In interpreting the binary regression models often used in the analysis of dose-response data, it is common to introduce the idea of an underlying continuous tolerance distribution. Different choices of link function lead to different tolerance distributions. A useful way of comparing these alternatives is to compare the hazard functions or tail functions associated with each tolerance distribution. Tail functions can also be applied to give numerically preferable formulas for the iterative weights and the adjusted dependent variable in the fitting of binary regression models by the iteratively reweighted least-squares algorithm.