Halo mass densities from a statistical viewpoint

During the past decades, large-scale N-body simulations have successfully reconstructed cosmic structure formation with increasing resolution and complexity, as observations corroborate. Complementary efforts have arrived at a hydrodynamical theory that explains cosmic structure evolution up to the non-linear regime. A very recent approach based on a kinetic field theory can derive an analytic, parameter-free equation for the non-linear cosmic power spectrum. 
While the statistical properties of mass density perturbations for the observable universe as a whole is currently being understood from first principles, it is still unknown why our heuristic approaches for the characterisation of individual, locally collapsed mass agglomerations work so well.

Using a minimum set of prerequisites and approximations, I would like to put forward a new idea to explain the shape of the most common parametric dark matter halo mass density models in the framework of probability theory. It allows for an interpretation of the scaling radii and scaling densities which gives the limiting behaviour in the halo centre and in the outskirts a physical reason. Joining forces with simulation groups, surprising insights into the bulge-halo conspiracy and the cusp-core problem could be gained.