalogs of compact high-velocity HI clouds extracted from the
LDS and HIPASS surveys and analyze the all-sky properties of the ensemble. Five
principal observables are defined for the CHVC population: (1) the spatial
deployment of the objects on the sky, (2) the kinematic distribution, (3) the
number distribution of observed HI column densities, (4) the number
distribution of angular sizes, and (5) the number distribution of HI linewidth.
Two classes of models are considered to reproduce the observed properties. The
agreement of models with the data is judged by extracting these same
observables from simulations, in a manner consistent with the sensitivities of
the observations and explicitly taking account of Galactic obscuration. We show
that models in which the CHVCs are the HI counterparts of dark-matter halos
evolving in the Local Group potential provide a good match to the observables.
The best-fitting populations have a maximum HI mass of 10^7 M_Sun a power-law
slope of the HI mass distribution in the range -1.7 to -1.8, and a Gaussian
dispersion for their spatial distributions of between 150 and 200 kpc centered
on both the Milky Way and M31. Given its greater mean distance, only a small
fraction of the M31 sub-population is predicted to have been detected in
present surveys. An empirical model for an extended Galactic halo distribution
for the CHVCs is also considered. While reproducing some aspects of the
population, this class of models does not account for some key systematic
features of the population.
