Synthetic aperture radar (SAR) image processing and analysis rely on statistical modeling and parameter estimation of the probability density functions that characterize data. The method of log-cumulants (MoLC) is a reliable alternative for parameter estimation of SAR data models and image processing. However, numerical methods are usually applied to estimate parameters using MoLC, and it may lead to a high computational cost. Thus, MoLC may be unsuitable for real-time SAR imagery applications such as change detection and marine search and rescue, for example. Our paper introduces a fast approach to overcome this limitation of MoLC, focusing on parameter estimation of single-channel SAR data modeled by the G⁰_I distribution. Experiments with simulated and real SAR data demonstrate that our approach performs faster than MoLC, while the precision of the estimation is comparable with that of the original MoLC. We tested the fast approach with multitemporal data and applied the arithmetic-geometric distance to real SAR images for change detection on the ocean. The experiments showed that the fast MoLC outperformed the original estimation method with regard to the computational time.