We consider a problem from stock market modeling, precisely, choice of adequate distribution of modeling extremal behavior of stock market data. Generalized extreme value (GEV) distribution and generalized Pareto (GP)...We consider a problem from stock market modeling, precisely, choice of adequate distribution of modeling extremal behavior of stock market data. Generalized extreme value (GEV) distribution and generalized Pareto (GP) distribution are the classical distributions for this problem. However, from 2004, [1] and many other researchers have been empirically showing that generalized logistic (GL) distribution is a better model than GEV and GP distributions in modeling extreme movement of stock market data. In this paper, we show that these results are not accidental. We prove the theoretical importance of GL distribution in extreme value modeling. For proving this, we introduce a general multivariate limit theorem and deduce some important multivariate theorems in probability as special cases. By using the theorem, we derive a limit theorem in extreme value theory, where GL distribution plays central role instead of GEV distribution. The proof of this result is parallel to the proof of classical extremal types theorem, in the sense that, it possess important characteristic in classical extreme value theory, for e.g. distributional property, stability, convergence and multivariate extension etc.展开更多
Storm surge is one of the predominant natural threats to coastal communities. Qingdao is located on the southern coast of the Shandong Peninsula in China. The storm surge disaster in Qingdao depends on various influen...Storm surge is one of the predominant natural threats to coastal communities. Qingdao is located on the southern coast of the Shandong Peninsula in China. The storm surge disaster in Qingdao depends on various influencing factors such as the intensity, duration, and route of the passing typhoon, and thus a comprehensive understanding of natural coastal hazards is essential. In order to make up the defects of merely using the warning water level, this paper presents two statistical distribution models(Poisson Bi- variable Gumbel Logistic Distribution and Poisson Bi-variable Log-normal Distribution) to classify the intensity of storm surge. We emphasize the joint return period of typhoon-induced water levels and wave heights measured in the coastal area of Qingdao since 1949. The present study establishes a new criterion to classify the intensity grade of catastrophic storms using the typhoon surge estimated by the two models. A case study demonstrates that the new criterion is well defined in terms of probability concept, is easy to implement, and fits well the calculation of storm surge intensity. The procedures with the proposed statistical models would be useful for the disaster mitigation in other coastal areas influenced by typhoons.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
This paper expounds the nitty-gritty of stock returns transitory, periodical behavior </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><...This paper expounds the nitty-gritty of stock returns transitory, periodical behavior </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">of </span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">its markets’ demands and cyclical-like tenure-changing of number of the stocks sold. Mingling of autoregressive random processes via Poisson and Extreme-Value-Distributions (Fréchet, Gumbel, and Weibull) error terms were designed, generalized and imitated to capture stylized traits of </span><span style="font-family:Verdana;">k-serial tenures (ability to handle cycles), Markov transitional mixing weights</span><span style="font-family:Verdana;">, switching of mingling autoregressive processes and full range shape changing </span><span style="font-family:Verdana;">predictive distributions (multimodalities) that are usually caused by large fluctuation</span><span style="font-family:Verdana;">s (outliers) and long-memory in stock returns. The Poisson and Extreme-Value-Distributions Mingled Autoregressive (PMA and EVDs) models were applied to a monthly number of stocks sold in Nigeria from 1960 to 2020. It was deduced that fitted Gumbel-MAR (2:1, 1) outstripped other linear models as well as best</span></span></span></span><span><span><span style="font-family:""> </span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">fitted among the Poisson and Extreme-Value-</span><span style="font-family:Verdana;">Distributions Mingled autoregressive models subjected to the discrete monthly</span><span style="font-family:Verdana;"> stocks sold series.展开更多
文摘We consider a problem from stock market modeling, precisely, choice of adequate distribution of modeling extremal behavior of stock market data. Generalized extreme value (GEV) distribution and generalized Pareto (GP) distribution are the classical distributions for this problem. However, from 2004, [1] and many other researchers have been empirically showing that generalized logistic (GL) distribution is a better model than GEV and GP distributions in modeling extreme movement of stock market data. In this paper, we show that these results are not accidental. We prove the theoretical importance of GL distribution in extreme value modeling. For proving this, we introduce a general multivariate limit theorem and deduce some important multivariate theorems in probability as special cases. By using the theorem, we derive a limit theorem in extreme value theory, where GL distribution plays central role instead of GEV distribution. The proof of this result is parallel to the proof of classical extremal types theorem, in the sense that, it possess important characteristic in classical extreme value theory, for e.g. distributional property, stability, convergence and multivariate extension etc.
基金supported by the National Natural Science Foundation of China (Nos. 51279186,51479183)the National Program on Key Basic Research Project (2011CB013704)+1 种基金the 111 Project (B14028)the Marine and Fishery Information Center Project of Jiangsu Province (SJC2014110338)
文摘Storm surge is one of the predominant natural threats to coastal communities. Qingdao is located on the southern coast of the Shandong Peninsula in China. The storm surge disaster in Qingdao depends on various influencing factors such as the intensity, duration, and route of the passing typhoon, and thus a comprehensive understanding of natural coastal hazards is essential. In order to make up the defects of merely using the warning water level, this paper presents two statistical distribution models(Poisson Bi- variable Gumbel Logistic Distribution and Poisson Bi-variable Log-normal Distribution) to classify the intensity of storm surge. We emphasize the joint return period of typhoon-induced water levels and wave heights measured in the coastal area of Qingdao since 1949. The present study establishes a new criterion to classify the intensity grade of catastrophic storms using the typhoon surge estimated by the two models. A case study demonstrates that the new criterion is well defined in terms of probability concept, is easy to implement, and fits well the calculation of storm surge intensity. The procedures with the proposed statistical models would be useful for the disaster mitigation in other coastal areas influenced by typhoons.
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This paper expounds the nitty-gritty of stock returns transitory, periodical behavior </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">of </span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">its markets’ demands and cyclical-like tenure-changing of number of the stocks sold. Mingling of autoregressive random processes via Poisson and Extreme-Value-Distributions (Fréchet, Gumbel, and Weibull) error terms were designed, generalized and imitated to capture stylized traits of </span><span style="font-family:Verdana;">k-serial tenures (ability to handle cycles), Markov transitional mixing weights</span><span style="font-family:Verdana;">, switching of mingling autoregressive processes and full range shape changing </span><span style="font-family:Verdana;">predictive distributions (multimodalities) that are usually caused by large fluctuation</span><span style="font-family:Verdana;">s (outliers) and long-memory in stock returns. The Poisson and Extreme-Value-Distributions Mingled Autoregressive (PMA and EVDs) models were applied to a monthly number of stocks sold in Nigeria from 1960 to 2020. It was deduced that fitted Gumbel-MAR (2:1, 1) outstripped other linear models as well as best</span></span></span></span><span><span><span style="font-family:""> </span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">fitted among the Poisson and Extreme-Value-</span><span style="font-family:Verdana;">Distributions Mingled autoregressive models subjected to the discrete monthly</span><span style="font-family:Verdana;"> stocks sold series.
