||The determination of the all-sky radiance distribution produced by artificial light sources is a computationally demanding task that generally requires intensive calculations. In this paper, we develop an analytical formulation that provides the all-sky radiance distribution produced by an artificial light source as an explicit and analytical function of the observation direction, depending on two single parameters that characterize the overall effects of the atmosphere. One of these parameters is related to the effective attenuation of the light beams, whereas the other accounts for the overall asymmetry of the combined scattering processes in molecules and aerosols. Using this formulation, a wide range of all-sky radiance distributions can be efficiently and accurately calculated in a short time. This substantial reduction in the number of required parameters, in comparison with other approaches that are currently used, is expected to facilitate the development of new applications in the field of light pollution research.