<scp>Quantile</scp> Estimation in Rainfall Frequency Analysis With Log‐Logistic Distribution Using Pivotal Quantities: Method, Effect, and Application

ABSTRACT Rainfall frequency analysis commonly presents results as confidence intervals around quantile estimates to account for uncertainty. However, standard bootstrap methods can introduce considerable errors, particularly when sample sizes are small. Focusing on the widely used Log‐logistic (LLO) distribution, this study proposes an approach based on pivotal quantities. By generating realizations from three joint pivotal quantities, the method enables the estimation of distribution parameters and return levels along with their associated uncertainties. Its performance is assessed through simulation experiments involving LLO distributions with varying shape parameters, and compared with the basic percentile bootstrap and the bias‐corrected and accelerated (BCa) bootstrap methods. The results indicate that the pivotal quantity method generally provides more accurate quantile estimates for both parameters and return levels, while showing lower sensitivity to the characteristics of the underlying distribution. The advantages are particularly evident under conditions commonly encountered in rainfall frequency analysis, such as small sample sizes, high return periods, and extreme confidence levels. The practical utility of the method is illustrated through a case study in Suzhou City, China, which highlights spatial variations in rainfall intensity and underscores the importance of accounting for heavy‐tail behavior at rain gauges with large values of the diagnostic variable Q k . Overall, the proposed pivotal quantity method provides a promising alternative for improving the reliability of statistical inference in rainfall frequency analysis.