Uncertainty inherent into empirical fitting of distributions to experimental data

Treatment of experimental data often entails fitting frequency functions, in order to draw inferences on the underlying distribution and/or identify plausible mechanistic models. Several families of functions are currently resorted to, capable of accommodating a broad range of shapes. An overview is given in the light of historical developments, and main 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 substantial uncertainty. A pragmatic approach to estimation of such an uncertainty component is proposed, based upon identification of a representative subset of distributions marginally compatible with the data at hand at a given level. An approximate confidence region is defined as the envelope of that subset of distributions, and graphs are shown enabling indicative estimation of the uncertainty component considered.