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.