This paper provides a nearly complete analysis of the key distributions encountered in single- and multi-look polarimetric synthetic aperture radar data under the bivariate Gaussian and K -distribution models. It contains new analytic results on the moments of the amplitude and phase difference in single look data and on the moments of the amplitude in multi-look data. As yet no analytic results for the moments of multi-look phase difference have been found, except in limiting cases. The maximum likelihood estimators of the covariance matrix elements of two jointly Gaussian channels are derived, together with their asymptotic variances. The problems in extending this analysis to the bivariate K distribution are also discussed.

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