Uncertainty analysis on the location and scale parameters for Pearson type Ⅲ distribution using pivotal quantities in rainfall frequency analysis

The Pearson type III (P-III) distribution is widely applied in rainfall frequency analysis, yet quantifying parameter uncertainty remains challenging due to reliance on prior assumptions or resampling from point estimates. This study proposes a pivotal-quantity-based method to construct interval estimations for the location and scale parameters, while the shape parameter is estimated separately. The proposed framework avoids prior specification and reduces dependence on point-estimate-based resampling. The method is applied to rainfall frequency analysis using annual maximum rainfall data from 13 gauges in Shanghai, and its performance is evaluated against Bayesian and bootstrap approaches through simulation experiments under varying sample sizes. Results indicate that uncertainty in design rainfall estimates tends to be higher in northern and central Shanghai. In addition, the proposed method reduces root mean square error (RMSE) by approximately 10–30% compared to the bootstrap method across different sample sizes, while showing comparable performance to the Bayesian approach. These results suggest that the proposed method provides an alternative framework for uncertainty analysis of the P-III distribution under the conditions considered in this study, particularly for small to moderate sample sizes.