Partial Probability Weighted Moments For Estimating Distribution Parameters In Flood Frequency Analysis

In this paper, in order to avoid the small values of the flood sample series producingnuisance value in the estimation of larger return period design flood, the principles andmethods of partial probability weighted moments (PPWM) were used to estimate parametersof flood frequency distribution which had been derived by Q.J.Wang (1990).Its purpose is toexplore the applicability of PPWM for parameter estimation of flood frequency distribution innorthern Shaanxi. On the basis of previous studies, MATLAB programs were used to achievethe parameters’ numerical solution of the GEV distribution and Pearson III distribution fromPPWM. Monte Carlo experiments were performed to assess the statistical properties ofparameters estimation by the method of PPWM under different lower bound censoredsamples. The method of estimating parameters of the GEV distribution and Pearson IIIdistribution using PPWM were used for flood frequency analysis of annual maximum floodspeak flow series of12gauging stations in northern Shaanxi. And the goodness of fit of thetheoretical distributions from different lower bound censored samples was assessed. The mainresults are as follows:(1)This paper has achieved the parameters’ numerical solution of the GEV distributionand Pearson III distribution from PPWM. This play a strong practical significance for thepromotion and application of PPWM.Apply integrating theory and special functions to derive the relationship between GEVdistribution parameters and PPWM. For given samples, we can use the sample PPWM toestimate unbiase parameter estimation.However, due to the parameters estimation of Pearson III distribution from PPWMcontains S special function, it is very difficult to solve the parameters derived by strictmathematical methods. In this paper, we use Particle Swarm Optimization (PSO) andMATLAB software to achieve the parameters’ numerical solution of Pearson III distributionfrom PPWM. This numerical methods have high precision, and the use of MATLAB softwaregreatly reduces the workload, so the application of estimating distribution parameters from PPWM becomes more convenient and effective.(2)Monte Carlo simulations show that, when take the moderate lower bound censoredvalue, the parameters estimation values have better statistical properties by the method ofPPWM from different lower bound censored samples. With lower bound censored valueincreasing, the effect of statistical parameter estimation is ncreasing, but still has goodeffectiveness in high quantile estimation, and in a certain range, it does not deteriorate withthe increase of lower bound censored values. In some cases, the statistical properties of theestimated design value from PPWM is better than the PWM. Thus, in order to get theestimation of the high quantile (large return period), the application of low censored samplefrom PPWM will not affect the validity of its estimates.Monte Carlo simulations also show that, using lower bound censored sample fromPPWM to estimate the distribution parameters, it is an effective means to improve the GEVdistribution parameter estimation effect when increasing the sample size. But it needs to dothe further study and analysis whether can improve the Pearson III distribution parameterestimation effect.(3)It is reasonable to estimate flood frequency analysis parameters of the GEVdistribution and Pearson III distribution from PPWM on the annual maximum floods peakflow series of12gauging stations in northern Shaanxi. The corresponding censored lowerbound value of each station is different in the optimal fitting effect theory distribution whenusing different evaluation methods. No matter what kind of evaluation methods, the optimalfitting effect theory distribution are better for most gauging stations. The method of PPWMon lower bound censored samples to estimating the GEV distribution and Pearson IIIdistribution can be used in the study area.