A Short Research Note on Calculating Exact Distribution Functions and
  Random Sampling for the 3D NFW Profile
  In this short note we publish the analytic quantile function for the Navarro,
Frenk & White (NFW) profile. All known published and coded methods for sampling
from the 3D NFW PDF use either accept-reject, or numeric interpolation
(sometimes via a lookup table) for projecting random Uniform samples through
the quantile distribution function to produce samples of the radius. This is a
common requirement in N-body initial condition (IC), halo occupation
distribution (HOD), and semi-analytic modelling (SAM) work for correctly
assigning particles or galaxies to positions given an assumed concentration for
the NFW profile. Using this analytic description allows for much faster and
cleaner code to solve a common numeric problem in modern astronomy. We release
R and Python versions of simple code that achieves this sampling, which we note
is trivial to reproduce in any modern programming language.
