  Measurements of the equation of state of dark energy from surveys of
thousands of Type Ia Supernovae (SNe Ia) will be limited by spectroscopic
follow-up and must therefore rely on photometric identification, increasing the
chance that the sample is contaminated by Core Collapse Supernovae (CC SNe).
Bayesian methods for supernova cosmology can remove contamination bias while
maintaining high statistical precision but are sensitive to the choice of
parameterization of the contaminating distance distribution. We use simulations
to investigate the form of the contaminating distribution and its dependence on
the absolute magnitudes, light curve shapes, colors, extinction, and redshifts
of core collapse supernovae. We find that the CC luminosity function dominates
the distance distribution function, but its shape is increasingly distorted as
the redshift increases and more CC SNe fall below the survey magnitude limit.
The shapes and colors of the CC light curves generally shift the distance
distribution, and their effect on the CC distances is correlated. We compare
the simulated distances to the first year results of the SDSS-II SN survey and
find that the SDSS distance distributions can be reproduced with simulated CC
SNe that are ~1 mag fainter than the standard Richardson et al. (2002)
luminosity functions, which do not produce a good fit. To exploit the full
power of the Bayesian parameter estimation method, parameterization of the
contaminating distribution should be guided by the current knowledge of the CC
luminosity functions, coupled with the effects of the survey selection and
magnitude-limit, and allow for systematic shifts caused by the parameters of
the distance fit.
