  We study the demographics of z ~ 6 broad-line quasars in the black hole (BH)
mass-luminosity plane using a sample of more than 100 quasars at 5.7 < z < 6.5.
These quasars have well quantified selection functions and nearly one third of
them also have virial BH masses estimated from near-IR spectroscopy. We use
forward modeling of parameterized intrinsic distributions of BH masses and
Eddington ratios, and account for the sample flux limits and measurement
uncertainties of the BH masses and luminosities. We find significant
differences between the intrinsic and observed distributions of the quantities
due to measurement uncertainties and sample flux limits. There is also marginal
evidence that the virial BH masses are susceptible to a positive
luminosity-dependent bias (BH mass is overestimated when luminosity is above
the average), and that the mean Eddington ratio increases with BH mass. Our
models provide reliable constraints on the z ~ 6 black hole mass function at
M_BH > 10^8.5 M_Sun, with a median 1-sigma uncertainty of ~0.5 dex in
abundance. The intrinsic Eddington ratio distribution of M_BH > 10^8.5 M_Sun
quasars can be approximated by a mass-dependent Schechter model, with a broad
peak around log(L_bol/L_Edd}) ~ -0.9. We also find that, at 4.5 < z < 6, the
number densities of more massive BHs tend to decline more rapidly with
increasing redshift, contrary to the trend at 2.5 < z < 4.5 reported
previously.
