负二项回归模型在过度离散车险数据中的应用

发布时间：2018-12-28 20:27

【摘要】：计数数据常出现在医学、社会学与心理学等领域,是一类重要的取值为非负整数的统计数据类型。分析计数数据常用的模型有泊松回归模型、负二项回归模型、广义泊松回归模型与Hurdle模型等。计数数据中的一类特殊情形是数据的条件方差大于条件均值,即数据存在过度离散现象,因而,过度离散数据的分析就成了一个重要的统计问题。车险数据包括索赔次数、索赔额与赔款总量等,其中索赔次数就属于计数数据。索赔次数数据的分析与模型拟合是车险费率厘定的基础。而负二项回归模型能够很好的解决数据中存在的过度离散问题,因此本文主要研究负二项回归模型在过度离散车险数据中的应用。首先,介绍本文讨论所用到的模型以及过度离散的定义、过度离散产生的原因、可能导致的后果与检验等。并通过一个实例对比研究说明线性回归模型不适用于响应变量取值为计数数据的情形。其次,通过实证分析讨论泊松回归模型与负二项回归模型用于分析过度离散车险数据的优良性。结果表明,无论从模型拟合效果、预测效果还是模型实际意义等都说明负二项回归模型更适用于过度离散车险数据。最后,通过数值模拟的方法比较研究泊松回归模型、负二项回归模型以及广义泊松回归模型对于处理不同程度的过度离散车险数据的优良性。结果表明:当数据存在过度离散时,负二项回归模型拟合效果随着离散程度的变化始终优于泊松回归模型与广义泊松回归模型;当数据不存在过度离散时,泊松回归模型与负二项回归模型拟合效果差异不大,且都优于广义泊松回归模型。总的来说,无论数据是否存在过度离散,负二项回归模型都是一个不错的选择。
[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.
【学位授予单位】：贵州民族大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.1

【相似文献】