为获得高层建筑围护结构设计风荷载,通常需要考虑其表面风压系数的概率特征,进而进行极值估计。针对当前基于超越阈值模型的风压系数极值估计方法存在阈值选取困难,需要较大样本的不足,基于高层建筑标准模型进行风洞试验,首先研究其表...为获得高层建筑围护结构设计风荷载,通常需要考虑其表面风压系数的概率特征,进而进行极值估计。针对当前基于超越阈值模型的风压系数极值估计方法存在阈值选取困难,需要较大样本的不足,基于高层建筑标准模型进行风洞试验,首先研究其表面风压系数的概率特征,结果表明迎风区测点接近高斯分布,分离区测点风压系数母体接近Gamma分布,风压系数极小值接近GEV(general extreme value,GEV)分布;提出一种改进的POT(peak over threshold,POT)极值估计方法进行表面风压系数极值估计,进而与几种传统极值估计方法进行对比,结果表明改进POT极值估计方法可实现小样本的风压系数极值估计,其估计结果与大样本容量的标准极值偏差小于5%,且稳定性较好;最后给出了标准高层建筑模型表面极值风压系数。展开更多
We present a novel method to analyze extreme events of flows over manifolds called Peaks Over Manifold (POM). Here we show that under general and realistic hypotheses, the distribution of affectation measures converge...We present a novel method to analyze extreme events of flows over manifolds called Peaks Over Manifold (POM). Here we show that under general and realistic hypotheses, the distribution of affectation measures converges to a Generalized Pareto Distribution (GPD). The method is applicable to floods, ice cover extent, extreme rainfall or marine heatwaves. We present an application to a synthetic data set on tide height and to real ice cover data in Antartica.展开更多
大坝监测效应量作为一种随机变量,采用以极值理论为基础的POT(Peaks over Threshold)模型研究监测效应量的监控指标是合适的,但现有的POT模型的阈值确定以图形法为主,需要人工判断,主观性和随意性较大,且难以实现计算机自动化识别。通...大坝监测效应量作为一种随机变量,采用以极值理论为基础的POT(Peaks over Threshold)模型研究监测效应量的监控指标是合适的,但现有的POT模型的阈值确定以图形法为主,需要人工判断,主观性和随意性较大,且难以实现计算机自动化识别。通过构建阈值递增序列,计算不同阈值Tj条件下相应的监控指标,然后利用概率论中的3σ准则,以监控指标危险值与警戒值的差值△j趋近于测值序列标准差S作为确定最合理阈值的原则,提出了一种改进的阈值确定方法,并给出了一个验证实例。改进方法理论基础明确,有效地克服了图形法的主观性和随机误差,且能采用计算机程序实现最合理阈值的自动识别,增强了POT模型法拟定大坝安全监控指标的实用性。展开更多
Extreme events are defined as values of the event below or above a certain value called threshold. A well chosen threshold helps to identify the extreme levels. Several methods have been used to determine threshold so...Extreme events are defined as values of the event below or above a certain value called threshold. A well chosen threshold helps to identify the extreme levels. Several methods have been used to determine threshold so as to analyze and model extreme events. One of the most successful methods is the maximum product of spacing (MPS). However, there is a problem encountered while modeling data through this method in that the method breaks down when there is a tie in the exceedances. This study offers a solution to model data even if it contains ties. To do so, an optimal threshold that gives more optimal parameters for extreme events, was determined. The study achieved its main objective by deriving a method that improved MPS method for determining an optimal threshold for extreme values in a data set containing ties, estimated the Generalized Pareto Distribution (GPD) parameters for the optimal threshold derived and compared these GPD parameters with GPD parameters determined through the standard MPS model. The study improved maximum product of spacing method and used Generalized Pareto Distribution (GPD) and Peak over threshold (POT) methods as the basis of identifying extreme values. This study will help the statisticians in different sectors of our economy to model extreme events involving ties. To statisticians, the structure of the extreme levels which exist in the tails of the ordinary distributions is very important in analyzing, predicting and forecasting the likelihood of an occurrence of the extreme event.展开更多
To Statisticians, the structure of the extreme levels which exist in the tails of the ordinary distributions is very important in analyzing, predicting and forecasting the likelihood of an occurrence of extreme event....To Statisticians, the structure of the extreme levels which exist in the tails of the ordinary distributions is very important in analyzing, predicting and forecasting the likelihood of an occurrence of extreme event. Extreme events are defined as values of the event below or above a certain value called threshold. A well chosen threshold helps to identify the extreme levels. Several methods have been used to determine threshold so as to analyze and model extreme events. One of the most successful methods is the maximum product of spacing (MPS). However, there is a problem encountered while modeling data through this method in that the method breaks down when there is a tie in the exceedances. This study offers a solution to model data even when it contains ties. In the study, a method that improved MPS method for determining an optimal threshold for extreme values in a data set containing ties was derived. The Generalized Pareto Distribution (GPD) parameters for the optimal threshold were derived and compared to GPD parameters determined through the standard MPS model. The study improved the standard MPS methodology by introducing the concept of frequency and used Generalized Pareto Distribution (GPD) and Peak over threshold (POT) methods as the basis of identifying extreme values. The improved MPS models and the standard models were applied to Nairobi Securities Exchange (NSE) trading volume data to determine the GPD parameters for different sectors registered in NSE market and their performance compared. It was realized that the improved MPS model performed better than the standard models. This study will help the Statisticians in different sectors of our economy to model extreme events involving ties.展开更多
利用1961～2011年江淮地区5～9月无缺测的71站逐日降水资料,做基于POT（Peaks-Over-Threshold）的广义Pareto 分布（GPD）,研究江淮地区极端降水的分布特征及其变化趋势.结果表明：（1）皖赣交界处阈值最大,西北和东南部较小,且江淮大...利用1961～2011年江淮地区5～9月无缺测的71站逐日降水资料,做基于POT（Peaks-Over-Threshold）的广义Pareto 分布（GPD）,研究江淮地区极端降水的分布特征及其变化趋势.结果表明：（1）皖赣交界处阈值最大,西北和东南部较小,且江淮大部分地区阈值的线性趋势系数为正,其中湖北东部和江西北部的站点,趋势达0.8 mm （10 a）^-1以上,并通过了显著性水平0.01的MK（Mann-Kendall）检验.（2）江淮地区中东部多存在连续性极端降水,因此文中采用基于极值指数的自动分串技术获得近似独立的极值样本.（3）尺度参数大值区位于江淮南部,西北、东南以及淮河以北较小,且线性趋势系数在大部分地区均表现为正值,表明出现降水极大值的概率增加.（4）皖赣鄂交界处是极端降水发生概率大值区,而西北、东南及安徽中部地区较小,且极端降水在大部分地区有增加的趋势,特别是在大别山附近及河南东部,2年和20年重现水平的趋势分别达6 mm （10 a）^-1和20 mm （10 a）^-1以上.展开更多
文摘为获得高层建筑围护结构设计风荷载,通常需要考虑其表面风压系数的概率特征,进而进行极值估计。针对当前基于超越阈值模型的风压系数极值估计方法存在阈值选取困难,需要较大样本的不足,基于高层建筑标准模型进行风洞试验,首先研究其表面风压系数的概率特征,结果表明迎风区测点接近高斯分布,分离区测点风压系数母体接近Gamma分布,风压系数极小值接近GEV(general extreme value,GEV)分布;提出一种改进的POT(peak over threshold,POT)极值估计方法进行表面风压系数极值估计,进而与几种传统极值估计方法进行对比,结果表明改进POT极值估计方法可实现小样本的风压系数极值估计,其估计结果与大样本容量的标准极值偏差小于5%,且稳定性较好;最后给出了标准高层建筑模型表面极值风压系数。
文摘We present a novel method to analyze extreme events of flows over manifolds called Peaks Over Manifold (POM). Here we show that under general and realistic hypotheses, the distribution of affectation measures converges to a Generalized Pareto Distribution (GPD). The method is applicable to floods, ice cover extent, extreme rainfall or marine heatwaves. We present an application to a synthetic data set on tide height and to real ice cover data in Antartica.
文摘极值理论关注风险损失分布的尾部特征,通常用来分析概率罕见的事件,它可以依靠少量样本数据,在总体分布未知的情况下,得到总体分布中极值的变化情况,具有超越样本数据的估计能力。因此,基于GPD(generalized pareto distribution)分布的POT(peak over threshold)模型可更有效地利用有限的巨灾损失数据信息,从而成为极值理论当前的主流技术(以下简称,POT-GPD模型)。针对地震巨灾发生频率低、损失高、数据不足且具有厚尾性等特点,利用POT-GPD模型对我国1969年至2013年间的地震直接经济损失数据进行了统计建模;采用样本Hill图及区间筛选算法选取阈值,并对形状参数及尺度参数进行了估计。模型检验表明,POT-GPD模型对巨灾风险厚尾特点具有较好的拟合效果和拟合精度,为地震巨灾风险估计的建模及巨灾债券的定价提供了理论依据。
文摘大坝监测效应量作为一种随机变量,采用以极值理论为基础的POT(Peaks over Threshold)模型研究监测效应量的监控指标是合适的,但现有的POT模型的阈值确定以图形法为主,需要人工判断,主观性和随意性较大,且难以实现计算机自动化识别。通过构建阈值递增序列,计算不同阈值Tj条件下相应的监控指标,然后利用概率论中的3σ准则,以监控指标危险值与警戒值的差值△j趋近于测值序列标准差S作为确定最合理阈值的原则,提出了一种改进的阈值确定方法,并给出了一个验证实例。改进方法理论基础明确,有效地克服了图形法的主观性和随机误差,且能采用计算机程序实现最合理阈值的自动识别,增强了POT模型法拟定大坝安全监控指标的实用性。
文摘Extreme events are defined as values of the event below or above a certain value called threshold. A well chosen threshold helps to identify the extreme levels. Several methods have been used to determine threshold so as to analyze and model extreme events. One of the most successful methods is the maximum product of spacing (MPS). However, there is a problem encountered while modeling data through this method in that the method breaks down when there is a tie in the exceedances. This study offers a solution to model data even if it contains ties. To do so, an optimal threshold that gives more optimal parameters for extreme events, was determined. The study achieved its main objective by deriving a method that improved MPS method for determining an optimal threshold for extreme values in a data set containing ties, estimated the Generalized Pareto Distribution (GPD) parameters for the optimal threshold derived and compared these GPD parameters with GPD parameters determined through the standard MPS model. The study improved maximum product of spacing method and used Generalized Pareto Distribution (GPD) and Peak over threshold (POT) methods as the basis of identifying extreme values. This study will help the statisticians in different sectors of our economy to model extreme events involving ties. To statisticians, the structure of the extreme levels which exist in the tails of the ordinary distributions is very important in analyzing, predicting and forecasting the likelihood of an occurrence of the extreme event.
文摘To Statisticians, the structure of the extreme levels which exist in the tails of the ordinary distributions is very important in analyzing, predicting and forecasting the likelihood of an occurrence of extreme event. Extreme events are defined as values of the event below or above a certain value called threshold. A well chosen threshold helps to identify the extreme levels. Several methods have been used to determine threshold so as to analyze and model extreme events. One of the most successful methods is the maximum product of spacing (MPS). However, there is a problem encountered while modeling data through this method in that the method breaks down when there is a tie in the exceedances. This study offers a solution to model data even when it contains ties. In the study, a method that improved MPS method for determining an optimal threshold for extreme values in a data set containing ties was derived. The Generalized Pareto Distribution (GPD) parameters for the optimal threshold were derived and compared to GPD parameters determined through the standard MPS model. The study improved the standard MPS methodology by introducing the concept of frequency and used Generalized Pareto Distribution (GPD) and Peak over threshold (POT) methods as the basis of identifying extreme values. The improved MPS models and the standard models were applied to Nairobi Securities Exchange (NSE) trading volume data to determine the GPD parameters for different sectors registered in NSE market and their performance compared. It was realized that the improved MPS model performed better than the standard models. This study will help the Statisticians in different sectors of our economy to model extreme events involving ties.
文摘利用1961～2011年江淮地区5～9月无缺测的71站逐日降水资料,做基于POT（Peaks-Over-Threshold）的广义Pareto 分布（GPD）,研究江淮地区极端降水的分布特征及其变化趋势.结果表明：（1）皖赣交界处阈值最大,西北和东南部较小,且江淮大部分地区阈值的线性趋势系数为正,其中湖北东部和江西北部的站点,趋势达0.8 mm （10 a）^-1以上,并通过了显著性水平0.01的MK（Mann-Kendall）检验.（2）江淮地区中东部多存在连续性极端降水,因此文中采用基于极值指数的自动分串技术获得近似独立的极值样本.（3）尺度参数大值区位于江淮南部,西北、东南以及淮河以北较小,且线性趋势系数在大部分地区均表现为正值,表明出现降水极大值的概率增加.（4）皖赣鄂交界处是极端降水发生概率大值区,而西北、东南及安徽中部地区较小,且极端降水在大部分地区有增加的趋势,特别是在大别山附近及河南东部,2年和20年重现水平的趋势分别达6 mm （10 a）^-1和20 mm （10 a）^-1以上.
