本文關(guān)鍵詞：基于Dirichlet過程的空間極值模型參數(shù)估計方法研究及其在降水極值分布的應(yīng)用　出處：《西南交通大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 廣義帕累托分布(GPD) 超門限(POT)閾值的選取 貝葉斯參數(shù)估計 狄利克萊過程模型 高斯連接模型

【摘要】：對于國內(nèi)的自然災(zāi)害分析方面,洪澇災(zāi)害是幾種常見的自然災(zāi)害之一,目前對于極端天氣氣候事件的不斷發(fā)生,已引起科學(xué)界和社會的極大關(guān)注,因?yàn)闃O值氣候或者自然災(zāi)害的發(fā)生對生產(chǎn)生活造成了重要的影響,對經(jīng)濟(jì)造成了嚴(yán)重了損失,由于它的研究對象發(fā)生頻率低損失程度大而特別具有吸引力,尤其目前對精算人員而言,吸引力更是巨大,因?yàn)榫闳藛T最關(guān)心的是損失數(shù)據(jù)的尾部準(zhǔn)確性。作為一種對隨機(jī)現(xiàn)象的研究,截止目前,最近幾十年,極值理論才被大家,被研究學(xué)者越來越重視,并開始對它建立模型進(jìn)行研究,而最早的極值理論的啟蒙源于19世紀(jì),這期間停滯了很長一段時間。極值理論的應(yīng)用最早是在工程研究方面的應(yīng)用,現(xiàn)如今已經(jīng)廣泛應(yīng)用于保險、金融等各個領(lǐng)域。本文基于北京某保險公司實(shí)際降雨量數(shù)據(jù),極端稀有事件具有概率小、損失強(qiáng)度高等特征,其事故的發(fā)生會造成直接或者間接的不同程度上的經(jīng)濟(jì)損失,特別是針對保險公司針對極值氣候具有非常關(guān)鍵的指導(dǎo)作用,因此,對極端稀有事件的準(zhǔn)確預(yù)測尤為重要。目前,對極端稀有事件的預(yù)測廣泛采用的方法的方法是極值理論然而極值理論對閾值的選取極為敏感,并且是使用的主觀的判斷,以前的對參數(shù)的估計也沒有相關(guān)明確的理論支持,本論文通過對數(shù)據(jù)進(jìn)行篩選,挑選超過閾值以上的數(shù)據(jù)集進(jìn)行研究,采用廣義帕累托分布模型(簡稱"GPD")建立模型,并運(yùn)用最大似然估計參數(shù)(MLE),MOM等方法進(jìn)行參數(shù)的估計,并作出了優(yōu)缺點(diǎn)的比較,然后運(yùn)用貝葉斯理論構(gòu)造的先驗(yàn)分布和馬爾可夫鏈蒙特卡羅(簡稱"MCMC")方法構(gòu)造的后驗(yàn)分布對參數(shù)進(jìn)行估計,最后會涉及到利用狄利克雷過程(The Dirichlet process簡稱:"DP")建立模型后的檢驗(yàn)或者利用混合正態(tài)分布建立模型進(jìn)行檢驗(yàn),本文用到的極值理論分布的方法有:超門限峰值(簡稱:POT),廣義帕累托分布(簡稱"GPD"),論文還包括了閾值的選取,厚尾的診斷,GPD的運(yùn)用,MLE的參數(shù)估計方法,貝葉斯的先驗(yàn)分布和MCMC的后驗(yàn)分布,最后通過實(shí)際的例子作為實(shí)證分析,得出結(jié)論。最后得出的結(jié)果是對于全國降雨量的數(shù)據(jù),針對極值理論的小概率的預(yù)測,發(fā)現(xiàn)廣義帕累托分布模型更精準(zhǔn),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.
【學(xué)位授予單位】：西南交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F842.3

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本文編號：1440819