A statistical model comprising nine different probability distributions used especially for flood frequency analysis was applied to annual flood peak series with at least 30 observations for 11 unregulated streams in the Rhine Basin in Germany and two streams in Scotland. The parameters of most of those distributions were estimated by the methods of maximum likelihood and probability-weighted moments. The distributions were first compared by classical goodness-of-fit tests on the observed series. Next, the goodness of predictions of the extreme right-tail events by all the models were evaluated through detailed analyses of long synthetically generated series. The general extreme value and 3-parameter lognormal distributions were found to predict the rare floods of return periods of 100 years or more better than the other distributions used. The general extreme value type 2 and log-Pearson type 3 (when skewness is positive) would usually yield slightly conservative peaks. The Wakeby distribution also gave peaks mostly on the conservative side. The log-logistic distribution with the method of maximum likelihood was found to overestimate greatly high return period floods.