  We present mass functions of distant actively accreting supermassive black
holes residing in luminous quasars discovered in the Large Bright Quasar
Survey, the Bright Quasar Survey, and the Fall Equatorial Stripe of the Sloan
Digital Sky Survey (SDSS). The quasars cover a wide range of redshifts (0 <~ z
<= 5) and were subject to different selection criteria and flux density limits.
These samples are thus complementary and can help us gain additional insight on
the true underlying black hole mass distribution, free from selection effects
and mass estimation errors through future studies. We see evidence that the
active z~4 black hole population is somewhat different than that at lower z. In
particular, there is a sharp increase in the space density of the detected
active black holes (M_BH >~ 10^8 Msun) between redshifts ~4 and ~2.5. Also, the
z~4 SDSS quasar mass function has a somewhat flatter high mass-end slope, beta
= -1.75 +- 0.56, compared to the mass functions based on quasars below z of 3,
which display typical slopes of beta =~ -3.3; the latter are consistent with
the mass functions at similar redshifts based on the SDSS Data Release 3 quasar
catalog presented by Vestergaard et al. We see clear evidence of cosmic
downsizing in the comoving space density distribution of active black holes in
the LBQS sample alone. In forthcoming papers, further analysis, comparison, and
discussion of these mass functions will be made with other existing black hole
mass functions, notably that based on the SDSS DR3 quasar catalog. We present
the relationships used to estimate the black hole mass based on the MgII
emission line; the relations are calibrated to the Hbeta and CIV relations by
means of several thousand high quality SDSS spectra. Mass estimates of the
individual black holes of these samples are also presented.
