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The authors address the design, analysis, and experimental validation of statistical models for the description of targets fluctuations. First some classical distributions commonly employed for the statistical characterisation of the target amplitude returns are reviewed. Then, the authors focus on the shadowed Rice and the two-state Rayleigh-chi target models, discussing their physical justification and relevant analytical properties. The capabilities of the considered models to fit real target data collected by the McMaster IPIX radar in 1993 are also studied. Finally, the performance of the optimum detector (in the Neyman-Pearson sense) for targets with uniformly distributed phases in the presence of shadowed Rice and two-state Rayleigh-chi fluctuations is studied and analytical expressions are provided for the detection probability.