The generalized fractal-diffusive SOC model predicts the probability distribution functions for each parameter as a function of the dimensionality, diffusive spreading exponent, fractal dimension, and type of (coherent/incoherent) radiation process. The waiting time distributions are predicted by the FD-SOC model to follow a power law with a slope of during active and contiguously flaring episodes, while an exponential cutoff is predicted for the time intervals of quiescent periods. This dual regime of the waiting time distribution predict both persistence and memory during the active periods, and stochasticity during the quiescent periods. These predictions provide useful constraints of the physical parameters and underlying scaling laws. Significant deviations from the size distributions predicted by the FD-SOC model could indicate problems with the measurements or data analysis. The generic FD-SOC model is considered to have universal validity and explains the statistics and scaling between SOC parameters but does not reveal the detailed physical mechanism that governs the instabilities and energy dissipation in a particular SOC process.