The generalized method of moments as applied to problems of flood frequency analysis: Some practical results for the log-Pearson type 3 distribution

The log-Pearson type 3 distribution is widely used in North America and Australia for fitting annual flood series. Four different versions of the method of moments used in fitting this distribution are compared using Monte Carlo simulated samples which reflect some of the characteristics of annual flood series observed at some Canadian rivers. The bias, standard error, root mean square error, and skew, of the parameter estimates, and of estimates of events associated with different probabilities of occurrence are examined. Also examined are the correlation coefficients between probabilities of occurrence are examined. Also examined are the correlation coefficients between the parameter estimates and between the sample moments that are used in each of the four methods of estimation. It is observed that variances, covariances and correlation coefficients calculated using the usual first-order asymptotic approximation might have considerable error and therefore should be used with caution. On the basis of mean square error of events with return period above the range covered by the sample it is observed that a method proposed earlier which uses moments of order 1, 2 and 3 in real space performs better than the other three methods although certain of the other methods follow the recommendation put forward by some investigators that higher order moments (moments of order 3 or more) should be avoided in flood frequency estimation. It is argued in the present study that the use of higher order moments should not be avoided simply because they have high variability because it is not only the variability of the moments which determines the degree of variability of the estimated design flood events but also the correlation that exists between these moments. Some recommendations are given at the end of the study aimed at achieving better efficiency in flood frequency research at a period where more and more distributions and methods of estimation are being proposed.