In non-equilibrium plasma spectroscopy it may happen to have to deal with ensembles of particles, whose velocity distribution is not the equilibrium (i.e. Maxwell) one. Consequently, the shape-profile-of the relevant emission or absorption coefficient is different from the profile (Gauss or Voigt) that corresponds to the equilibrium velocity distribution function. The computation of the emission and absorption coefficients in the case of an arbitrary velocity distribution can be painstaking and, above all, risky from the numerical point of view. In this paper, we present an easy way to perform the above computations. As a consequence, the treatment of the corresponding inverse problem also becomes easy: the reconstruction of a velocity distribution function, once the values of the corresponding emission (or absorption) coefficient are known for all the directions and frequencies.