The data were used to create number density functions of supermassive black holes (SMBH) for redshifts 0.5 < z < 3.0. The goal of this research is to discern whether galaxy-black hole scaling relations produce black hole masses that are consistent with each other at high redshift. These number density functions were used to compare the high-mass SMBH distributions from each relation. In massive black hole binary based models, the highest-mass SMBHs have a significant influence on the gravitational wave background characteristic strain amplitude. To inform our understanding of the gravitational wave background, that pulsar timing arrays now show evidence for, we need to therefore have a solid foundation on the underlying SMBH population. In our paper we found that using different galaxy properties to inform our estimations of SMBH mass resulted in different distributions, especially at the high-mass end.
