Based on annual maximum daily precipitation data series at 96 gauging 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 po - sition formula Pi∶n=（i+A）/（n+B），B>A>-1 on quantile estimates has been discussed and assessed. The criterion of 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=-0.35 and 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.