This paper puts forward a Poisson-generalized Pareto (Poisson-GP) distribution. This new form of compound extreme value distribution expands the existing application of compound extreme value distribution, and can be ...This paper puts forward a Poisson-generalized Pareto (Poisson-GP) distribution. This new form of compound extreme value distribution expands the existing application of compound extreme value distribution, and can be applied to predicting financial risk, large insurance settlement and high-grade earthquake, etc. Compared with the maximum likelihood estimation (MLE) and compound moment estimation (CME), probability-weighted moment estimation (PWME) is used to estimate the parameters of the distribution function. The specific formulas are presented. Through Monte Carlo simulation with sample sizes 10, 20, 50, 100, 1 000, it is concluded that PWME is an efficient method and it behaves steadily. The mean square errors (MSE) of estimators by PWME are much smaller than those of estimators by CME, and there is no significant difference between PWME and MLE. Finally, an example of foreign exchange rate is given. For Dollar/Pound exchange rates from 1990-01-02 to 2006-12-29, this paper formulates the distribution function of the largest loss among the investment losses exceeding a certain threshold by Poisson-GP compound extreme value distribution, and obtains predictive values at different confidence levels.展开更多
In using the PGCEVD （Poisson-Gumbel Compound Extreme Value Distribution） model to calculate return values of typhoon wave height, the quantitative selection of the threshold has blocked its application. By analyzing...In using the PGCEVD （Poisson-Gumbel Compound Extreme Value Distribution） model to calculate return values of typhoon wave height, the quantitative selection of the threshold has blocked its application. By analyzing the principle of the threshold selection of PGCEVD model and in combination of the change point statistical methods, this paper proposes a new method for quantitative calculation of the threshold in PGCEVD model. Eleven samples from five engineering points in several coastal waters of Guangdong and Hainan, China, are calculated and analyzed by using PGCEVD model and the traditional Pearson type III distribution （P-III） model, respectively. By comparing the results of the two models, it is shown that the new method of selecting the optimal threshold is feasible. PGCEVD model has more stable results than that of P-III model and can be used for the return wave height in every direction.展开更多
In this paper, a new type of distribution, multivariate compound extreme value distribution (MCEVD), is introduced by compounding a discrete distribution with a multivariate continuous distribution of extreme sea even...In this paper, a new type of distribution, multivariate compound extreme value distribution (MCEVD), is introduced by compounding a discrete distribution with a multivariate continuous distribution of extreme sea events. In its engineering application the number over certain threshold level per year is fitting to Poisson distribution and the corresponding extreme sea events are fitting to Nested Logistic distribution, then the Poisson-Nested logistic trivariate compound extreme value distribution (PNLTCED) is proposed to predict extreme wave heights, periods and wind speeds in Yellow Sea. The new model gives more stable and reasonable predicted results.展开更多
Extreme value analysis is an indispensable method to predict the probability of marine disasters and calculate the design conditions of marine engineering.The rationality of extreme value analysis can be easily affect...Extreme value analysis is an indispensable method to predict the probability of marine disasters and calculate the design conditions of marine engineering.The rationality of extreme value analysis can be easily affected by the lack of sample data.The peaks over threshold(POT)method and compound extreme value distribution(CEVD)theory are effective methods to expand samples,but they still rely on long-term sea state data.To construct a probabilistic model using shortterm sea state data instead of the traditional annual maximum series(AMS),the binomial-bivariate log-normal CEVD(BBLCED)model is established in this thesis.The model not only considers the frequency of the extreme sea state,but it also reflects the correlation between different sea state elements(wave height and wave period)and reduces the requirement for the length of the data series.The model is applied to the calculation of design wave elements in a certain area of the Yellow Sea.The results indicate that the BBLCED model has good stability and fitting effect,which is close to the probability prediction results obtained from the long-term data,and reasonably reflects the probability distribution characteristics of the extreme sea state.The model can provide a reliable basis for coastal engineering design under the condition of a lack of marine data.Hence,it is suitable for extreme value prediction and calculation in the field of disaster prevention and reduction.展开更多
每年由台风诱发暴雨引起洪水、滑坡等灾害在我国沿海地区造成巨大损失。作者采用多维复合极值分布理论(Multivariate compound extreme value distribution),以受台风暴雨危害较严重的浙江温州地区为例,对台风诱发暴雨的降水量进行了概...每年由台风诱发暴雨引起洪水、滑坡等灾害在我国沿海地区造成巨大损失。作者采用多维复合极值分布理论(Multivariate compound extreme value distribution),以受台风暴雨危害较严重的浙江温州地区为例,对台风诱发暴雨的降水量进行了概率预测。该理论以影响暴雨强度的台风中心气压差和降水量为研究对象,并考虑导致极端降水的台风过程的出现频次的概率特性,预测结果较传统方法更为合理和安全。展开更多
The accurate prediction of the typhoon （hurricane） induced extreme sea environments is very important for the coastal structure design in areas influenced by typhoon （hurricane）. In 2005 Hurricane Katrina brought ...The accurate prediction of the typhoon （hurricane） induced extreme sea environments is very important for the coastal structure design in areas influenced by typhoon （hurricane）. In 2005 Hurricane Katrina brought a severe catastrophe in New Orleans by combined effects of hurricane induced extreme sea environments and upper flood of the Mississippi River. Like the New Orleans City, Shanghai is located at the estuarine area of the Changjiang River and the combined effect of typhoon induced extreme sea en- vironments, flood peak runoff from the Changjiang River coupled with the spring tide is the dominate factor for disaster prevention design criteria. The Poisson-nested logistic trivariate compound extreme value distribution （PNLTCEYD） is a new type of joint probability model which is proposed by compounding a discrete distribution （typhoon occurring frequency） into a continuous multivariate joint distribution （ typhoon induced extreme events）. The new model gives more reasonable predicted results for New Orleans and Shanghai disaster prevention design criteria.展开更多
基金National Natural Science Foundation of China (No.70573077)
文摘This paper puts forward a Poisson-generalized Pareto (Poisson-GP) distribution. This new form of compound extreme value distribution expands the existing application of compound extreme value distribution, and can be applied to predicting financial risk, large insurance settlement and high-grade earthquake, etc. Compared with the maximum likelihood estimation (MLE) and compound moment estimation (CME), probability-weighted moment estimation (PWME) is used to estimate the parameters of the distribution function. The specific formulas are presented. Through Monte Carlo simulation with sample sizes 10, 20, 50, 100, 1 000, it is concluded that PWME is an efficient method and it behaves steadily. The mean square errors (MSE) of estimators by PWME are much smaller than those of estimators by CME, and there is no significant difference between PWME and MLE. Finally, an example of foreign exchange rate is given. For Dollar/Pound exchange rates from 1990-01-02 to 2006-12-29, this paper formulates the distribution function of the largest loss among the investment losses exceeding a certain threshold by Poisson-GP compound extreme value distribution, and obtains predictive values at different confidence levels.
基金supported by the National Natural Science Foundation of China(Grant No.10902039)the Major Project Research of the Ministry of Railways of the People's Republic of China(Grant No.2010-201)
文摘In using the PGCEVD （Poisson-Gumbel Compound Extreme Value Distribution） model to calculate return values of typhoon wave height, the quantitative selection of the threshold has blocked its application. By analyzing the principle of the threshold selection of PGCEVD model and in combination of the change point statistical methods, this paper proposes a new method for quantitative calculation of the threshold in PGCEVD model. Eleven samples from five engineering points in several coastal waters of Guangdong and Hainan, China, are calculated and analyzed by using PGCEVD model and the traditional Pearson type III distribution （P-III） model, respectively. By comparing the results of the two models, it is shown that the new method of selecting the optimal threshold is feasible. PGCEVD model has more stable results than that of P-III model and can be used for the return wave height in every direction.
基金This work was supported by the National Natural Science Foundation of China(Grant No.50379051).
文摘In this paper, a new type of distribution, multivariate compound extreme value distribution (MCEVD), is introduced by compounding a discrete distribution with a multivariate continuous distribution of extreme sea events. In its engineering application the number over certain threshold level per year is fitting to Poisson distribution and the corresponding extreme sea events are fitting to Nested Logistic distribution, then the Poisson-Nested logistic trivariate compound extreme value distribution (PNLTCED) is proposed to predict extreme wave heights, periods and wind speeds in Yellow Sea. The new model gives more stable and reasonable predicted results.
文摘Extreme value analysis is an indispensable method to predict the probability of marine disasters and calculate the design conditions of marine engineering.The rationality of extreme value analysis can be easily affected by the lack of sample data.The peaks over threshold(POT)method and compound extreme value distribution(CEVD)theory are effective methods to expand samples,but they still rely on long-term sea state data.To construct a probabilistic model using shortterm sea state data instead of the traditional annual maximum series(AMS),the binomial-bivariate log-normal CEVD(BBLCED)model is established in this thesis.The model not only considers the frequency of the extreme sea state,but it also reflects the correlation between different sea state elements(wave height and wave period)and reduces the requirement for the length of the data series.The model is applied to the calculation of design wave elements in a certain area of the Yellow Sea.The results indicate that the BBLCED model has good stability and fitting effect,which is close to the probability prediction results obtained from the long-term data,and reasonably reflects the probability distribution characteristics of the extreme sea state.The model can provide a reliable basis for coastal engineering design under the condition of a lack of marine data.Hence,it is suitable for extreme value prediction and calculation in the field of disaster prevention and reduction.
文摘每年由台风诱发暴雨引起洪水、滑坡等灾害在我国沿海地区造成巨大损失。作者采用多维复合极值分布理论(Multivariate compound extreme value distribution),以受台风暴雨危害较严重的浙江温州地区为例,对台风诱发暴雨的降水量进行了概率预测。该理论以影响暴雨强度的台风中心气压差和降水量为研究对象,并考虑导致极端降水的台风过程的出现频次的概率特性,预测结果较传统方法更为合理和安全。
基金supported by the National Natural Foundation of China(No.50679076)the Office of State Flood Control and Drought Relief Headquarters P.R.of China(No.20060120)~~
基金supported by the National Natural Science Foundation of China under contract No.50379051.
文摘The accurate prediction of the typhoon （hurricane） induced extreme sea environments is very important for the coastal structure design in areas influenced by typhoon （hurricane）. In 2005 Hurricane Katrina brought a severe catastrophe in New Orleans by combined effects of hurricane induced extreme sea environments and upper flood of the Mississippi River. Like the New Orleans City, Shanghai is located at the estuarine area of the Changjiang River and the combined effect of typhoon induced extreme sea en- vironments, flood peak runoff from the Changjiang River coupled with the spring tide is the dominate factor for disaster prevention design criteria. The Poisson-nested logistic trivariate compound extreme value distribution （PNLTCEYD） is a new type of joint probability model which is proposed by compounding a discrete distribution （typhoon occurring frequency） into a continuous multivariate joint distribution （ typhoon induced extreme events）. The new model gives more reasonable predicted results for New Orleans and Shanghai disaster prevention design criteria.
