在再保险中,对高超额层选取及定价等问题的讨论有着重要意义,从而引出对如何选取好的统计模型来拟合大的观测值这一问题的讨论。针对这一问题,我们考虑了POT方法(peaks over thoreholdapproach),即根据极值理论(EVT),用模拟的方法对这...在再保险中,对高超额层选取及定价等问题的讨论有着重要意义,从而引出对如何选取好的统计模型来拟合大的观测值这一问题的讨论。针对这一问题,我们考虑了POT方法(peaks over thoreholdapproach),即根据极值理论(EVT),用模拟的方法对这一方法进行评价,指出了POT方法的若干优缺点陷。展开更多
考虑历史洪水的超定量(Peak-over-Threshold,POT)洪水频率分析方法能使洪水信息的利用最大化,并有效提高洪水频率分析的合理性。本文以武江流域犁市(二)站为例,以泊松分布为超定量年发生次数分布,用广义Pareto(GP)分布拟合POT样本,线性...考虑历史洪水的超定量(Peak-over-Threshold,POT)洪水频率分析方法能使洪水信息的利用最大化,并有效提高洪水频率分析的合理性。本文以武江流域犁市(二)站为例,以泊松分布为超定量年发生次数分布,用广义Pareto(GP)分布拟合POT样本,线性矩法(L-M)估计不连续POT样本的分布参数,探讨了历史洪水在POT洪水频率分析中的应用。结果表明,武江选取门限值为1079m3/s能兼顾分布稳定性和样本独立性;对连续POT样本和不连续POT样本的洪水频率分析对比得出,对历史洪水的考虑有效改善了POT方法对大洪水的拟合,由不连续POT样本所得的GP频率分布曲线对"2006·07"洪水的重现期估计为501年,而基于连续POT样本的频率分析估计结果为330年,表明超定量洪水频率分析时必须考虑历史洪水;考虑历史洪水条件下,POT方法的拟合优度略优于年最大值(Annual Maximum Series,AMS)方法。展开更多
为得到大功率拖拉机传动轴在田间作业工况下的载荷谱,该文针对传统传动系载荷谱编制过程中雨流计数及雨流域外推方法的局限性,提出基于POT(peak over threshold)模型的大功率拖拉机传动轴载荷时域外推方法。首先搭建了拖拉机传动轴扭矩...为得到大功率拖拉机传动轴在田间作业工况下的载荷谱,该文针对传统传动系载荷谱编制过程中雨流计数及雨流域外推方法的局限性,提出基于POT(peak over threshold)模型的大功率拖拉机传动轴载荷时域外推方法。首先搭建了拖拉机传动轴扭矩测试系统,利用无线扭矩传感器采集大功率拖拉机传动轴在田间犁耕作业工况下的载荷数据;基于极值理论建立POT模型,利用灰色关联度分析方法选取最优阈值,确定时域载荷数据中上限、下限阈值分别为497和333 N·m。对超越阈值的极值载荷进行提取并利用广义帕累托分布(generalized pareto distribution,GPD)对极值载荷的分布进行拟合,拟合结果与极值载荷样本之间的相关系数均大于0.99,将生成服从GPD的新极值点取代原样本中的极值点从而实现时域载荷数据的外推。结果表明,GPD能够准确描述大功率拖拉机传动轴载荷超越阈值的分布情况,与雨流域外推方法相比,基于POT模型的载荷时域外推方法不仅可以获得任意里程的载荷时域序列,还能够极大程度保留实测载荷循环的次序,为今后大功率拖拉机传动系的室内载荷谱加载试验提供更加真实可靠的数据支持。展开更多
It has been theoretically proven that at a high threshold an approximate expression for a quantile of GEV （Generalized Extreme Values） distribution can be derived from GPD （Generalized Pareto Distribution）. Afterw...It has been theoretically proven that at a high threshold an approximate expression for a quantile of GEV （Generalized Extreme Values） distribution can be derived from GPD （Generalized Pareto Distribution）. Afterwards, a quantile of extreme rainfall events in a certain return period is found using L-moment estimation and extreme rainfall events simulated by GPD and GEV, with all aspects of their results compared. Numerical simulations show that POT （Peaks Over Threshold）-based GPD is advantageous in its simple operation and subjected to practically no effect of the sample size of the primitive series, producing steady high-precision fittings in the whole field of values （including the high-end heavy tailed）. In comparison, BM （Block Maximum）-based GEV is limited, to some extent, to the probability and quantile simulation, thereby showing that GPD is an extension of GEV, the former being of greater utility and higher significance to climate research compared to the latter.展开更多
文摘在再保险中,对高超额层选取及定价等问题的讨论有着重要意义,从而引出对如何选取好的统计模型来拟合大的观测值这一问题的讨论。针对这一问题,我们考虑了POT方法(peaks over thoreholdapproach),即根据极值理论(EVT),用模拟的方法对这一方法进行评价,指出了POT方法的若干优缺点陷。
文摘考虑历史洪水的超定量(Peak-over-Threshold,POT)洪水频率分析方法能使洪水信息的利用最大化,并有效提高洪水频率分析的合理性。本文以武江流域犁市(二)站为例,以泊松分布为超定量年发生次数分布,用广义Pareto(GP)分布拟合POT样本,线性矩法(L-M)估计不连续POT样本的分布参数,探讨了历史洪水在POT洪水频率分析中的应用。结果表明,武江选取门限值为1079m3/s能兼顾分布稳定性和样本独立性;对连续POT样本和不连续POT样本的洪水频率分析对比得出,对历史洪水的考虑有效改善了POT方法对大洪水的拟合,由不连续POT样本所得的GP频率分布曲线对"2006·07"洪水的重现期估计为501年,而基于连续POT样本的频率分析估计结果为330年,表明超定量洪水频率分析时必须考虑历史洪水;考虑历史洪水条件下,POT方法的拟合优度略优于年最大值(Annual Maximum Series,AMS)方法。
基金supported jointly Science Foundation of China （Grant No. 40675043） Program of the Jiangsu Key Laboratory of Meteorological Disaster （Grant No. KLME050209）.
文摘It has been theoretically proven that at a high threshold an approximate expression for a quantile of GEV （Generalized Extreme Values） distribution can be derived from GPD （Generalized Pareto Distribution）. Afterwards, a quantile of extreme rainfall events in a certain return period is found using L-moment estimation and extreme rainfall events simulated by GPD and GEV, with all aspects of their results compared. Numerical simulations show that POT （Peaks Over Threshold）-based GPD is advantageous in its simple operation and subjected to practically no effect of the sample size of the primitive series, producing steady high-precision fittings in the whole field of values （including the high-end heavy tailed）. In comparison, BM （Block Maximum）-based GEV is limited, to some extent, to the probability and quantile simulation, thereby showing that GPD is an extension of GEV, the former being of greater utility and higher significance to climate research compared to the latter.
