  We characterise the conditional distributions of the HI gas-to-stellar mass
ratio, $R_{HI}\equiv M_{HI}/M_{\ast}$, given the stellar mass, $M_{\ast}$, of
local galaxies from $M_{\ast}\sim 10^7$ to $10^{12}$ $M_{\odot}$ separated into
centrals and satellites as well as into late- and early-type galaxies (LTGs and
ETGs, respectively). To do so, we use 1) the homogeneous "eXtended GALEX
Arecibo SDSS Survey", xGASS (Catinella et al. 2018), by re-estimating their
upper limits and taking into account them in our statistical analysis; and 2)
the results from a large compilation of HI data reported in Calette et al.
(2018). We use the $R_{HI}$ conditional distributions combined with the Galaxy
Stellar Mass Function to infer the bivariate $M_{HI}$ and $M_{\ast}$
distribution of all galaxies as well of the late/early-type and
central/satellite subsamples and their combinations. Satellites are on average
less HI gas-rich than centrals at low and intermediate masses, with differences
being larger for ETGs than LTGs; at $M_{\ast}>3-5\times 10^{10}$ $M_{\odot}$
the differences are negligible. The differences in the HI gas content are much
larger between LTGs and ETGs than between centrals and satellites. Our
empirical HI Mass Function is strongly dominated by central galaxies at all
masses. The empirically constrained bivariate $M_{HI}$ and $M_{\ast}$
distributions presented here can be used to compare and constrain theoretical
predictions as well as to generate galaxy mock catalogs.
