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We compile and carrefully homogenize local galaxy samples with availableinformation on stellar, $\rm HI$ and/or $\rm H_{2}$ masses, and morphology.After processing the information on upper limits in the case of non gasdetections, we determine the $\rm HI$- and $\rm H_{2}$-to-stellar massrelations and their $1\sigma$ scatter for both late- and early-type galaxies.The obtained relations are fitted to single or double power laws. Late-typegalaxies are significantly gas richer than early-type ones, specially at highmasses. The respective $\rm H_{2}$-to-$\rm HI$ mass ratios as a function of$M_{\ast}$ are discussed. Further, we constrain the full mass-dependentdistribution functions of the $\rm HI$- and $\rm H_{2}$-to-stellar mass ratios.We find that they can be described by a Schechter function for late types and a(broken) Schechter + uniform function for early types. By using the observedgalaxy stellar mass function and the volume-complete late-to-early-type galaxyratio as a function of $M_{\ast}$, these empirical distribution functions aremapped into $\rm HI$ and $\rm H_{2}$ mass functions. The obtained massfunctions are consistent with those inferred from large surveys. The empiricalgas-to-stellar mass relations and their distributions for local late- andearly-type galaxies presented here can be used to constrain models andsimulations of galaxy evolution.

The $HI$- and $H_{2}$-to-stellar mass correlations of late- and early-type galaxies and their consistency with the observational mass functions