We present a comprehensive solar flare forecast model with a probability and a statistically significant range of daily peak X-ray flux. For this, we consider μ-corrected total unsigned radial magnetic fluxes from the SOHO/MDI and SDO/HMI, and flare lists from GOES from 1996 to 2021. Our model predicts two types of forecast results when a magnetic flux of an active region (AR) is given. First, using a relationship between magnetic fluxes and flaring rates, a probability of C1.0 or greater flares and a probability of M1.0 or greater flares within a day are predicted respectively. Second, a mean (μ) and standard deviation (σ) of daily peak X-ray fluxes are given from a historical distribution between magnetic fluxes and daily peak X-ray fluxes. Using the mean and standard deviation, we provide the statistical range of possible flare sizes. We verify two forecast results by using various performance metrics and investigate the performance depending on the climatology event rate. Based on the metric values, our model can give a better performance than the climatology forecast. Solar flares are considered to be caused by specific triggers and physical mechanisms that have not yet been precisely identified. In addition, there is another perspective that the size of the flare that will occur due to a trigger is close to random because the flaring loop is in a self-organized critical state. Our model can give the simplest forecasting results considering these two perspectives.

Introduction
Data and Method
    Total Unsigned Magnetic Fluxes
    GOES X-ray Flares
    Flare Identification
    Modeling and Test Data Sets
    Forecast Methods
Results and Discussions
Summary and Conclusions
Acknowledgments
References

• Daye Lim(Centre for mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, 3001 Leuven, Belgium, Solar-Terrestrial Centre of Excellence – SIDC, Royal Observatory of Belgium, 1180 Brussels, Belgium)
• Hyun-Jin Jeong(Centre for mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, 3001 Leuven, Belgium, School of Space Research, Kyung Hee University, Yongin-si, Gyeonggi-do 17104, Republic of Korea)
• Yong-Jae Moon(School of Space Research, Kyung Hee University, Yongin-si, Gyeonggi-do 17104, Republic of Korea, Department of Astronomy and Space Science, Kyung Hee University, Yongin-si, Gyeonggi-do 17104, Republic of Korea) Corresponding author