The $HI$- and $H_{2}$-to-stellar mass correlations of late- and
  early-type galaxies and their consistency with the observational mass
  functions
  We compile and carrefully homogenize local galaxy samples with available
information on stellar, $\rm HI$ and/or $\rm H_{2}$ masses, and morphology.
After processing the information on upper limits in the case of non gas
detections, we determine the $\rm HI$- and $\rm H_{2}$-to-stellar mass
relations and their $1\sigma$ scatter for both late- and early-type galaxies.
The obtained relations are fitted to single or double power laws. Late-type
galaxies are significantly gas richer than early-type ones, specially at high
masses. The respective $\rm H_{2}$-to-$\rm HI$ mass ratios as a function of
$M_{\ast}$ are discussed. Further, we constrain the full mass-dependent
distribution 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 observed
galaxy stellar mass function and the volume-complete late-to-early-type galaxy
ratio as a function of $M_{\ast}$, these empirical distribution functions are
mapped into $\rm HI$ and $\rm H_{2}$ mass functions. The obtained mass
functions are consistent with those inferred from large surveys. The empirical
gas-to-stellar mass relations and their distributions for local late- and
early-type galaxies presented here can be used to constrain models and
simulations of galaxy evolution.
