halo mass function

A halo mass function (HMF) is a distribution function (essentially an unnormalized probability density function) mapping mass quantities to the quantity of dark matter halos with that mass. They are of use in cosmology and cosmological simulations. The Press-Schechter formalism is an example HMF.

A sub-halo mass function is such a distribution of sub-halos within a dark matter halo, and a conditional sub-halo mass function is one parameterized by the mass of the particular dark matter halo (analogous to a conditional stellar mass function).

Note that the term mass function used here indicates a function having to do with (physical) mass rather than the sense of the phrase probability mass function (PMF), which is a function yielding the probability that some discrete random variable takes on a given value.