An analytical and adjustable model is proposed, by which the probability density of hourly global irradiance may be derived from long-term mean global irradiation. The model explicitly accounts for the bimodal character of the probability density of solar irradiance, and it is tuned to a developmental data sample and verified against an independent data base. In combination with previously published deterministic models this probability density model even forms a composite model which yields the probability density of hourly irradiance (total, beam or diffuse) on arbitrarily orientated planes. This composite model is also verified against the independent data base.