In this paper, we introduce two new families of probability density functions (PDFs) for the polarimetric target vector and covariance matrix. These families complete the diagram spanned by the second and third-order matrix log-cumulants of the data, and contribute to a holistic theory for statistical modeling of Polarimetric Synthetic Aperture Radar (PolSAR) data based on the Spherically Invariant Random Vector (SIRV) model. The new PDFs result from using a Beta and an Inverse Beta distributed texture variable, and are referred to as the W and M distributions. They are able to model data with low variance but extreme skewness, which proves particularly relevant for speckle filtered data with textural variability. The usefulness of the models is demonstrated with multi-frequency real data.