Often, solar irradiation estimation from simply measureable sunshine duration data is achieved by linear and nonlinear regression expressions, which depicts the statistical regression equation between the sunshine duration and solar irradiation data. These models are based on statistical parameters only, and therefore, the estimations do not take into consideration deviations from the averages. In this paper, an innovative probability methodology is proposed for solar irradiation estimation, which is based on the cumulative probability distribution functions (CDFs) of the sunshine duration and solar irradiation data. For this purpose, the sunshine duration data are converted to match the solar irradiation data cumulative distribution (CDF), which is then employed for the solar irradiation estimation. Hence, the CDFs of sunshine duration and solar irradiation data are preserved, and rather than global average, pointwise solar irradiation estimations are achieved. The application of the innovative probabilistic methodology is presented for seven solar irradiation measurements stations from different climate regions in Turkey. It is shown that the suggested method over performs other methodologies with very high improvements. Copyright (C) 2016 John Wiley & Sons, Ltd.