基于Dirichlet过程的空间极值模型参数估计方法研究及其在降水极值分布的应用

发布时间：2018-01-18 11:45

本文关键词：基于Dirichlet过程的空间极值模型参数估计方法研究及其在降水极值分布的应用　出处：《西南交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：对于国内的自然灾害分析方面,洪涝灾害是几种常见的自然灾害之一,目前对于极端天气气候事件的不断发生,已引起科学界和社会的极大关注,因为极值气候或者自然灾害的发生对生产生活造成了重要的影响,对经济造成了严重了损失,由于它的研究对象发生频率低损失程度大而特别具有吸引力,尤其目前对精算人员而言,吸引力更是巨大,因为精算人员最关心的是损失数据的尾部准确性。作为一种对随机现象的研究,截止目前,最近几十年,极值理论才被大家,被研究学者越来越重视,并开始对它建立模型进行研究,而最早的极值理论的启蒙源于19世纪,这期间停滞了很长一段时间。极值理论的应用最早是在工程研究方面的应用,现如今已经广泛应用于保险、金融等各个领域。本文基于北京某保险公司实际降雨量数据,极端稀有事件具有概率小、损失强度高等特征,其事故的发生会造成直接或者间接的不同程度上的经济损失,特别是针对保险公司针对极值气候具有非常关键的指导作用,因此,对极端稀有事件的准确预测尤为重要。目前,对极端稀有事件的预测广泛采用的方法的方法是极值理论然而极值理论对阈值的选取极为敏感,并且是使用的主观的判断,以前的对参数的估计也没有相关明确的理论支持,本论文通过对数据进行筛选,挑选超过阈值以上的数据集进行研究,采用广义帕累托分布模型(简称"GPD")建立模型,并运用最大似然估计参数(MLE),MOM等方法进行参数的估计,并作出了优缺点的比较,然后运用贝叶斯理论构造的先验分布和马尔可夫链蒙特卡罗(简称"MCMC")方法构造的后验分布对参数进行估计,最后会涉及到利用狄利克雷过程(The Dirichlet process简称:"DP")建立模型后的检验或者利用混合正态分布建立模型进行检验,本文用到的极值理论分布的方法有:超门限峰值(简称:POT),广义帕累托分布(简称"GPD"),论文还包括了阈值的选取,厚尾的诊断,GPD的运用,MLE的参数估计方法,贝叶斯的先验分布和MCMC的后验分布,最后通过实际的例子作为实证分析,得出结论。最后得出的结果是对于全国降雨量的数据,针对极值理论的小概率的预测,发现广义帕累托分布模型更精准,更有效。
[Abstract]:For the analysis of natural disasters in China, flood disaster is one of several common natural disasters. At present, the continuous occurrence of extreme weather and climate events has attracted great attention of the scientific community and society. Because the extreme climate or natural disasters have an important impact on the production and life, have caused serious losses to the economy, because of its low frequency of loss of the object of study, it is particularly attractive. Especially for the actuary, the attraction is even more great, because the actuarial staff is most concerned about the tail accuracy of loss data. As a study of random phenomena, so far, in recent decades. The extreme value theory has just been paid more and more attention to by researchers, and began to study its model, and the earliest enlightenment of extreme value theory originated in 19th century. The application of extreme value theory was first applied in engineering research, but now it has been widely used in insurance. Based on the actual rainfall data of an insurance company in Beijing, extreme rare events are characterized by small probability and high loss intensity. The occurrence of the accident will cause direct or indirect economic losses in varying degrees, especially for the insurance companies for extreme climate has a very critical role in guiding. Accurate prediction of extreme rare events is particularly important. At present, extreme value theory is widely used to predict extreme rare events. However, extreme value theory is very sensitive to the selection of threshold. And the use of subjective judgment, the previous estimation of the parameters are not related to clear theoretical support, this paper through the screening of data, the selection of data set above the threshold for research. The generalized Pareto distribution model ("GPD") is used to establish the model, and the maximum likelihood estimation method is used to estimate the parameters, and the advantages and disadvantages are compared. Then the parameters are estimated by using the prior distribution constructed by Bayesian theory and the posterior distribution constructed by Markov chain Monte Carlo ("MCMC") method. Finally, it will involve the use of the Dirichlet process ("DP") using the Delikley process. The test after the establishment of the model or the use of mixed normal distribution to establish the model to test. The methods of extreme value distribution used in this paper are as follows: Super threshold peak (GPD), generalized Pareto distribution (abbreviated as "GPD"). The paper also includes the selection of threshold and the diagnosis of thick tail. GPD uses the parameter estimation method of MLE, the prior distribution of Bayes and the posteriori distribution of MCMC. Finally, an example is given as an empirical analysis. The final result is that the generalized Pareto distribution model is more accurate and effective for the data of national rainfall and the prediction of the small probability of extreme value theory.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F842.3

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