Abstract: K-distribution has been proved to be a good model for describing the statistical properties of clutter in multi-look synthetic aperture radar (SAR) images. However, the form of characteristic functions and the statistics are rare in reports. The close form s of the first and second characteristic function of the first and second kind are derived using the Fourier and Mellin transform, respectively. The formulas of moments, cumulants, log-moments and log-cumulants are also deduced, and also the method of log-cumulants (MOLC) and the method of moments (MOM) parameter estimators. Finally, the normalized biases and variances are calculated through Kendall's approach of approximate expansion. Theoretical analysis results show that MOLC has better performance in comparison with MOM when the true order parameter is small and the number of SAR imagery samples is relatively low.