  We present measurements of the local core collapse supernova (SN) rate using
SN discoveries from the Palomar Transient Factory (PTF). We use a Monte Carlo
simulation of hundreds of millions of SN light curve realizations coupled with
the detailed PTF survey detection efficiencies to forward-model the SN rates in
PTF. Using a sample of 86 core collapse SNe, including 26 stripped-envelope SNe
(SESNe), we show that the overall core collapse SN volumetric rate is
$r^\mathrm{CC}_v=9.10_{-1.27}^{+1.56}\times10^{-5}\,\text{SNe
yr}^{-1}\,\text{Mpc}^{-3}\, h_{70}^{3}$ at $ \langle z \rangle = 0.028$, and
the SESN volumetric rate is
$r^\mathrm{SE}_v=2.41_{-0.64}^{+0.81}\times10^{-5}\, \text{SNe
yr}^{-1}\,\text{Mpc}^{-3}\, h_{70}^{3}$. We further measure a volumetric rate
for hydrogen-free superluminous SNe (SLSNe-I) using 8 events at $z{\le}0.2$ of
$r^\mathrm{SLSN-I}_v=35_{-13}^{+25}\, \text{SNe yr}^{-1}\text{Gpc}^{-3}\,
h_{70}^{3}$, which represents the most precise SLSN-I rate measurement to date.
Using a simple cosmic star-formation history to adjust these volumetric rate
measurements to the same redshift, we measure a local ratio of SLSN-I to SESN
of $\sim1/810^{+1500}_{-94}$, and of SLSN-I to all CCSN types of $\sim
1/3500^{+2800}_{-720}$. However, using host galaxy stellar mass as a proxy for
metallicity, we also show that this ratio is strongly metallicity dependent: in
low-mass ($\mathrm{log} M_{*} < 9.5 \mathrm{M}_\odot$) galaxies, which are the
only environments that host SLSN-I in our sample, we measure a SLSN-I to SESN
fraction of $1/300^{+380}_{-170}$ and $1/1700^{+1800}_{-720}$ for all CCSN. We
further investigate the SN rates a function of host galaxy stellar mass and
show that the specific rates of all core collapse SNe decrease with increasing
stellar mass.
