and $t>0.5\;\rm{Gyr}$. The two free parameters can be determined by fitting the model to the rates inferred from observations. We carry out the fit using a compilation of observational determinations of the volumetric type Ia supernova rates from [@Gra2014] updated with the results from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey [CANDLES; @Rod2014]. Minimization of $\chi^{2}$ with errors including statistical and systematic uncertainties yields $\eta_{0}=1.02_{-0.15}^{+0.27}\times10^{-4}\;h_{70}^{2}\;\rm{yr}^{-1}\;{{\ifmmode{{\rm {M_{\odot}}}}\else{${\rm{M_{\odot}}}$}\fi}}^{-1}$ and $\eta_{1}/\eta_{0}=11.98^{+3.37}_{-4.49}$. Fig. \[sn\_rate\] compares the resulting best fit model to the observational data. The obtained constraints imply a fraction of prompt supernovae $f_{\rm p}=0.63_{-0.11}^{+0.07}$, consistent with the results obtained by @Rod2014.

The rate of core-collapse supernovae is directly proportional to the star formation history $\psi(z)$: $$n_{\rm SNCC}(z)=k_{\rm CC}\psi(z),$$ where $k_{\rm CC}$ is the number of stars that explode as supernovae per unit mass. For our study, we adopt $k_{\rm CC}=0.0068{{\ifmmode{{\rm {M_{\odot}}}}\else{${\rm{M_{\odot}}}$}\fi}}^{-1}$ expected for a mass range of supernova progenitors $(8\;M_{\odot},\;40\;M_{\odot})$ and a Salpeter initial mass function. Since the same initial function was consistently assumed in the derivation of the star formation rate from observations, the predicted rate of core-collapse supernovae is practically independent of the initial mass function [@Mad2014]. The resulting core-collapse supernova rate is shown in Fig. \[sn\_rate\].

![Distribution of absolute 