In this paper, statistical distribution functions are developed for distance determination of stellar groups. This method depends on the assumption that absolute magnitudes and apparent magnitudes follow a Gaussian distribution function. Due to the limits of the integrands of the frequency function of apparent and absolute magnitudes, we introduce Case A, B, and C Gaussian distributions. The developed approaches have been implemented to determine distances to some clusters and stellar associations. The comparison with the distances derived by different authors reveals good agreement.

A new method has been developed to solve the star cluster membership problem. It is based on synthetic photometry employing the Black Body concept as stellar radiation simulator. Synthetic color-magnitude diagram is constructed showing the main sequence band and the positions of binary star systems of combinations of various components through different photometric tracks. The method has been applied to the Hyades. The cluster membership problem has been re-appraised for the cluster (both single and binary) stars. For the binary members, the components' spectral types have been derived by the method. The results obtained agree very well with those found in literature, The method is simpler than the others and can be developed to undertake other cases as multiple star systems.