Radiation forecast accounting for daily and instantaneous variability was pursued by means of a new bi-parametric statistical model that builds on a model previously proposed by the same authors. The statistical model is developed with direct reference to the Liu-Jordan clear sky theoretical expression but is not bound by a specific clear sky model; it accounts separately for the mean daily variability and for the variation of solar irradiance during the day by means of two corrective parameters. This new proposal allows for a better understanding of the physical phenomena and improves the effectiveness of statistical characterization and subsequent simulation of the introduced parameters to generate a synthetic solar irradiance time series. Furthermore, the analysis of the experimental distributions of the two parameters’ data was developed, obtaining opportune fittings by means of parametric analytical distributions or mixtures of more than one distribution. Finally, the model was further improved toward the inclusion of weather prediction information in the solar irradiance forecasting stage, from the perspective of overcoming the limitations of purely statistical approaches and implementing a new tool in the frame of solar irradiance prediction accounting for weather predictions over different time horizons.