Uncertainty inherent in empirical fitting of distributions to experimental data

Treatment of experimental data often entails fitting frequency functions, in order to draw inferences on the population underlying the sample at hand, and/or identify plausible mechanistic models. Several families of functions are currently resorted to, providing a broad range of forms; an overview is given in the light of historical developments, and some issues in identification and fitting procedure are considered. But for the case of fairly large, well behaved data sets, empirical identification of underlying distribution among a number of plausible candidates may turn out to be somehow arbitrary, entailing a substantial uncertainty component. A pragmatic approach to estimation of an approximate confidence region is proposed, based upon identification of a representative subset of distributions marginally compatible at a given level with the data at hand. A comprehensive confidence region is defined by the envelope of the subset of distributions considered, and indications are given to allow first order estimation of uncertainty component inherent in empirical distribution fitting.