Estimation of the weibull shape parameter in small-sample bioassay

The Weibull distribution has been used as a dose-response curve to model survival rates in aquatic toxicity testing, and tumor risk in carcenogenesis research. For estimating risks at low dose levels, especially when experimental data at these levels is sparse, the Weibull shape parameter is of primary importance. Several standard statistical methods of estimation, including least squares and maximum likelihood, are commonly used to estimate shape; the results of a simulation study, designed to compare their small-sample properties, is presented. Both point and interval estimation are considered, and some recommendations concerning choice of method are given.