  Low-ionization (MgII, FeII, FeIII) broad absorption line quasars (LoBALs)
probe a relatively obscured quasar population, and could be at an early
evolutionary stage for quasars. We study the intrinsic fractions of LoBALs
using the SDSS, 2MASS, and FIRST surveys. We find that the LoBAL fractions of
the near infra-red (NIR) and radio samples are approximately 5--7 times higher
than those measured in the optical sample. This suggests that the fractions
measured in the NIR and radio bands are closer to the intrinsic fractions of
the populations, and that the optical fractions are significantly biased due to
obscuration effects, similar to high-ionization broad absorption line quasars
(HiBALs). We also find that the LoBAL fractions decrease with increasing radio
luminosities, again, similar to HiBALs. In addition, we find tentative evidence
for high fractions of LoBALs at high NIR luminosities, especially for FeLoBALs
with a fraction of ~18 per cent at M_K_s < -31 mag. This population of NIR
luminous LoBALs may be at an early evolutionary stage of quasar evolution. We
use a two-component model of LoBALs including a pure geometric component and a
luminosity dependent component at high NIR luminosities, and obtain better fits
than those from a pure geometric model. Therefore, the LoBAL population can be
modelled as a hybrid of both the geometric and evolutionary models, where the
geometric component constitutes 3.4\pm0.3, 5.8\pm0.4, and 1.5\pm0.3 per cent of
the quasar population for BI-LoBALs, AI-LoBALs, and FeLoBALs, respectively.
Considering a population of obscured quasars that do not enter the SDSS survey,
which could have a much higher LoBAL fraction, we expect that intrinsic
fraction of LoBALs could be even higher.
