Influence Of Plotting Position Formulas On Quantile Estimates In L-moments Analysis

Studies have shown that in frequency analysis, linear moment has good unbiasedness and robustness to outliers.The major advantage of the L-moments over the conventional moments is that L-mements are more robust to the parameters value of frequency eurve.In frequency analysis by using L-Moments methods for parameter estimation, there is an unsolved issue of whether to consider using plotting position formula or not in quantile estimation? What is the influence of different plotting position formulas on quantile estimates? This was discussed in the paper. Based on annual maximum daily precipitation data series at 96 precipitation stations in the Taihu Lake Basin in East China, via L-Moment Analysis in combination with Monte Carlo Simulation method, the influence of different A and B in the plotting position formula Pi:n=(i+A)/(n+B), B>A>-1 on quantile estimates has been discussed and assessed. The criterion of Relative RMSE between the actual data frequency estimates and the average of quantiles obtained based on the generated data was applied to computation and analysis in the assessment, focusing on the influence on quantiles for rare frequencies such as 100-y,1,000-y and 10,000-y events. It is found out that the unbiased estimator of Pi:n=i/n,i.e. A=0 and B=0 in the plotting formula, has a little influence on frequency estimates in terms of uncertainties for frequent estimates such as 2-y,5-y and 10-y events in the L-moments Analysis, but a considerable influence for rare frequency estimates such as 100-y,1,000-y and 10,000-y events. It is recommended that the plotting position formula of Pi:n=(i-0.35)/n,i.e.A=-0.35and B=0, is good for quantile estimates for all frequencies, particularly for the rare frequencies events though the unbiased estimator of Pi:n=i/n is also suitable to the frequent events.