We characterize 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 $M_{ast}>3-5times 10^{10}$ $M_{odot}$ 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 catalogues.
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