A linear approach is presented for analysing flood discharge series affected by measurement errors which are random in nature. A general model based upon the conditional probability concept is introduced to represent random errors and to analyse their effect on flood estimates. Flood predictions provided by quantiles are shown to be positively biased when performed from a sample of measured discharge. Though for design purposes such an effect is conservative, this bias cannot be neglected if the peak discharges are determined from stage measurements by means of the extrapolated tail of the rating curve for the gauging station concerned. Monte Carlo experiments, which have been carried out to analyse small sample effects, have finally shown that the use of the method of maximum likelihood is able to reduce the bias due to measurement errors in discharge data.