Maximum Likelihood Estimation in Quantal Response Experiments

This paper is concerned with maximum likelihood estimates for the population parameters in experiments in which the responses are quantal and the distributions are assumed to be normal. A set of necessary and sufficient conditions is developed for the existence of a unique maximum of the likelihood function. A modified form of the Newton-Raphson procedure is described, for which global convergence can be proved for cases in which the given conditions are satisfied. These results extend the earlier developments of Golub and Grubbs.