基于轮廓似然函数的PM_(10)极值浓度分析

以R软件为分析工具,选择GEV(generalized extreme value distribution)模型拟合四川省泸州市2003～2007年期间PM10每月最高日平均浓度数据,采用极大似然法估计模型的3个参数即位置参数、尺度参数、形状参数,利用所得的参数估计值计算得出某一标准值(如GB3095—1996)的重现期;进一步利用参数估计值计算轮廓似然函数,估计某一段固定时间间隔的PM10浓度的重现值以及其置信区间。结果表明,GEV模型能很好地拟合泸州市PM10数据,利用轮廓似然函数估计的不同时间间隔的重现值准确度高,统计结果可以为环境主管部门发布污染状况预警信息提供参考。     

基于平稳与非平稳GEV模型的鄱阳湖流域极值降水模拟

论文基于鄱阳湖流域降水数据,采用平稳和非平稳GEV模型进行极值降水的模拟和分析。检测各站年最大1 d降水量序列（AMS1）的非平稳特征,将时间作为位置参数的协变量进行非平稳AMS1序列的GEV模拟。结果表明：1）鄱阳湖流域AMS1序列的形状参数基本均大于0,服从Fréchet分布;位置和尺度参数的空间分布较一致,形状参数则有差异。2）在较高重现期下由轮廓似然方法估计的置信区间比Delta方法更准确;重现水平的轮廓似然函数曲线在较高重现期之下呈较显著不对称性。3）不同重现期下的鄱阳湖流域极值降水等值线图的空间分布特征,与位置和尺度参数的分布图更为接近,与形状参数的差别则较大。4）基于非平稳GEV模型得到赣县站随时间变化的极值降水设计值,其在1951年的100 a一遇设计值到2010年下降为接近50 a一遇,预示着未来发生极值降水和洪灾的风险加大。     

基于广义极值分布的流化床压力波动风险预警

为预警气泡运动所引起的流化床粉煤气化压力波动风险,提出预测压力波动极值以及压力波动重现水平的方法;首先采用自相关分析法将压力波动母样本数据合理分段,再用区间极值法统计子样本的压力波动极值数据,以广义极值(GEV)分布方法建立GEV分布模型和Gumbel分布模型,并经过模型诊断选择最优模型;然后通过子样本与母样本的参数关...     

极值理论在重金属污染土壤修复中的应用

为了准确预测重金属污染地块不同区域内重金属的最大值,以便于后续筛选重金属修复技术、确定重金属修复药剂使用量等提供依据,采用极值理论方法对某重金属砷污染地块三块区域内的重金属砷浓度数据进行极值分布的统计分析,对比不同分布形式对重金属砷浓度数据拟合的效果.结果 表明:广义极值分布可以很好地描述重金属砷浓度数据的分布情况,通...     

TWO PRACTICAL APPROACHES FOR DETERMINING THE CONFIDENCE INTERVAL OF RAINFALL DEPTH PERCENTILES1

ABSTRACT: A simple simulation type approach and a statistical method are proposed for determining the confidence interval of the T‐year frequency rainfall percentiles (or precipitation extremes) for generalized extreme value (GEV) distributions. The former method is based on the Monte Carlo testing procedure. To generate realizations, the covariance structure of the three parameters of GEV is investigated using an observed information matrix of the likelihood function. For distributions with realistic parameters, the correlation between the location and the scale parameters is practically constant when the shape parameter varies around values close to its optimal value. The latter method is based on likelihood ratio statistics. In the case where the joint confidence surface for shape parameters and estimates is plotted with lines of best estimates, the region where the estimated best percentile value can be chosen as a possible estimate is part of the joint confidence surface. The projection of this bounded region on axis of percentile is defined as the effective confidence interval in this research. The use of this effective interval as the confidence interval of the percentile of T‐year frequency rainfall is particularly recommended because it is stable for T and it reflects variations in all three parameters of GEV appropriately.     

Time-varying models for extreme values

We propose a new approach for modeling extreme values that are measured in time and space. First we assume that the observations follow a Generalized Extreme Value (GEV) distribution for which the location, scale or shape parameters define the space–time structure. The temporal component is defined through a Dynamic Linear Model (DLM) or state space representation that allows to estimate the trend or seasonality of the data in time. The spatial element is imposed through the evolution matrix of the DLM where we adopt a process convolution form. We show how to produce temporal and spatial estimates of our model via customized Markov Chain Monte Carlo (MCMC) simulation. We illustrate our methodology with extreme values of ozone levels produced daily in the metropolitan area of Mexico City and with rainfall extremes measured at the Caribbean coast of Venezuela.