In remotely sensed data analysis, a crucial problem is represented by the need to develop accurate models for the statistics of the pixel intensities. This paper deals with the problem of parametric probability density function (PDF) estimation in the context of Synthetic Aperture Radar (SAR) amplitude data analysis. Several theoretical and heuristic models for the PDFs of SAR data have been proposed in the literature, that have been proved to be effective for different land-cover typologies, thus making the choice of a single optimal SAR parametric PDF a hard task. In this paper, an innovative estimation algorithm is described, that faces such a problem by adopting a finite mixture model (FMM) for the amplitude PDF, with mixture components belonging to a given dictionary of SAR-specific PDFs. The method automatically integrates the procedures of selection of the optimal model for each component, of parameter estimation, and of optimization of the number of components by combining the Stochastic Expectation Maximization (SEM) iterative methodology with the recently developed "method-of-log-cumulants" (MoLC) for parametric PDF estimation. Experimental results on several real SAR images are reported, showing that the proposed method accurately models the statistics of SAR amplitude data.