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

by (Matthew Joseph), 1975- Atkinson

The Generalized Extreme Value (GEV) model’s relevance to the extremes of a distribution, and the Generalized Pareto (GP) model’s relevance to the exceedences above a threshold in a distribution are equivalent to the Gaussian model’s 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. Index words: extreme value, return period, tolerance limit, radiocesium, non-human biota Extreme Value Methods in Body Burden Analysis: with application to inference from long-term data sets by Matthew J. Atkinson Bachelor of Mathematics, The University of Waterloo, 1999 A Thesis Submitted to the Graduate Faculty of The University of Georgia in Partial Fulfillment of the Requirements for the Degree Master of Science Athens, Georgia 2004 c? 2004 Matthew J. Atkinson All Rights Reserved Extreme Value Methods in Body Burden Analysis: with application to inference from long-term data sets by Matthew J. Atkinson Approved: Major Professor: Machelle Wilson Committee: William P. McCormick Lynne Seymour Electronic Version Approved: Maureen Grasso Dean of the Graduate School The University of Georgia May 2004