We use Monte Carlo simulations of the Calán/Tololo photographic supernova survey to show that a simple model of the survey ’ s selection effects accounts for the observed distributions of recession velocity , apparent magnitude , angular offset , and projected radial distance between the supernova and the host galaxy nucleus for this sample of Type Ia supernovæ ( SNe Ia ) .
The model includes biases due to the flux-limited nature of the survey , the different light curve morphologies displayed by different SNe Ia , and the difficulty of finding events projected near the central regions of the host galaxies .
From these simulations we estimate the bias in the zero-point and slope of the absolute magnitude-decline rate relation used in SNe Ia distance measurements .
For an assumed intrinsic scatter of 0.15 mag about this relation , these selection effects decrease the zero-point by 0.04 mag .
The slope of the relation is not significantly biased .
We conclude that despite selection effects in the survey , the shape and zero-point of the relation determined from the Calán/Tololo sample are quite reliable .
We estimate the degree of incompleteness of the survey as a function of decline rate and estimate a corrected luminosity function for SNe Ia in which the frequency of SNe appears to increase with decline rate ( the fainter SNe are more common ) .
Finally , we compute the integrated detection efficiency of the survey in order to infer the rate of SNe Ia from the 31 events found .
For a value of H _ { 0 } =65 km sec ^ { -1 } Mpc ^ { -1 } we obtain a SN Ia rate of 0.21 ^ { +0.30 } _ { -0.13 } SNu .
This is in good agreement with the value 0.16 \pm 0.05 SNu recently determined by [ Capellaro et al .
1997 ] .