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We combine the catalog of compact high–velocity H <ns0:sc>i </ns0:sc>clouds extracted by de Heij et al. ([CITE]) from the Leiden/Dwingeloo Survey in the northern hemisphere with the catalog extracted by Putman et al. ([CITE]) from the Parkes HIPASS data in the southern hemisphere, and analyze the all–sky properties of the ensemble. Compact high–velocity clouds are a subclass of the general high–velocity cloud phenomenon which are isolated in position and velocity from the extended high–velocity Complexes and Streams down to column densities below $1.5\times10^{18}$ cm-2. Objects satisfying these criteria for isolation are found to have a median angular size of less than one degree. We discuss selection effects relevant to the two surveys; in particular the crucial role played by obscuration due to Galactic H <ns0:sc>i</ns0:sc>. 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 H <ns0:sc>i </ns0:sc>column densities, (4) the number distribution of angular sizes, and (5) the number distribution of H <ns0:sc>i </ns0:sc> 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 H <ns0:sc>i </ns0:sc>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 $10^7\;M_\odot$, 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 M 31. Given its greater mean distance, only a small fraction of the M 31 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.