A generalization of the probit and logit methods for dose response curves

The relationship between response probability and dosage in quantal response bioassay is modelled using a four parameter class. In addition to location and scale quantities the model includes two shape parameters that essentially index skewness and heaviness of tails of the dose-response curve. The class of models includes such special cases as the logistic, normal, extreme minimum value, extreme maximum value, double exponential, exponential and reflected exponential distribution functions. Score tests are derived for logistic and normal hypotheses and certain submodels are discussed for which the model fitting is computationally convenient. The data of Bliss (1935) illustrates the potential improvement over usual methods in the estimation of critical dose levels.