Statistics of CMB polarization angles

We study the distribution functions of the CMB polarization angle, focusing on the Planck 2018 CMB maps. We extend the model of Preece & Battye (2014) of Gaussian correlated Q and U Stokes parameters to allow nonzero means. When the variances of Q and U are equal and their covariance and means are zero, the polarization angle is uniformly distributed. Otherwise the uniform distribution will be modulated by harmonics with 2 and 4 phases. These modulations are visible in the Planck 2018 CMB maps. Furthermore, the mean value of U is peculiar compared to the power spectrum.