Maximum likelihood estimation of the mean parallax and the kinematic parameters of moving clusters.

On the basis of the maximum likelihood principle, a new approach for simultaneous determination of the distance and the kinematic parameters including their dispersions of a moving cluster is developed in this paper so as to theoretically improve the conventional standard convergent point method. It is shown from applying this approach to the Hyades cluster that it is not only theoretically rigorous but also practically feasible, with which we have derived that the distance of the cluster is d=45.53+/-0.43 pc with the dispersion σ_d_=2.65+/-0.41 pc (corresponding to a distance modulus m-M=3.29^+0.03^_-0.02_mag and its dispersion σ_(m-M)_=0.13+/-0.02mag), its space velocity V=48.26+/-0.09km/s with the dispersion σ_v_=0.44+/-0.04km/s, and the coordinates of the convergent point (A,D)=(98.33+/-0.24deg, 6.62+/-0.16deg). It is indicated from detailed discussions that in order to reduce the effect of field star contamination as much as possible adopting a sample of cluster stars with high membership probabilities is of great importance for studies on star clusters.