Predictions for the apparent velocity statistics under simple beaming models are presented and compared to the observations. The potential applications for tests of unification models and for cosmology (source counts, measurements of the Hubble constant H0 and the deceleration parameter q0) are discussed. First results from a large homogeneous survey are presented. The data do not show compelling evidence for the existence of intrinsically different populations of galaxies, BL Lacertae objects, or quasars. Apparent velocities betaapp in the range 1-5 h-1, where h = H0/100 km.s-1.Mpc-1 [1 megaparsec (Mpc) = 3.09 x 10(22) m], occur with roughly equal frequency; higher values, up to betaapp = 10 h-1, are rather more scarce than appeared to be the case from earlier work, which evidently concentrated on sources that are not representative of the general population. The betaapp distribution suggests that there might be a skewed distribution of Lorentz factors over the sample, with a peak at gammab approximately 2 h-1 and a tail up to at least gammab approximately 10 h-1. There appears to be a clearly rising upper envelope to the betaapp distribution when plotted as a function of observed 5-GHz luminosity; a combination of source counts and the apparent velocity statistics in a larger sample could provide much insight into the properties of radio jet sources.