The K and G0 distributions are widely used to establish models for polarimetric synthetic aperture radar (PolSAR) data. The estimation of their texture parameters is an important factor in their utilization. Traditionally, the method of matrix log cumulants (MoMLC) is adopted for its low bias and variance properties. Recently, the MFM, which is an estimator based on fractional moments of the multilook polarimetric whitening filter (MPWF), is exploited due to its lower mean square error. However, these estimators are implemented by solving the implicit equations, which are computationally complicated. We propose two new estimators based on the moments for each of the K and G0 distributions. Both estimators have analytical expressions, which allow rapid calculations. Using the simulated data, comparisons about the accuracy and speed are presented to demonstrate the performance of our estimators. The results show that the proposed estimators yield a faster calculating speed while retaining the accuracy. Finally, a goodness-of-fit test based on MLCs has been used to assess the fitting accuracy of the estimators for real PolSAR data, and the results are according to those from the simulated data.