【摘要】：計數數據常出現在醫(yī)學、社會學與心理學等領域,是一類重要的取值為非負整數的統(tǒng)計數據類型。分析計數數據常用的模型有泊松回歸模型、負二項回歸模型、廣義泊松回歸模型與Hurdle模型等。計數數據中的一類特殊情形是數據的條件方差大于條件均值,即數據存在過度離散現象,因而,過度離散數據的分析就成了一個重要的統(tǒng)計問題。車險數據包括索賠次數、索賠額與賠款總量等,其中索賠次數就屬于計數數據。索賠次數數據的分析與模型擬合是車險費率厘定的基礎。而負二項回歸模型能夠很好的解決數據中存在的過度離散問題,因此本文主要研究負二項回歸模型在過度離散車險數據中的應用。首先,介紹本文討論所用到的模型以及過度離散的定義、過度離散產生的原因、可能導致的后果與檢驗等。并通過一個實例對比研究說明線性回歸模型不適用于響應變量取值為計數數據的情形。其次,通過實證分析討論泊松回歸模型與負二項回歸模型用于分析過度離散車險數據的優(yōu)良性。結果表明,無論從模型擬合效果、預測效果還是模型實際意義等都說明負二項回歸模型更適用于過度離散車險數據。最后,通過數值模擬的方法比較研究泊松回歸模型、負二項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數據的優(yōu)良性。結果表明:當數據存在過度離散時,負二項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;當數據不存在過度離散時,泊松回歸模型與負二項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,無論數據是否存在過度離散,負二項回歸模型都是一個不錯的選擇。
[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.
【學位授予單位】：貴州民族大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：O212.1

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