The Maximally Exposed IndividuaI-Comparison of Maximum Likelihood Estimation of High Quantiles to an Extreme Value Estimate
Machelle D. Wilson,1 William P. McCormick,2 and
T. G. Hinton1
The dose to human and nonhuman individuals inflicted by anthropogenic
radiation is an important issue in international and domestic policy.
The current paradigm for nonhuman populations asserts that if the dose
to the maximally exposed individuals in a population is below a certain
criterion (e.g., <10 mGy d-1) then the population is adequately
protected. Currently, there is no consensus in the regulatory community
as to the best statistical approach. Statistics, currently considered,
include the maximum likelihood estimator for the 95th percentile of the
sample mean and the sample maximum. Recently, the investigators have proposed
the use of the maximum likelihood estimate of a very high quantile as
an estimate of dose to the maximally exposed individual. In this study,
we compare all of the above-mentioned statistics to an estimate based
on extreme value theory. To determine and compare the bias and variance
of these statistics, we use Monte Carlo sinIulation techniques, in a procedure
sinIilar to a parametric bootstrap. Our results show that a statistic
based on extreme value theory has the least bias of those considered here,
but requires reliable estimates of the population size. We recommend establishing
the criterion based on what would be considered acceptable if only a small
percentage of the population exceeded the limit, and hence recommend using
the maximum likelihood estimator of a high quantile in the case that reliable
estimates of the population size are not available.
KEY WORDS: Body burden; bootstrap; cesium 137; dose;
extreme value; maximum likelihood; Monte Carlo
SREL Reprint #2795
Wilson, M., W. P. McCormick and T. G. Hinton. 2004. The maximally exposed individual — comparison of maximum likelihood estimation of high quantiles to an extreme value estimate. Risk Analysis 24:1143-1151.
