Estimation of Poisson-Generalized Pareto Compound Extreme Value Distribution by Probability-Weighted Moments and Empirical Analysis

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.

二项-二维对数正态分布及其在极端海况预测中的应用

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.

Disaster prevention design criteria for the estuarine cities:New Orleans and Shanghai The lesson from Hurricane Katrina

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.

A New Method for Determining Threshold in Using PGCEVD to Calculate Return Values of Typhoon Wave Height

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.

Design Code Calibration of Offshore Platform Against Typhoon/Hurricane Attacks

Hurricanes Katrina and Rita resulted in the largest number of platforms destroyed and damaged in the history of Gulf of Mexico operations. With the trend of global warming, sea level rising and the frequency and intensity of typhoon increase. How to determine a reasonable deck elevation against the largest hurricane waves has become a key issue in offshore platforms design and construction for the unification of economy and safety. In this paper, the multivariate compound extreme value distribution （MCEVD） model is used to predict the deck elevation with different combination of tide, surge height, and crest height. Compared with practice recommended by American Petroleum Institute （API）, the prediction by MCEVD has probabilistic meaning and universality.