The frequency analysis of flood flows recommended in textbooks yields different results by the graphical method of plotting on probability paper using e.g. the Weibull plotting position formula and the analytical method assuming e.g. log-normal or log Pearson type III distributions. If both methods were correct, the results of the two methods should be identical.
The plotting position formulas assume that the plotting position should coincide with the mean (or median) of the probabilities which the observation of a rank m has in a great number of samples, each of the same size N. A study of the problem by using synthetic samples shows that these positions do not coincide with the line of the population.
A further study shows, however, that the positions of the probabilities of the expected – mean – values of the largest, next largest etc. observation coincide with the line of the population. Thus, it is not the mean value of p of a rank m, but the value of p of the mean value of log q of the rank m, which agrees with the line of population. Therefore, the author finds it essential that the logarithm of the annual peak flows obtain a plotting probability equal to the probability of the expected value of the logarithm of the observations. A new plotting position formula which corresponds to the probability of the expected values of log q is derived.