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In the context of synthetic aperture radar (SAR) image processing and applications, the precise modeling of statistical knowledge is a crucial problem. In this paper, an efficient and flexible statistical model, called generalized Gamma Rayleigh (G??R) distribution, for amplitude SAR images is proposed by assuming a two-sided generalized Gamma distribution for the real and imaginary parts of the complex SAR backscattered signal. It is shown that the Rayleigh and recently proposed generalized Gaussian Rayleigh distributions can be regarded as special cases of G??R distribution. Considering that the probability density function estimation problem is formulated as a parameter estimation one for the parametric statistical analysis of SAR images, a two-stage estimator based on second-kind cumulants is derived for the parameters of G??R distribution. Furthermore, experimental results on several actual SAR images are given to demonstrate the validity and flexibility of the proposed model.