Many practical problems require the fitting of a probability distribution to a data sample, and in many fields of application the available data consist of not just a single sample but a set of samples drawn from similar probability distributions. It is natural to wonder whether the distribution for one sample can be more accurately estimated by using information not just from that sample but also from the other related samples. In the environmental sciences the data samples are typically measurements of the same kind of data made at different sites, and the process of using data from several sites to estimate the frequency distribution is known as regional frequency analysis. We have developed an approach to regional frequency analysis that is statistically efficient and reasonably straightforward to implement. Our aim in this monograph is to present a complete description of our approach: the specification of all necessary computations, a description of the theoretical statistical background, an assessment of the method's performance in plausible practical situations, recommendations to assist with the subjective decisions that are inevitable in any statistical analysis, and consideration of how to overcome some of the difficulties often encountered in practice. The technical level of exposition is intended to be comprehensible to practitioners with no more than a basic knowledge of probability and statistics, including an understanding of the concepts defined in Sections 2.1–2.3.