Bootstrap upper bounds for the arithmetic mean of right‐skewed data, and the use of censored data

Environmental contamination data frequently follow an extremely right skewed distribution, which is often approximated by a log‐normal distribution. For the purpose of risk assessment it is of interest to use the sample data to calculate an upper bound on the population arithmetic mean. This article reviews the usual upper bound estimator calculated assuming a log‐normal distribution and shows that, when the log‐normal assumption is not satisfied, this method can result in severe over‐estimation of the upper bound for the arithmetic mean. We then show, using Monte Carlo simulation, that a bootstrap upper bound is a much better approximation to the true upper bound on the population arithmetic mean. Finally, we present a bootstrap procedure for use when the data are left censored by detection/quantification limits and discuss Monte Carlo results that support the use of this procedure when as much as one‐half of the sample consists of censored observations. Copyright © 2002 John Wiley & Sons, Ltd.