  Quasar luminosity function (QLF) shows the active galactic nucleus (AGN)
demography as a result of the combination of the growth and the evolution of
black holes, galaxies, and dark matter halos along the cosmic time. The recent
wide and deep surveys have improved the census of high-redshift quasars, making
it possible to construct reliable ultraviolet (UV) QLFs at $2\lesssim
z\lesssim6$ down to $M_{1450}=-23$ mag. By parameterizing these up-to-date
observed UV QLFs that are the most extensive in both luminosity and survey area
coverage at a given redshift, we show that the UV QLF has a universal shape,
and their evolution can be approximated by a pure density evolution (PDE). In
order to explain the observed QLF, we construct a model QLF employing the halo
mass function, a number of empirical scaling relations, and the Eddington ratio
distribution. We also include the outshining of AGN over its host galaxy, which
made it possible to reproduce a moderately flat shape of the faint end of the
observed QLF (slope of $\sim-1.1$). This model successfully explains the
observed PDE behavior of UV QLF at $z>2$, meaning that the QLF evolution at
high redshift can be understood under the framework of halo mass function
evolution. The importance of the outshining effect in our model also implies
that there could be a hidden population of faint AGNs ($M_{1450}\gtrsim-24$
mag), which are buried under their host galaxy light.
