Modified weighted function method with the incorporation of historical floods into systematic sample for parameter estimation of Pearson type three distribution

- Extending modified weighted function for parameters estimate of non-simple sample.
- Monte Carlo experiments show that the proposed approach (PA) is satisfactory.
- The performance of PA is obviously superior to the original Weighted Function (WF).
- The performance of PA is slightly better than Linear moments (L-M).
- Real flood extremes data from 26 gauges are analyzed by PA, WF and L-M respectively.

SummaryIncorporating the historical flood and paleoflood information to systematical observed data (i.e. simple sample) is extremely useful approach for enriching the datasets and improving the accuracy of parameter estimation, in turn to improve the reliability of hydrological frequency analysis. In this paper, the formulas for using Modified Weighted Function (MWF) method to estimate parameters of Pearson Type Three Distribution (PE3) in term of non-simple sample (with the incorporation of historical flood information to systematically recorded sample) are developed, called as MWFIHF, which makes MWF method available for non-simple sample. Monte Carlo experiment is carried out to simulate a large number of non-simple samples upon which statistical properties of MWFIHF are investigated. The results show that the proposed formulas for MWFIHF are satisfactory. Besides, the results of MWFIHF are compared to that of the original Weighted Function (WF) and Linear moments (L-M). It indicates that MWFIHF is obviously superior to WF and slightly better than L-M in terms of statistical unbiasness and effectiveness. These three approaches are also used to analyze flood extremes data collected at 26 gauges around China. It also demonstrates that, MWFIHF fits well to most of these real flood extremes events.