This text presents several single-variable statistical distributions that engineers and scientists use to describe the uncertainty and variation inherent in measured information. It lists significant properties of these distributions and describes methods for estimating their parameters, constructing confidence intervals, and testing hypotheses. Each distribution is illustrated by working through typical applications including some of the special methods associated with them. The intention is to provide the professional with a ready source of information on a useful range of distribution models and the techniques of analysis specific to each.

The need to deal rationally with the uncertainties that enter engineering analysis and design appears now well recognized by the engineering profession. This need is driven, on the one hand, by the competitive pressure to optimize designs and, on the other hand, by market demand for reliable products. Hence, engineers design their products closer to the limits of the materials used, while improving product durability. The result of these opposing pressures is that the engineer needs to replace traditional “contingency factors” by careful uncertainty analysis.

What is perhaps less well understood by the professional is the need to choose a distribution model that closely represents the entire range of measured values. This need arises from the skewness typical of the frequency functions of engineering data, coupled with the usual focus of engineering decisions on the location of distribution tails.