  This article introduces a novel probability distribution model, namely
Complex Isotropic {\alpha}-Stable-Rician (CI{\alpha}SR), for characterizing the
data histogram of synthetic aperture radar (SAR) images. Having its foundation
situated on the L\'evy {\alpha}-stable distribution suggested by a generalized
Central Limit Theorem, the model promises great potential in accurately
capturing SAR image features of extreme heterogeneity. A novel parameter
estimation method based on the generalization of method of moments to
expectations of Bessel functions is devised to resolve the model in a
relatively compact and computationally efficient manner. Experimental results
based on both synthetic and empirical SAR data exhibit the CI{\alpha}SR model's
superior capacity in modelling scenes of a wide range of heterogeneity when
compared to other state-of-the-art models as quantified by various performance
metrics. Additional experiments are conducted utilizing large-swath SAR images
which encompass mixtures of several scenes to help interpret the CI{\alpha}SR
model parameters, and to demonstrate the model's potential application in
classification and target detection.
