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.
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