The statistics of the covariance matrix with the Wishart distribution is fully developed to be used in the data analysis of multilook polarimetric radar images.The determinant of the covariance matrix describes the distributed degree of target scattering

which gives a good performance in parameter estimation.In this paper a comparison has been performed among the determinant of the normalized covariance matrix

polarization entropy and polarization diversity

which all characterize the distributed degree of the random scattering.The mathematical relations among them are been presented with the two variables:the degree of polarization and the degree of direction.The differences among three characterizing methods only lie on the different combination of the two variables.Then the statistics of the determinant of the Wishart distribution is analyzed via Mellin transform.The log-cumulants are obtained from the distribution of the determinant of a complex Wishart distributed matrix based on its characteristic function of the logarithm of the determinant of a complex covariance matrix.The probability density function of the determinant of the matrix is derived.The maximum likelihood estimation (MLE) is put up to improve the precision of parameter estimation based on the distribution of the determinant of the matrix.Finally the simulated data and experiment data are used to verify the correctness of the above theory

and the results are according to our derivation.The statistics of the determinant and the novel ML estimator of the equivalent number of looks are helpful to target detection

parameter estimation and segmentation.