Quantile estimation in frequency analysis of hydrologic variables for the generalized Pareto distribution: An approach based on specially formulated pivotal quantities
摘要
The Generalized Pareto (GP) distribution is widely used to model peaks-over-threshold (POT) series in frequency analysis of hydrologic variables. Because of various sources of uncertainty, results are commonly reported using confidence intervals, which rely on quantile estimations. However, previous studies have shown that confidence intervals may conceal biases in quantile estimates, potentially leading to misleading conclusions about reliability. This study proposes a novel pivotal quantity method (PQM) for quantile estimation in the GP distribution. The method constructs three pivotal quantities for the GP parameters, whose distributions depend only on the sample size, and uses them to estimate quantiles of both parameters and return levels. Its performance is evaluated for GP distributions with different tail behaviors and compared with six standard bootstrap methods. Results show that PQM generally provides more reliable quantile estimates for both parameters and return levels, particularly for the shape parameter and high return periods. Under the conditions commonly encountered in hydrological practice—such as small sample sizes, high return periods, and high confidence levels—PQM tends to outperform the standard bootstrap methods. The proposed approach is applicable to GP distributions with different tail behaviors and performs slightly better for heavy-tailed distributions. In addition, the designed pivotal quantities can be extended to other three-parameter distributions for uncertainty analysis in frequency analysis of hydrologic variables.