Copulas相依结构下完全和非完全样本极值的联合渐近分布

在日常生活中,观察某一组数据时,各种偶然因素或不可避免的因素都会导致数据出现随机丢失。通过研究满足阿基米德Copula相依结构极值的联合分布,可以减少或避免极端事件发生时所带来的损失。本文研究了随机缺失情形下,随机序列满足阿基米德Copula相依结构时完全样本与非完全样本极值的联合渐近分布,并给出几种典型的示例来说明主要结论。这不仅在理论中具有重要意义,在实际生活中也具有一定的意义。

Joint Return Value Estimation of Significant Wave Heights and Wind Speeds with Bivariate Copulas

The joint design criteria of significant wave heights and wind speeds are quite important for the structural reliability of fixed offshore platforms.However,the design method that regards different ocean environmental variables as independent is conservative.In the present study,we introduce a bivariate sample consisting of the maximum wave heights and concomitant wind speeds of the threshold by using the peak-over-threshold and declustering methods.After selecting the appropriate bivariate copulas and univariate distributions and blocking the sample into years,the bivariate compound distribution of annual extreme wave heights and concomitant wind speeds is constructed.Two joint design criteria,namely,the joint probability density method and the conditional probability method,are applied to obtain the joint return values of significant wave heights and wind speeds.Results show that(28.5±0.5)m s^(-1)is the frequently obtained wind speed based on the Atlantic dataset,and these joint design values are more appropriate than those calculated by univariate analysis in the fatigue design.

Inference for accelerated bivariate dependent competing risks model based on Archimedean copulas under progressive censoring

Dependent competing risks model is a practical model in the analysis of lifetime and failure modes.The dependence can be captured using a statistical tool to explore the re-lationship among failure causes.In this paper,an Archimedean copula is chosen to describe the dependence in a constant-stress accelerated life test.We study the Archimedean copula based dependent competing risks model using parametric and nonparametric methods.The parametric likelihood inference is presented by deriving the general expression of likelihood function based on assumed survival Archimedean copula associated with the model parameter estimation.Combining the nonparametric estimation with progressive censoring and the non-parametric copula estimation,we introduce a nonparametric reliability estimation method given competing risks data.A simulation study and a real data analysis are conducted to show the performance of the estimation methods.

基于Copulas函数的二维干旱变量联合分布

通过构建干旱变量的联合分布揭示干旱演变规律,可作为干旱分析的重要手段。基于8种单参数族的Copulas函数进行新疆乌鲁木齐和石河子气象站二维干旱变量的联合分布。经拟合优度评价:Frank Copula对干旱历时和干旱烈度、干旱历时和烈度峰值的拟合度最好;Clayton Copula对于干旱烈度和烈度峰值的拟合效果最好。二维变量联合超越概率值随单变量值的减小而增大;单变量的重现期介于二维变量联合重现期与同现重现期之间。表明Copulas函数能够描述二维干旱特征变量的联合分布。

Archimedean族Copulas函数在多变量干旱特征分析中的应用

以甘肃省陇西站月降水资料为例,应用9种3维Archimedean Copulas函数构造了干旱历时、干旱烈度和烈度峰值的联合概率分布,并进行了多变量的拟合优度评价,利用优选出的3维非对称型M12 Copula函数,计算联合分布的重现期以及不同组合下的条件概率与条件重现期。结果表明,M12Copula函数可以描述干旱历时、干旱烈度和烈度峰值间的联合分布。由于Copula函数能够用来构建不同边缘分布的联合分布,可以获得变量间不同组合下的重现期,因而能够更全面客观地反映干旱的特征,是描述干旱多变量分布的一种有效途径。

非对称Archimedean Copulas函数在干旱分析中应用

在选定干旱历时、干旱烈度和烈度峰值来描述干旱事件的基础上,应用非对称Archimedean Copulas函数构建了干旱特征变量的联合分布模型。以渭河流域西安气象站的月降水序列为例,采用极大似然法估计M5、M6和M12三种非对称Archimedean Copulas函数的参数,进行了Copulas拟合优度评价。采用拟合效果最好的M12 Copula构造了西安气象站干旱变量间的联合分布,计算了相应的条件概率和条件重现期。结果表明:非对称Archimedean Copulas函数能够用来构建不同边际分布的联合分布,具有灵活方便和应用范围广等特点,是描述干旱多变量分布的一种有效途径。

基于Copulas函数的干旱特征变量联合概率分析

采用Frank和Gaussian copulas函数分析二维干旱特征变量联合分布,构建Frank pair-copula、Gaussiancopula、M3copula函数,对比分析三维干旱联合特性。以渭河流域华阴站降雨资料为例,表明copulas函数能够很好地描述多变量干旱联合特性,体现了copulas函数在多变量联合特性研究中的可行性和适用性。

配备FGM Copulas二维随机向量之和的相依性

本文研究了配备Farlie-Gumbel-Morgenstern Copulas的二维随机向量之和的相依性,得到了在这类Copulas函数下两个独立的随机向量之和的Kendall及Spearman相依系数的一般公式;并针对边缘分布分别为指数分布的情况推导出了具体的公式;证明了当边缘分布满足一定的条件时,不存在尾部相依性.此外,对于几种不同边缘分布的情况进行了随机模拟与比较.这些方法及结果对两个企业(公司)合并后某两个随机指标之间的相依性问题的研究具有理论指导意义,为这类问题的进一步探索提供了理论基础.

Copulas函数在二维干旱变量空间分析中的应用

根据新疆地区41个气象站的长系列月降水资料,提取干旱历时、干旱烈度和烈度峰值3个干旱特征变量,基于8种单参数族的Copulas函数,结合ArcGIS9.3软件进行二维干旱变量的空间分析。经拟合优度评价,FrankCopula对干旱历时和干旱烈度、干旱历时和烈度峰值的拟合度最好;而Clayton Copula对于干旱烈度和烈度峰值的拟合效果最佳。二维变量联合超越概率值随单变量的值减小而增大;二维干旱变量中任一特征变量的条件概率随另一变量的增大而减小;干旱特征变量的条件发生概率在新疆地区从北到南依次递增。表明Copulas函数结合ArcGIS9.3软件能够描述二维干旱特征变量的空间演变规律。

D-vine copulas混合模型及其在故障检测中的应用

过程监控技术是保证现代流程工业安全平稳运行及产品质量的有效手段。传统的过程监控方法大多采用维度约简方法提取数据特征,且要求过程数据必须服从高斯分布、线性等限制条件,对复杂工况条件下发生的故障难以取得较好的检测效果。因此,提出了混合D-vine copulas故障诊断模型,在不降维的情况下直接刻画数据中存在的复杂相关关系,构建过程变量的统计模型实现对存在非线性与非高斯性过程的精确描述。通过EM算法和伪极大似然估计优化混合模型参数,然后结合高密度区域(HDR)与密度分位数法等理论,构建广义贝叶斯概率(GBIP)指标实现对过程的实时监测。数值例子及在TE过程上的仿真结果说明了该混合模型的有效性及在故障检测中的良好性能。

几种Copulas模拟不同历时降雨量的影响分析

为减小水文频率分析中的不确定性,采用4种不同的Copulas联结函数来模拟不同历时降雨量的相关关系,并得出边际分布分别为广义极限和广义逻辑斯特的两元联合分布.模拟结果表明,Farlie-Gumbel-Morgenstern和Gaussian Copulas能较好地模拟变量之间的相关关系,而Gumbel和Clayton Copulas则相对较差.通过计算Copula的条件分布可以得到不同历时降雨量组合的概率.根据Copula联结函数来推求不同重现期的设计暴雨,可以同时考虑不同历时降雨量的相关性,该方法科学合理,为水文频率分析方法提供了新的思路.

椭圆型Copulas函数在西安站干旱特征分析中的应用

本文研究了干旱发生的联合概率、条件概率和重现期等干旱特征。以陕西省西安站月降水为例,应用Meta-Gaussian Copula和Student t Copula构造了干旱历时、干旱烈度和烈度峰值的联合概率分布,并进行了多变量分布拟合优质评价及拟合检验,在此基础上计算了联合分布的重现期以及2变量和3变量情形下的条件概率与条件重现期。研究表明,Meta-Gaussian Copula可以描述干旱历时、干旱烈度和烈度峰值三者的联合分布。由于多元联合分布可以考虑到多个变量之间的不同组合,能够求得不同干旱历时、干旱烈度或烈度峰值下的条件概率和条件重现期,因而能够更加全面客观地反映干旱的特征。

Copulas函数在多变量干旱联合分布中的应用

以渭河流域西安站77年的月降水资料为例,采用7种单参数族Copulas函数,建立干旱特征变量之间的联合分布。经拟合优度评价,Plackett Copula函数对干旱历时和干旱烈度、干旱历时和干旱烈度峰值之间拟合程度最好;而Clayton Copula函数对于干旱烈度和烈度峰值拟合程度最好。分别应用这2种Copulas函数对西安站进行干旱特征变量之间的二维条件概率分布及组合重现期计算。结果表明,Copulas函数能较好的描述干旱特征变量间的联合分布;并且具有灵活性和应用范围广等特点,在多变量干旱特征分析中具有广泛的应用前景。

基于Copulas加速寿命试验中竞争失效模型的统计分析(英文)

在已有讨论竞争失效数据统计分析的文献中, 大多数都假设失效机理之间相互独立. 本文使用copula作为连接函数来考查加速寿命试验中的竞争失效模型. 通过模拟, 把失效机理相关时得到的结果与失效机理独立时得到的结果做了比较.最后分析了文献中的一个实际数据.

Archimedean Copulas在降水变异概率分布特征研究中的应用——以新疆福海县为例

探究二维情况下变异不同步,也就是一个变量发生变异,而另一个变量不发生变异的情况,对Copula联合分布的影响。在气温变化的环境下,降水过程发生了显著变异,而年降水量和年总降水天数的联合分布对长期旱涝情况有重要意义。以Copula函数为基础,计算新疆福海站年降水量和年总降水天数联合分布,用传统变异分析方法进行变异分析。针对年降水量发生变异,而年总降水天数没有发生变异的情况,探讨其Copula联合分布的影响。计算结果表明,年降水变异对年降水量和年总降水天数Kendall相关系数τ影响不大,但对Copula种类的选择影响较大。

一族两个参数自相似Copulas函数与其关联性度量

运用Fredricks et al构造自相似Copulas函数族的方法,研究由一族两个参数自相似Copulas函数Cr,a导出的三个关联性度量指标Kendall’sτ,Spearman’sρ和Gini’sγ,得到Cr,a所满足的泛函方程.

Goodness-of-fit tests for multi-dimensional copulas:Expanding application to historical drought data

The question of how to choose a copula model that best fits a given dataset is a predominant limitation of the copula approach, and the present study aims to investigate the techniques of goodness-of-fit tests for multi-dimensional copulas. A goodness-of-fit test based on Rosenblatt＇s transformation was mathematically expanded from two dimensions to three dimensions and procedures of a bootstrap version of the test were provided. Through stochastic copula simulation, an empirical application of historical drought data at the Lintong Gauge Station shows that the goodness-of-fit tests perform well, revealing that both trivariate Gaussian and Student t copulas are acceptable for modeling the dependence structures of the observed drought duration, severity, and peak. The goodness-of-fit tests for multi-dimensional copulas can provide further support and help a lot in the potential applications of a wider range of copulas to describe the associations of correlated hydrological variables. However, for the application of copulas with the number of dimensions larger than three, more complicated computational efforts as well as exploration and parameterization of corresponding copulas are required.

Copulas于二维样本极值概率积分变换分布分析中的应用

借助于Copula这一工具对在具有联合分布H(x,y)的二维总体(X,Y)经概率积分变换得到的随机变量H(X,Y)的分布函数K(V)给定条件下,求出关于次序统计量X(n)=max{X1,X2,…,Xn}和Y(n)=max{Y1,Y2,…,Yn}经概率积分变换得到的随机变量Hn(X(n),Y(n))的分布函数Kn(v)的方法进行了研究,并找出了Kn(v)不随样本容量n变化的情形,进而得到了较准确地刻画二维R.V相依性的相关性指标Kendall'sτ.

Distribution Functions of Copulas

A general method was proposed to evaluate the distribution function of （C1｜C2 ） . Some examples were presented to validate the application of the method. Then the sufficient and necessary condition for that the distribution function of （ C1 ｜ C2 ） is uniform was proved.

On Trivariate Copulas with Bivariate Linear Spearman Marginal Copulas

Based on the trivariate reduction technique two different trivariate Bernoulli mixtures of univariate uniform distributions and their associated trivariate copulas with bivariate linear Spearman marginal copulas are considered. Mathematical characterizations of these Bernoulli mixture models are obtained. Since Bernoulli mixture trivariate reduction copulas are not compatible with all valid grade correlation coefficients, and there exist linear Spearman compatible non-Bernoulli mixture trivariate copulas, one can ask when there exists at all a trivariate copula with given linear Spearman marginal copulas. Based on a known concordance ordering compatibility criterion, a set of grade correlation inequalities, which must necessarily be satisfied for compatibility, is derived. The existence question for trivariate copulas with compatible linear Spearman marginal copulas is settled in the main result, which states that this set of inequalities is also sufficient for compatibility. The constructive proof makes use of two new classes of trivariate copulas that are obtained from the Bernoulli mixture trivariate copulas through a natural parametric extension. Finally, the obtained classes of trivariate copulas are compared with another class that contains as special case some trivariate copulas with linear Spearman marginal copulas. Since the latter class is incompatible with some type of linear Spearman copulas, the new classes of trivariate copulas build a richer class in this respect. Moreover, in contrast to the mentioned class, which requires in general 11 different elementary copulas in the defining convex linear combination, the new classes require at most five of them, which results in a more parsimonious parametric modelling.