Extreme value methods in body-burden analysis: with application to inference from long-term data sets

The Generalized Extreme Value (GEV) models relevance to the extremes of a distribution, and the Generalized Pareto (GP) models relevance to the exceedences above a threshold in a distribution are equivalent to the Gaussian models relevance to the center of a distribution. Limit theorems are presented which unify the extreme values of samples from sufficiently smooth distributions under the GEV model, and similarly unify exceedences under the GP model. These models are fit (via maximum likelihood estimation of model parameters) to radiocesium body-burden data in a population of deer at increased risk of exposure. Analysis suggests that a member of the Frechet EV family best quantifies maxima from this dataset. Return levels are estimated, and a formula for estimating tolerance limits is developed from the GEV functional form.