The most probable number and the Spearman–Kärber estimator for the estimation of a bacterial density in a suspension assume that the limit of detection of the quantal response bioassay is equal to one viable organism or cell. These traditional estimation methods can be used to confirm or reject a limit of detection of one for the validation of such bioassays, if the testing conditions are perfect, if the statistical assumptions are truly correct, and if an a priori precise estimate of the number of viable organisms contained in the suspension is given. Pearson's minimum chi-square estimator and an approximate maximum likelihood estimator are proposed as generalizations to explicitly estimate the limit of detection, additional to the estimation of the bacterial density. A real case study for the validation of a rapid microbiological absence/presence test is presented to illustrate both the traditional and generalized estimation methods. Asymptotic results and simulation studies are used to evaluate the performance of the two general approaches. It is concluded that Pearson's minimum chi-square estimator is preferred over the other estimation methods for these types of estimation problems. Copyright © 2010 John Wiley & Sons, Ltd.