The purpose of this paper is to undertake a statistical analysis to specify empirical distributions and to estimate univariate parametric probability distributions for air exchange rates for residential structures in the United States. To achieve this goal, we used data compiled by the Brookhaven National Laboratory using a method known as the perfluorocarbon tracer (PFT) technique. While these data are not fully representative of all areas of the country or all housing types, they are judged to be by far the best available. The analysis is characterized by four key points: the use of data for 2,844 households; a four-region breakdown based on heating degree days, a best available measure of climatic factors affecting air exchange rates; estimation of lognormal distributions as well as provision of empirical (frequency) distributions; and provision of these distributions for all of the data, for the data segmented by the four regions, for the data segmented by the four seasons, and for the data segmented by a 16 region by season breakdown. Except in a few cases, primarily for small sample sizes, air exchange rates were found to be well fit by lognormal distributions (adjusted R2 > 0.95). The empirical or lognormal distributions may be used in indoor air models or as input variables for probabilistic human health risk assessments.

We propose 14 principles of good practice to assist people in performing and reviewing probabilistic or Monte Carlo risk assessments, especially in the context of the federal and state statutes concerning chemicals in the environment. Monte Carlo risk assessments for hazardous waste sites that follow these principles will be easier to understand, will explicitly distinguish assumptions from data, and will consider and quantify effects that could otherwise lead to misinterpretation of the results. The proposed principles are neither mutually exclusive nor collectively exhaustive. We think and hope that these principles will evolve as new ideas arise and come into practice.

Most public health risk assessments assume and combine a series of average, conservative, and worst-case values to derive a conservative point estimate of risk. This procedure has major limitations. This paper demonstrates a new methodology for extended uncertainty analyses in public health risk assessments using Monte Carlo techniques. The extended method begins as do some conventional methods--with the preparation of a spreadsheet to estimate exposure and risk. This method, however, continues by modeling key inputs as random variables described by probability density functions (PDFs). Overall, the technique provides a quantitative way to estimate the probability distributions for exposure and health risks within the validity of the model used. As an example, this paper presents a simplified case study for children playing in soils contaminated with benzene and benzo(a)pyrene (BaP).

We fit lognormal distributions to data collected in a national survey for both total water intake and tap water intake by children and adults for these age groups in years: 0 less than age less than 1; 1 less than or equal to age less than 11; 11 less than or equal to age less than 20; 20 less than or equal to age less than 65; 65 less than or equal to age; and all people in the survey taken as a single group. These distributions are suitable for use in public health risk assessments.

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In recent years the U.S. Environmental Protection Agency has been challenged both externally and internally to move beyond its traditional conservative single-point treatment of various input parameters in risk assessments. In the first section, we assess when more involved distribution-based analyses might be indicated for such common types of risk assessment applications as baseline assessments of Superfund sites. Then in two subsequent sections, we give an overview with some case studies of technical analyses of (A) variabilityheterogeneity and (B) uncertainty. By "interindividual variability" is meant the real variation among individuals in exposure-producing behavior, in exposures, or some other parameter (such as differences among individual municipal solid waste incinerators in emissions). In contrast, "uncertainty" is a description of the imperfection in knowledge of the true value of a particular parameter or its real variability in an individual or a group. In general uncertainty is reducible by additional information-gathering or analysis activities (better data, better models), whereas real variability will not change (although it may be more accurately known) as a result of better or more extensive measurements. The purpose of the rather long-winded exposition of these two final sections is to show the differences between analyses of these two different things, both of which are described using the language of probability distributions.

Variability arises due to differences in the value of a quantity among different members of a population. Uncertainty arises due to lack of knowledge regarding the true value of a quantity for a given member of a population. We describe and evaluate two methods for quantifymg both variability and uncertainty. These methods, bootstrap simulation and a likelihood-based method, are applied to three datasets. The datasets include a synthetic sample of 19 values from a Lognormal distribution, a sample of nine values obtained from measurements of the PCB concentration in leafy produce, and a sample of five values for the partitioning of chromium in the flue gas desulfurization system of coal-fired power plants. For each of these datasets, we employ the two methods to characterize uncertainty in the arithmetic mean and standard deviation, cumulative distribution functions based upon fitted parametric distributions, the 95th percentile of variability, and the 63rd percentile of uncertainty for the 81st percentile of variability. The latter is intended to show that it is possible to describe any point within the uncertain frequency distribution by specifying an uncertainty percentile and a Variability percentile. Using the bootstrap method, we compare results based upon use of the method of matching moments and the method of maximum likelihood for fitting distributions to data. Our results indicate that with only 5-19 data points as in the datasets we have evaluated, there is substantial uncertainty based upon random sampling error. Both the boostrap and likelihood-based approaches yield comparable uncertainty estimates in most cases.

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