In this paper. the influence of the measurement interval of solar radiation data on the cumulative probability distribution of the clearness index is studied. The distribution observed in southern Spain is bimodal using 5 min data, and this property fades away as the data are aggregated over larger time intervals, and it also depends on the air mass. This is used to confirm the existence of two kinds of types of radiation associated with clear or cloudy skies. Also, with 5 min radiation data, anew statistical model is proposed, based on a mixture of two normal distributions, which provides a good Bt for the data measured in Seville.