Developing univariate distributions from data for risk analysis

The importance of fitting distributions to data for risk analysis continues to grow as regulatory agencies, like the Environmental Protection Agency (EPA), continue to shift from deterministic to probabilistic risk assessment techniques. The use of Monte Carlo simulation as a tool for propagating variability and uncertainty in risk requires specification of the risk model's inputs in the form of distributions or tables of data. Several software tools exist to support risk assessors in their efforts to develop distributions. However, users must keep in mind that these tools do not replace clear thought about judgments that must be made in characterizing the information from data. This overview introduces risk assessors to the statistical concepts and physical reasons that support important judgments about appropriate types of parametric distributions and goodness-of-fit. In the context of using data to improve risk assessment and ultimately risk management, this paper discusses issues related to the nature of the data (representativeness, quantity, and quality, cell-elation with space and time, and distinguishing between variability and uncertainty for a set of data), and matching data and distributions appropriately. All data analysis (whether "Frequentist" or "Bayesian" or oblivious to the distinction) requires the use of subjective judgment. The paper offers an iterative process for developing distributions using data to characterize variability and uncertainty for inputs to risk models that provides incentives for collecting better information when the value of information exceeds its cost. Risk analysts need to focus attention on characterizing the information appropriately for purposes of the risk assessment (and risk management questions at hand), not on characterization for its own sake.