Abstract

We present a method to obtain the completeness limit of a sample of proper motions using Hanson's approximation {Hanson [MNRAS, 186, 875 (1979)]} and to obtain the distance up to which the detection of moving group members is complete. We also generalize Eddington's position angle distribution analysis to the case of different velocity dispersions in each of the tangential coordinates, a nonzero velocity centroid (V(alpha-O, V(delta-O), and a nonzero correlation coefficient r. Using that generalization we suggest a way to fit the observed position angle distribution to obtain the number of objects and a nonbiased velocity dispersion estimation for the moving group. In order to apply the above-mentioned formalism, we calculate the velocity ellipsoid parameters for the Hyades and UMa moving groups using their most probable members distributed in half of the celestial sphere and brighter than V = 7.1 mag, as given by Eggen [PASP, 97, 807 (1985); 98, 423 (1986)].