Estimate of the Integrated Normal Curve by Minimum Normit Chi-Square with Particular Reference to Bio-Assay

This is the authors' abstract. We don't add key points for this paper.

therefore if the normit of P is plotted against x, the points will fall on a straight line with a as the intercept and ,B as the slope. The integrated normal curve (1) has been advanced extensively in recent years for use in bio-assay with quantal response. Here Pi represents the true probability of death (or some other all-or-none effect) at x =xi. In this statistical model it is assumed that pi, the observed proportion of individuals affected out of ni exposed at xi, can be considered a random variable binomially distributed around the true Pi, with variance {2 = PiQi/ni. For the estimation of the parameters a, ,B of (1), the method of maximum likelihood has been advocated, on the basis of the optimum asymptotic properties of the maximum likelihood estimate [10]. In this paper is presented another estimate, formally analogous with the logit x2 estimate of the logistic function,2 called the minimum normit x2 estimate.