  We present the neutral hydrogen mass ($M_{\text{HI}}$) function (HIMF) and
velocity width ($w_{50}$) function (HIWF) based on a sample of 7857 galaxies
from the 40% data release of the ALFALFA survey ($\alpha.40$). The low mass
(velocity width) end of the HIMF (HIWF) is dominated by the blue population of
galaxies whereas the red population dominates the HIMF (HIWF) at the high mass
(velocity width) end. We use a deconvolution method to estimate the HI
rotational velocity ($V_{\text{rot}}$) functions (HIVF) from the HIWF for the
total, red, and blue samples. The HIWF and HIVF for the red and blue samples
are well separated at the knee of the function compared to their HIMFs. We then
use recent stacking results from the ALFALFA survey to constrain the halo mass
($M_{\text{h}}$) function of HI-selected galaxies. This allows us to obtain
various scaling relations between $M_{\text{HI}} - w_{50} - V_{\text{rot}} -
M_{\text{h}}$, which we present. The $M_{\text{HI}} - M_{\text{h}}$ relation
has a steep slope ~2.10 at small masses and flattens to ~0.34 at masses larger
than a transition halo mass, $\log_{10}(M_{\text{ht}}
h^2_{70}/M_{\odot})=10.62$. Our scaling relation is robust and consistent with
a volume-limited sample of $\alpha.40$. The $M_{\text{HI}} - M_{\text{h}}$
relation is qualitatively similar to the $M_{\text{star}} - M_{\text{h}}$
relation but the transition halo mass is smaller by ~1.4 dex compared to that
of the $M_{\text{star}} - M_{\text{h}}$ relation. Our results suggest that
baryonic processes like heating and feedback in larger mass halos suppress HI
gas on a shorter time scale compared to star-formation.
