Abstract: With a multiplicative speckle model, the unconditional density function of the mutli-look polarimetric synthetic aperture radar (SAR) data is derived, and the result is shown to be a generalized K-distribution. The multi-look intensity K-distribution is particularly compared with histograms of physical radar measurements of several typical terrain types and several empirical distributions. The relationship between the heterogeneity coefficient of the scene texture and the proper statistical distribution model is experimentally established. In addition, based on the results of the statistical analysis, an adaptive classification scheme is presented, and the improved classification shows the importance of the statistical analysis.