Probability distribution functions for solar and stellar magnetic fields

Magneto-convection structures the magnetic field in solar and stellar atmospheres over scales that for the Sun span about 8 orders of magnitudes, down to the magnetic diffusion scale of order 10 m. The statistical properties of this structuring are governed by probability density functions (PDFs), for the vertical and transverse field components as well as for the field inclination. Due to the fractal nature of the field pattern these PDFs appear to have a high degree of scale invariance. There are serious pitfalls in the derivations of empirical PDFs, pitfalls that are particularly severe in the case of the field inclination. This explains the fragmentary and rather unreliable PDF information available in the published literature. Here we discuss the nature of these pitfalls and indicate how they may be avoided, using Hinode quiet-sun Stokes vector data to derive PDFs for the field strength and field inclination.