Comparison between the area-normalized probability distribution functions (PDF) for the field strengths (solid line) and the flux densities as observed with the Hinode resolution (dotted line for the vertical flux densities, dashed line for the total flux densities). The extended wings that decline quadratically are mainly due to the collapsed flux tubes. The large width of the Gaussian core region for the field strength PDF is required to satisfy the observational constraints from the Hanle effect. Due to cancellation of mixed polarities this Gaussian core contracts to become the narrow stretched exponential core for the flux density PDFs.