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

A saddlepoint approximation is derived for the cumulative distribution function of the sample mean of n independent bivariate random vectors. The derivations use Lugannani and Rice's saddlepoint formula and the standard bivariated normal distribution function. The separate versions of the approximation for the discrete cases are also given. A Monte Carlo study shows that the new approximation is very accurate.