Semi-analytic Models (SAMs) try to boil down everything we know about the evolution of black holes and galaxies into a concise set of equations.  In the era of large cosmological simulations, these are still excellent tools when you need large effective volumes and small galaxies.  The plot to the left contains chirp mass functions as observable by the LISA mission, which will detect gravitational waves from black hole mergers.  Two different seeding models are shown (Light and Heavy) as well as two different accretion prescriptions (PL* and MS*).  By measuring this mass function, LISA will directly constrain models of black hole seeding.  You can learn more about this model here

You can download luminosity functions and gravitational wave distributions from this model here and here.