在极端值分析中对四参数卡帕分布的间距方法的L时刻,最大概率和最大产物的比较分析
Muhammad Shafeeq Ul Rehman Khan1, Zamir Hussain2, Sadaf Sher3
1Department of Civil, Environmental Engineering and Architecture, University of Cagliari, Via Marengo, 2, Cagliari, 09123, Italy.
Scientific reports
|January 3, 2025
概括
间距最大积 (MPS) 方法是最好的估计卡帕分布 (KAPD) 参数,显示最小的误差. 对于形状参数分析的低偏差,建议使用L-时刻.
科学领域:
- 水文学的水文学
- 统计建模 统计建模
- 极端价值理论 极端价值理论
背景情况:
- 精确估计极端值在水文学中至关重要.
- 四个参数的卡帕分布 (KAPD) 是一种极端价值分析的灵活模型.
- 不同的参数估计方法可以显著影响模型性能.
研究的目的:
- 为了比较L-时刻,最大概率和最大间距产物 (MPS) 的性能,用于装配KAPD.
- 用蒙特卡洛模拟来评估参数估计的准确性和偏差.
- 评估估计方法对使用现实水文数据进行量子估计的影响.
主要方法:
- 使用蒙特卡洛模拟来生成用于评估估计方法的数据.
- 根平均平方误差 (RMSE) 和偏差被用作主要准确度指标.
- 分析了每年最大峰值流量的现实数据,并使用通用正常分布进行错误分析.
主要成果:
- 间距最大产物 (MPS) 方法显示了最低的RMSE,表明了更高的准确性,特别是在重尾和斜数据.
- L-moments方法显示偏差较低,因此适用于分析形状参数,略微或中度的斜率.
- 对峰值流量数据的实证分析证实了对估计方法性能的模拟结果.
结论:
- 由于其准确性,MPS是KAPD参数估计的首选方法,特别是在斜和重尾分布中.
- 当低偏差是形状参数估计的优先事项时,L-时刻提供了一个可靠的替代方案.
- 该研究为选择适合于水文应用的极端价值分析的估计方法提供了宝贵的见解.
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