ABSTRACT We present the neutral hydrogen mass (MHI) function (HIMF) and velocity width (w50) function (HIWF) based on a sample of 7857 galaxies from the 40 per cent data release of the ALFALFA survey (α.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 (Vrot) 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 (Mh) function of HI-selected galaxies. This allows us to obtain various scaling relations between MHI−w50−Vrot−Mh, which we present. The MHI−Mh relation has a steep slope ∼2.10 at small masses and flattens to ∼0.34 at masses larger than a transition halo mass, $\log _{10}(M_{\rm{ht}}h_{70}^2/M_{\odot })=10.62$. Our scaling relation is robust and consistent with a volume-limited sample of α.40. The MHI−Mh relation is qualitatively similar to the Mstar−Mh relation but the transition halo mass is smaller by ∼1.4 dex compared to that of the Mstar−Mh relation. Our results suggest that baryonic processes like heating and feedback in larger mass haloes suppress HI gas on a shorter time-scale compared to star formation.