<p>Given the various uncertainties inherent in hydrological processes, interval estimations of return levels are frequently required. However, conventional methods may produce overly wide or overly narrow confidence intervals, particularly when the sample size is small. For the commonly used Weibull distribution in rainfall frequency analysis, three joint pivotal quantities are designed to obtain the confidence intervals of parameters and return levels. Comparisons with standard non-parametric and parametric bootstrap methods are conducted through simulation experiments to evaluate the reliability of the proposed method. The results show that the pivotal quantity method performs better in confidence interval estimations for parameters than the bootstrap methods particularly noticeable with small sample sizes. As for return level, the proposed method can provide more reliable interval estimations in case of small values for either sample size or the significance level. To validate its effectiveness, the pivotal quantity method is applied to rainfall frequency analysis at 11 rain gauges in Jiangsu Province, China. The pivotal quantity method exhibits high efficiency in estimating the intervals for location parameter and yields reliable point estimations based on the realizations. In samples with distinct regional characteristics, the interval width of the location parameter correlates directly with the shape parameter and that of the shape parameter correlates inversely with the coefficient of variation. The proposed pivotal quantity method performs well in frequency analysis based on Weibull distribution and is recommended for application in various fields of hydrology research. The three pivotal quantities hold promise for extension to a more generalized distribution.</p>

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Rainfall frequency analysis: interval estimations for Weibull distribution based on specially formulated pivotal quantities

  • Weiqiang Zheng,
  • Shuguang Liu,
  • Zhengzheng Zhou

摘要

Given the various uncertainties inherent in hydrological processes, interval estimations of return levels are frequently required. However, conventional methods may produce overly wide or overly narrow confidence intervals, particularly when the sample size is small. For the commonly used Weibull distribution in rainfall frequency analysis, three joint pivotal quantities are designed to obtain the confidence intervals of parameters and return levels. Comparisons with standard non-parametric and parametric bootstrap methods are conducted through simulation experiments to evaluate the reliability of the proposed method. The results show that the pivotal quantity method performs better in confidence interval estimations for parameters than the bootstrap methods particularly noticeable with small sample sizes. As for return level, the proposed method can provide more reliable interval estimations in case of small values for either sample size or the significance level. To validate its effectiveness, the pivotal quantity method is applied to rainfall frequency analysis at 11 rain gauges in Jiangsu Province, China. The pivotal quantity method exhibits high efficiency in estimating the intervals for location parameter and yields reliable point estimations based on the realizations. In samples with distinct regional characteristics, the interval width of the location parameter correlates directly with the shape parameter and that of the shape parameter correlates inversely with the coefficient of variation. The proposed pivotal quantity method performs well in frequency analysis based on Weibull distribution and is recommended for application in various fields of hydrology research. The three pivotal quantities hold promise for extension to a more generalized distribution.