【摘要】：計(jì)數(shù)數(shù)據(jù)常出現(xiàn)在醫(yī)學(xué)、社會(huì)學(xué)與心理學(xué)等領(lǐng)域,是一類重要的取值為非負(fù)整數(shù)的統(tǒng)計(jì)數(shù)據(jù)類型。分析計(jì)數(shù)數(shù)據(jù)常用的模型有泊松回歸模型、負(fù)二項(xiàng)回歸模型、廣義泊松回歸模型與Hurdle模型等。計(jì)數(shù)數(shù)據(jù)中的一類特殊情形是數(shù)據(jù)的條件方差大于條件均值,即數(shù)據(jù)存在過度離散現(xiàn)象,因而,過度離散數(shù)據(jù)的分析就成了一個(gè)重要的統(tǒng)計(jì)問題。車險(xiǎn)數(shù)據(jù)包括索賠次數(shù)、索賠額與賠款總量等,其中索賠次數(shù)就屬于計(jì)數(shù)數(shù)據(jù)。索賠次數(shù)數(shù)據(jù)的分析與模型擬合是車險(xiǎn)費(fèi)率厘定的基礎(chǔ)。而負(fù)二項(xiàng)回歸模型能夠很好的解決數(shù)據(jù)中存在的過度離散問題,因此本文主要研究負(fù)二項(xiàng)回歸模型在過度離散車險(xiǎn)數(shù)據(jù)中的應(yīng)用。首先,介紹本文討論所用到的模型以及過度離散的定義、過度離散產(chǎn)生的原因、可能導(dǎo)致的后果與檢驗(yàn)等。并通過一個(gè)實(shí)例對比研究說明線性回歸模型不適用于響應(yīng)變量取值為計(jì)數(shù)數(shù)據(jù)的情形。其次,通過實(shí)證分析討論泊松回歸模型與負(fù)二項(xiàng)回歸模型用于分析過度離散車險(xiǎn)數(shù)據(jù)的優(yōu)良性。結(jié)果表明,無論從模型擬合效果、預(yù)測效果還是模型實(shí)際意義等都說明負(fù)二項(xiàng)回歸模型更適用于過度離散車險(xiǎn)數(shù)據(jù)。最后,通過數(shù)值模擬的方法比較研究泊松回歸模型、負(fù)二項(xiàng)回歸模型以及廣義泊松回歸模型對于處理不同程度的過度離散車險(xiǎn)數(shù)據(jù)的優(yōu)良性。結(jié)果表明:當(dāng)數(shù)據(jù)存在過度離散時(shí),負(fù)二項(xiàng)回歸模型擬合效果隨著離散程度的變化始終優(yōu)于泊松回歸模型與廣義泊松回歸模型;當(dāng)數(shù)據(jù)不存在過度離散時(shí),泊松回歸模型與負(fù)二項(xiàng)回歸模型擬合效果差異不大,且都優(yōu)于廣義泊松回歸模型�？偟膩碚f,無論數(shù)據(jù)是否存在過度離散,負(fù)二項(xiàng)回歸模型都是一個(gè)不錯(cuò)的選擇。
[Abstract]:Counting data often appear in the fields of medicine, sociology and psychology. It is an important type of statistical data with nonnegative integer values. Poisson regression model, negative binomial regression model, generalized Poisson regression model and Hurdle model are commonly used to analyze the counting data. A special case of counting data is that the conditional variance of the data is greater than the conditional mean value, that is, the phenomenon of over-discretization exists in the data, so the analysis of the over-discrete data becomes an important statistical problem. Auto insurance data include the number of claims, the amount claimed and the total amount of compensation, among which the number of claims belongs to the count data. The analysis of claim number data and model fitting are the basis of vehicle insurance rate determination. But the negative binomial regression model can solve the problem of excessive dispersion in the data well, so this paper mainly studies the application of the negative binomial regression model in the excessive discrete vehicle insurance data. First of all, this paper introduces the model used in this paper, the definition of excessive discretization, the causes of excessive discretization, the possible consequences and tests, etc. A case study shows that the linear regression model is not suitable for the case where the response variable is counted. Secondly, the paper discusses the advantages of Poisson regression model and negative binomial regression model to analyze the over-discrete vehicle insurance data through empirical analysis. The results show that the negative binomial regression model is more suitable for excessive discrete vehicle insurance data in terms of model fitting effect, prediction effect and actual significance of the model. Finally, the advantages of Poisson regression model, negative binomial regression model and generalized Poisson regression model are compared by numerical simulation. The results show that the fitting effect of negative binomial regression model is better than that of Poisson regression model and generalized Poisson regression model. When there is no excessive dispersion of data, there is no difference between Poisson regression model and negative binomial regression model, and both of them are superior to generalized Poisson regression model. In general, the negative binomial regression model is a good choice regardless of whether the data is over discrete or not.
【學(xué)位授予單位】：貴州民族大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O212.1

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