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...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.展开更多
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 pape...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.展开更多
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,...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。展开更多
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 mul...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.展开更多
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 dis...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.展开更多
基金the National Natural Science Foundation of China(No.52171284)。
文摘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.
基金Supported by the National Natural Science Foundation of China(12101476,12061091,11901134)the Fundamental Research Funds for the Central Universities(ZYTS23054,QTZX22054)+1 种基金the Yunnan Funda-mental Research Projects(202101AT070103)the Natural Science Basic Research Program of Shaanxi Province(2020JQ-285).
文摘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.
文摘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。
基金supported by the Program of Introducing Talents of Disciplines to Universities of the Ministry of Education and State Administration of the Foreign Experts Affairs of China (the 111 Project, Grant No.B08048)the Special Basic Research Fund for Methodology in Hydrology of the Ministry of Sciences and Technology of China (Grant No. 2011IM011000)
文摘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.
文摘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.
