These are the canonical distributions used in the Monte Carlo simulations. Redshift is volume weighted. Stretch has an asymmetric Gaussian distribution centered on 1.0 with the side less than 1.0 having a sigma of 0.13 and the side greater than 1.0 having a sigma of 0.08. This matches the distribution for the SNLS SN Ia sample published in Astier et al. (2005). Host extinction, E(B-V), is a positive valued Gaussian with a sigma of 0.2. The dispersion in the peak magnitude is a Gaussian centered on 0.0 with a sigma of 0.17 magnitudes, from Hamuy et al. (1996).