  Accreted stellar populations are comprised of the remnants of destroyed
galaxies, and often dominate the `stellar haloes' of galaxies such as the Milky
Way (MW). This ensemble of external contributors is a key indicator of the past
assembly history of a galaxy. We introduce a novel statistical method that uses
the unbinned metallicity distribution function (MDF) of a stellar population to
estimate the mass spectrum of its progenitors. Our model makes use of the
well-known mass-metallicity relation of galaxies and assumes Gaussian MDF
distributions for individual progenitors: the overall MDF is thus a mixture of
MDFs from smaller galaxies. We apply the method to the stellar halo of the MW,
as well as the classical MW satellite galaxies. The stellar components of the
satellite galaxies have relatively small sample sizes, but we do not find any
evidence for accreted populations with L > L_host/100. We find that the MW
stellar halo has N~1-3 massive progenitors (L > 10^8 L_Sun) within 10 kpc, and
likely several hundred progenitors in total. We also test our method on
simulations of MW-mass haloes, and find that our method is able to recover the
true accreted population within a factor of two. Future datasets will provide
MDFs with orders of magnitude more stars, and this method could be a powerful
technique to quantify the accreted populations down to the ultra-faint dwarf
mass-scale for both the MW and its satellites.
