ABSTRACT
This chapter presents a strategy to help assessors choose probability distributions when some data are available. Three common and equivalent ways of displaying probability information are reviewed. They are the probability density function (or probability mass function for discrete random variables), the cumulative distribution function, and the survival function. The strategy for selecting a probability distribution begins by considering whether the data can be used as is, that is as an empirical distribution, without selecting a specific distribution. For those seeking a specific distribution the process begins by understanding the data. What is its source, is it discrete or continuous, is it bounded, unbounded, or partially bounded, is it parametric on nonparametric, univariate or multivariate? Plot the data to see what it looks like. Theory may be the strongest reason for selecting a distribution. Calculating some descriptive statistics can sometimes be helpful as can previous experience. Distribution fitting should not, generally, be used as the basis for choosing a distribution but it is a powerful tool for testing hypotheses based on the previous steps. Expert opinion and sensitivity analysis may also be useful in difficult instances. Two examples illustrate the use of this strategy.
