Plotting formula for pearson type III distribution considering historical information

Most of the existing plotting position formulas have been proposed for use in the analysis of systematic flood records, but little has been reported on the plotting formulas for historical or non-systematic flood samples. In particular, no previous investigations have specifically examined the probability plots for the Pearson type III (P3) distribution in the analysis of historical flood information. The present paper suggests a new plotting position formula for the P3 distribution for use with both systematic and historical flood records. The proposed formula has a simple structure as do most existing formulas, but it is more flexible because in can take explicitly into account the skewness coefficient of the underlying distribution. Further, results of graphical and numerical comparisons have demonstrated that the suggested formula provided the least bias in flood quantile estimation as compared with many available plotting formulas, including the well-known Weibull formula. Finally, results of a numerical example using actual flood data have indicated the practica convenience of the proposed plotting formula. It can be concluded that the formula developed in this study is the most appropriate for the P3 distribution in the analysis of flood records considering historical information.