Applications of a quadratic variance model for counting data

A quadratic variance model expressed as a function of sample mean is used to describe counting variance for a mechanical system that exhibits extra-Poisson variance. The nonlinear term describes the extra-Poisson variance, and the linear terms describe the intrinsic and propagated Poisson variance. The quadratic variance model also is applied to repetitive bioassay data, where the nonlinear term describes the well-known phenomenon of biological variance, which is a special case of extra-Poisson variance. The model was found to be suitable for the bioassay data as well. Detection limits for extra-Poisson variance are discussed, as well as the estimation of net signal detection limits, intake, and committed effective dose equivalent using the quadratic variance model.