This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tai...This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.展开更多
The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lo...The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.展开更多
为响应黄河流域生态保护的国家战略,对流域干旱做出更全面的评估。根据渭河1960—2010年20个气象站的气象数据和华县水文站的水文数据,采用数字滤波法获得基流数据,基于Copula函数构建了新的关于基流和降水的综合干旱指数(CPBI,Comprehe...为响应黄河流域生态保护的国家战略,对流域干旱做出更全面的评估。根据渭河1960—2010年20个气象站的气象数据和华县水文站的水文数据,采用数字滤波法获得基流数据,基于Copula函数构建了新的关于基流和降水的综合干旱指数(CPBI,Comprehensive Precipitation and Base Flow Index),探讨了CPBI的适用性,并运用该指数分析了渭河流域的干旱特征。结果表明,CPBI能够同时捕捉到气象和水文的干旱事件,并综合表征其干旱特征;CPBI在各个尺度上都有下降趋势,干旱情况日趋严重;经过游程理论识别后,CPBI更准确地反映了渭河华县站的严重干旱情况,能够更好地提供干旱预警;CPBI存在变异,在四季及年尺度上变异点分别为1994、1993、1985、1999和1975年。CPBI在渭河是一种有效的干旱监测指数,可为渭河的干旱预警和应对工作提供参考。展开更多
基金The National Natural Science Foundation of China(No.11001052,11171065)the National Science Foundation of Jiangsu Province(No.BK2011058)the Science Foundation of Nanjing University of Posts and Telecommunications(No.JG00710JX57)
文摘This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.
基金supported by the National Natural Science Foundation of China (51279186,51479183)the 111 Project (B14028)The first author thanks the Chinese Scholarship Council for funding his research in University of Washington
文摘The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.
文摘为响应黄河流域生态保护的国家战略,对流域干旱做出更全面的评估。根据渭河1960—2010年20个气象站的气象数据和华县水文站的水文数据,采用数字滤波法获得基流数据,基于Copula函数构建了新的关于基流和降水的综合干旱指数(CPBI,Comprehensive Precipitation and Base Flow Index),探讨了CPBI的适用性,并运用该指数分析了渭河流域的干旱特征。结果表明,CPBI能够同时捕捉到气象和水文的干旱事件,并综合表征其干旱特征;CPBI在各个尺度上都有下降趋势,干旱情况日趋严重;经过游程理论识别后,CPBI更准确地反映了渭河华县站的严重干旱情况,能够更好地提供干旱预警;CPBI存在变异,在四季及年尺度上变异点分别为1994、1993、1985、1999和1975年。CPBI在渭河是一种有效的干旱监测指数,可为渭河的干旱预警和应对工作提供参考。
