ASSESSMENT OF FITTING TECHNIQUES FOR THE LOG PEARSON TYPE-3 DISTRIBUTION USING MONTE-CARLO SIMULATION

The distribution parameter space for the log Pearson type 3 distribution has been defined for annual maximum floods at 37 long‐term Canadian flow‐gauging stations. Within this parameter space, log Pearson type 3 independent variates were generated in samples of size 25, 50, and 100. For each sample, parameters and specified quantiles were estimated by using three techniques: the method of maximum likelihood, the method of moments, and a method which preserves the moments of the untransformed flows. The parameter estimates were generally very poor; they were highly biased and exhibited large variances, However, there was no evidence of significant bias in the quantile estimates. On the basis of statistical efficiency, no one method was superior for the whole of the parameter space. The third method was generally superior for negative values of skewness of the logarithmically transformed flows, and the method of moments was the best method for positive values of skewness. The differences in standard error were generally small. The expressions for the standard error of the T‐year flood were found to be biased for N equal to 25, 50, and 100. In general, the asymptotic maximum likelihood relation gave underestimates, whereas the moments relation gave overestimates. Copyright 1979 by the American Geophysical Union.