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Non-conventional modeling of extreme significant wave height through random sets

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Acta Oceanologica Sinica 2014年第7期33卷 125-130页

作者： ZHANG Yi LAM Jasmine Siu Lee Division of Infrastructure Systems and Maritime Studies School of Civil and Environmental EngineeringN1-B1a-25 Nanyang Technological UniversitySingapore Division of Infrastructure Systems and Maritime Studies School of Civil and Environmental EngineeringN1-01b-43 Nanyang Technological UniversitySingapore

The analysis and design of offshore structures necessitates the consideration of wave loads. Realistic modeling of wave loads is particularly important to ensure reliable performance of these structures. Among the available methods for the modeling of the extreme significant wave height on a statistical basis, the peak over threshold method has attracted most attention. This method employs Poisson process to character- ize time-varying properties in the parameters of an extreme value distribution. In this paper, the peak over threshold method is reviewed and extended to account for subjectivity in the modeling. The freedom in selecting the threshold and the time span to separate extremes from the original time series data is incorpo- rated as imprecision in the model. This leads to an extension from random variables to random sets in the probabilistic model for the extreme significant wave height. The extended model is also applied to different periods of the sampled data to evaluate the significance of the climatic conditions on the uncertainties of the parameters.

关键词： offshore engineering extreme value distribution wave height peak over threshold randomset pareto distribution

A fuzzy quantification approach of uncertainties in an extreme wave height modeling

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Acta Oceanologica Sinica 2015年第3期34卷 90-98页

作者： ZHANG Yi CAO Yingyi Division of Infrastructure Systems and Maritime Studies School of Civil and Environmental EngineeringNanyang Technological University College of Preschool Education Zibo Normal College

A non-traditional fuzzy quantification method is presented in the modeling of an extreme significant wave height. First, a set of parametric models are selected to fit time series data for the significant wave height and the extrapolation for extremes are obtained based on high quantile estimations. The quality of these results is compared and discussed. Then, the proposed fuzzy model, which combines Poisson process and gener-alized pareto distribution （GPD） model, is applied to characterizing the wave extremes in the time series data. The estimations for a long-term return value are considered as time-varying as a threshold is regarded as non-stationary. The estimated intervals coupled with the fuzzy theory are then introduced to construct the probability bounds for the return values. This nontraditional model is analyzed in comparison with the traditional model in the degree of conservatism for the long-term estimate. The impact on the fuzzy bounds of extreme estimations from the non stationary effect in the proposed model is also investigated.

关键词： offshore engineering extreme value distribution wave height peak over threshold fuzzy set pareto distribution

Explicit Expressions for the Ruin Probabilities of Erlang Risk Processes with pareto Individual Claim distributions

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Acta Mathematicae Applicatae Sinica 2004年第3期20卷 495-506页

作者： LiWei Hai-liangYang AcademyofMathematicsandSystemsScience ChineseAcademyofSciencesBeijing100080China DepartmentofStatisticsandActuarialScience theUniversityofHongKong

In this paper we first consider a risk process in which claim inter-arrival times and the time until the first claim have an Erlang (2) distribution. An explicit solution is derived for the probability of ultimate ruin, given an initial reserve of u when the claim size follows a pareto distribution. Follow Ramsay[8], Laplace transforms and exponential integrals are used to derive the solution, which involves a single integral of real valued functions along the positive real line, and the integrand is not of an oscillating kind. Then we show that the ultimate ruin probability can be expressed as the sum of expected values of functions of two different Gamma random variables. Finally, the results are extended to the Erlang(n) case. Numerical examples are given to illustrate the main results.

关键词： Ruin probability Erlang process pareto distribution Laplace transform removable singularity contour integration

市场风险资产损失服从pareto分布的VaR计量

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pareto分布背景下分布式模糊OS-CFAR检测

统计与精算 2009年第5期 9-12页

作者：钱艺平林祥

目前VaR模型是测量和管理商业银行市场风险的主流方法。运用VaR的计算原理，利用pareto分布描述风险资产损失的尖峰厚尾特征，得到市场风险资产VaR计算公式，并且分析了VaR的影响因素，最后利用历史数据进行VaR的实例计算。

关键词： pareto分布市场风险 VaR 极大似然估计 pareto distribution market risk VaR maximum likelihood estimate

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Pareto分布背景下分布式模糊OS-CFAR检测

第十二届全国信号和智能信息处理与应用学术会议

作者：徐达郝程鹏侯朝焕中国科学院声学研究所中国科学院大学电子电气与通信工程学院

针对分布式系统中恒虚警（CFAR）检测问题,基于模糊融合准则和有序统计（OS）方法,研究了pareto混响背景下分布式OS-CFAR检测器,并推广到分布式检测系统中。该分布式系统由两个检测器和一个融合中心构成。两个检测器结果分别输出至融合... 详细信息

针对分布式系统中恒虚警（CFAR）检测问题,基于模糊融合准则和有序统计（OS）方法,研究了pareto混响背景下分布式OS-CFAR检测器,并推广到分布式检测系统中。该分布式系统由两个检测器和一个融合中心构成。两个检测器结果分别输出至融合中心,融合中心再根据融合准则输出最终判决结果。给出了模糊隶属函数,分析了在pareto分布混响背景下的性能。利用蒙特卡洛仿真方法,对比使用不同模糊融合准则的分布式模糊OS-CFAR检测器的性能。结果表明,在均匀背景下和有干扰目标存在的情况下,代数和融合准则具有更好的检测性能和鲁棒性。

关键词： ordered statistic constant false alarm pareto distribution clutter reverberation

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居民财富不平等的理论与实证研究