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We characterize the conditional distributions of the HI gas-to-stellar massratio, $R_{HI}\equiv M_{HI}/M_{\ast}$, given the stellar mass, $M_{\ast}$, oflocal galaxies from $M_{\ast}\sim 10^7$ to $10^{12}$ $M_{\odot}$ separated intocentrals and satellites as well as into late- and early-type galaxies (LTGs andETGs, respectively). To do so, we use (1) the homogeneous "eXtended GALEXArecibo SDSS Survey", xGASS (Catinella et al. 2018), by re-estimating theirupper 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 GalaxyStellar Mass Function to infer the bivariate $M_{HI}$ and $M_{\ast}$distribution of all galaxies as well of the late/early-type andcentral/satellite subsamples and their combinations. Satellites are on averageless HI gas-rich than centrals at low and intermediate masses, with differencesbeing 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 muchlarger between LTGs and ETGs than between centrals and satellites. Ourempirical HI Mass Function is strongly dominated by central galaxies at allmasses. The empirically constrained bivariate $M_{HI}$ and $M_{\ast}$distributions presented here can be used to compare and constrain theoreticalpredictions as well as to generate galaxy mock catalogues.

The HI and stellar mass bivariate distribution of centrals and satellites for all, late- and early-type local galaxies