Alceon Corporation (United States)

Finite mixture models, that is, weighted averages of parametric distributions, provide a powerful way to extend parametric families of distributions to fit data sets not adequately fit by a single parametric distribution. First-order finite mixture models have been widely used in the physical, chemical, biological, and social sciences for over 100 years. Using maximum likelihood estimation, we demonstrate how a first-order finite mixture model can represent the large variability in data collected by the U.S. Environmental Protection Agency for the concentration of Radon 222 in drinking water supplied from ground water, even when 28% of the data fall at or below the minimum reporting level. Extending the use of maximum likelihood, we also illustrate how a second-order finite mixture model can separate and represent both the variability and the uncertainty in the data set.

Second-order random variables, i.e., parametric random variables with uncertain parameters, give risk assessors a way to distinguish and represent both the variability and the uncertainty in an exposure variable. In this manuscript, we explore ways to fit second order random variables to data using maximum likelihood estimation (MLE).

With 13 new procedures and many new features just added in the latest upgrade, Systat 7.0 is an extremely powerful software package for research‐quality graphics and statistics. With a standard Windows “graphical user interface,”; Systat gives users such an extensive library of integrated graphics and statistics that no single person is likely to use all the features or techniques. Program: Systat for Windows, Version 7.0 Source: Systat, a Division of SPSS, Inc. 444 North Michigan Drive Chicago, IL 60611 Tel: 312–329–2400; Fax: 312–329–3668 http://www.spss.com System: Windows 3.1, Windows 95, or Windows NT 3.51 or higher 80386 processor or higher, 8MB RAM or more recommended, 25 MB available disk space with a swap file, VGA or higher graphics adapter Cost: Commercial price, $995. for program plus manuals Academic price, $695. for program plus manuals Upgrade prices available directly from the company

When evaluating a probabilistic health risk assessment, say at a hazardous waste site, risk managers need a risk management policy that distinguishes an acceptable distribution of risks to individuals in a population from an unacceptable one. If a risk manager decides that the distribution of risk for the status quo is unacceptable, then a risk assessor needs a way to compute cleanup targets, i.e., the risk assessor needs a policy statement against which to estimate distributions of exposure point concentrations which, if engineered at a site, will achieve an acceptable distribution of risk. Some regulatory agencies base acceptability on whether the 95th percentile of the risk distribution falls at or below a given value, without considering the behavior of the rest of the distribution. As regulatory agencies adopt risk management policies for use with probabilistic risk assessments, we recommend that they base their new policies on two simultaneously binding constraints‐one on an upper percentile and one on the arithmetic mean of the distribution of risk‐in addition to other non‐risk criteria.

Click to increase image sizeClick to decrease image sizeKey Words: probabilistic risk assessmentMonte Carlohazardtoxicityreference doseprobability density functions

Abstract When evaluating a fully probabilistic risk assessment, say at a hazardous waste site, the risk manager needs a risk management policy that distinguishes an acceptable distribution of risk from an unacceptable one. This manuscript explores several alternative ways to define the acceptability of a distribution of risk. This manuscript also presents methods to backcalculate distributions for cleanup targets under the alternative risk management policies if the need arises.

RiskQ is a computer program designed to enable users to perform analyses involving probability, uncertainty, and statistics. It is written in the Mathematica programming language. RiskQ is intended for individuals who have experience with Mathematica and a good working knowledge of probabilistic and statistical concepts. In this article the authors discuss the features of RiskQ, its performance as compared with Crystal Ball and Risk, documentation, ease of learning and use, error handling, and support. 2 refs., 2 figs.

Most public health risk assessments combine a series of average, conservative, and worst-case assumptions to derive a conservative point estimate of risk or a conservative point estimate for a cleanup target. This paper demonstrates a risk assessment methodology (probabilistic sensitivity analysis) that overcomes many of the limitations in current practices under the federal Superfund program and corresponding state programs. The methodology begins, as do many conventional methods, with the preparation of a spreadsheet to estimate soil cleanup targets. Following this key inputs are then modeled as random variables described by probability density functions (PDFs) or cumulative distribution functions (CDFs). The method then estimates PDFs or CDFs for the soil cleanup target using commercial Monte Carlo software on a desktop computer. With appropriate precautions to consider various pitfalls, we use the probabilistic method to estimate distributions for soil cleanup targets for two compounds in soils regulated by the New Jersey Department of Environmental Protection. In this manuscript, rather than advocate specific numerical results, we instead emphasize a general approach to probabilistic sensitivity analysis through visualization of results too granular to understand through tabulations.