Data generation processes and statistical management of interval data

Statistical methods for dealing with interval data have been developed for some time. Real intervals are the natural extension of real point values. They are commonly considered to generalize the nature of the experimental outcomes from the classical scenario to a more imprecise situation. Interval data have been mainly treated in the context of fuzzy models, as a particular case of increasing the level of imprecision of the data. However, specific methods to deal explicitly with interval data have also been developed. It is described which experimental settings might result in interval-valued data. Some of the major statistical procedures used to deal with interval data are presented. Given the quite different data generation processes resulting in interval data, it is discussed which method appears most appropriate for specific types of interval data. Some practical applications demonstrate the link between data generation processes, specific type of interval data, and statistical methods used for the analysis of these data.