  For collisionless (or collision-poor) plasma populations which are well
described by the $\kappa$-distribution functions (also known as the Kappa or
Lorentzian power-laws) a macroscopic interpretation has remained largely
questionable, especially because of the diverging moments of these
distributions. Recently significant progress has been made by introducing a
generic regularization for the isotropic $\kappa$-distribution, which resolves
this critical limitation. Regularization is here applied to the anisotropic
forms of $\kappa$-distributions, commonly used to describe temperature
anisotropies, and skewed or drifting distributions of beam-plasma systems.
These regularized distributions admit non-diverging moments which are provided
for all positive $\kappa$, opening promising perspectives for a macroscopic
(fluid-like) characterization of non-ideal plasmas.
