在费率厘定中,当索赔次数数据存在过离散(over-dispersion)特征时,通常会采用负二项回归模型,但当索赔数据中同时又出现零膨胀(zero-inflated)问题时,负二项回归模型不再适合对这样的数据进行分析.在传统的零膨胀负二项回归模型为基础,并将其推广到更为一般的形式,同时利用解决费率厘定中出现的既有过离散又有零膨胀的问题.通过对一组汽车 损失数据的拟合,推广后的零膨胀负二项回归模型有效地改善了拟合效果.
Abstract
When the claim numbers appear to be over-dispersed in ratemaking, negative binomial regression model will be usually applied. However, it is also possible that the claim numbers may be zero-inflated, and then the negative binomial regression is not suitable for those data. The paper makes generalization of zero-inflated negative binomial distribution based on traditional ones to deal with the over-dispersed and zero-inflated data simultaneously. At the end of the paper, the extended model is applied to a data set of automobile insurance loss and the result shows that the goodness-of-fit can be effectively improved.
关键词
负二项回归 /
零膨胀负二项回归 /
过离散 /
费率厘定
{{custom_keyword}} /
Key words
negative binomial regression /
zero-inflated negative binomial regression /
over-dispersed /
ratemaking
{{custom_keyword}} /
中图分类号：
O212
{{custom_clc.code}}
({{custom_clc.text}})
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Lemaire J. Automobile Insurance: ActuarialModels[M]. 2nd ed. Boston: Kluwer, 1996.
[2] Kass R, Goovaerts M, Dhaene J, et al. Modern Actuarial Risk Theory[M]. Boston: Kluwer, 2001.
[3] Klugman S A, Panjer H H, Willmot G E. Loss Models: Form Data to Decisions[M]. 2nd ed. New York: John Willey & Sons Inc, 2004.
[4] Denuit M, Marechal X, Pitrebois S, et al. Actuarial Modeling of Claim Counts: Risk Classification, Credibility and Bonus-Mallus Scales[M]. NewYork: Wilely, 2007.
[5] Lambert D. Zero-inflated poisson regression with an application to defects in manufacturing[J]. Technometric, 1992, 34: 1-14.
[6] Miaou S P. The relationship between truck accidents and geometric design of road section: Poisson versus negative binomial regression[J]. Accident Analysis and Preventation, 1994, 26: 471-482.
[7] Lee A H, Stevenson M R, Wang K, et al. Modeling young driver motor vehicle crashes: Data with extra zeros[J]. Accident Analysis and Prevention, 2002, 34: 515-521.
[8] Yip Karen C H, Yau Kelvin K W. On modeling claim frequency data in general insurance with extra zeros[J]. Insurance: Mathematics and Economics, 2005, 36: 153-163.
[9] Jean-Philippe B, Michel D, Montserrat G. Risk classification for claim counts: A comparative analysis of various zero-inflated mixed poisson and hurdle models[J]. North American Actuarial Journal, 2007(11): 110-131.
[10] 韦金芬, 董理. 利用ZIP 模型估计备品备件需求量[J]. 海军工程大学学报, 2007, 19(6): 71-74. Wei J F, Dong L. Research of spare demand based on zero-inflated Poisson model[J]. Journal of Naval University of Engineering, 2007, 19(6): 71-74.
[11] 李爱萍, 谷政, 解锋昌. ZIP 回归模型的数据删除度量和广义杠杆[J]. 南京林业大学学报:自然科学版, 2007, 31(6): 109-112. Li A P, Gu Z, Xie F C. Case deletion measures and generalized leverage for the zero inflated poisson regression models[J]. Journal of Nanjing Forestry University: Natural Sciences Edition, 2007, 31(6): 109-112.
[12] 缪柏其, 韦剑, 宋卫国, 等. 林火数据的Logistic和零膨胀Poisson (ZIP)回归模型[J]. 火灾科学, 2008, 17(3): 143-149. Miao B Q, Wei J, Song W G, Logistic and ZIP regression model for forest fire data[J]. Fire Safety Science, 2008, 17(3): 143-149.
[13] 曾平, 刘桂芬, 曹红艳. 零膨胀模型在心肌缺血节段数影响因素研究中的应用[J]. 中国卫生统计, 2008, 25(5): 464-466. Zeng P, Liu G F, Cao H Y. Application of zero-inf lated models in study of the impacting factors about segment number of myocardial ischemia[J]. Chinese Journal of Health Statistics, 2008, 25(5): 464-466.
[14] 徐昕, 袁卫, 孟生旺. 零膨胀广义泊松回归模型与保险费率厘定[J]. 数学的实践与认识, 2009, 39(24): 99-107. Xu X, Yuan W, Meng S W. Zero-inflated generalized poisson regression model and its application to insurance ratemaking[J]. Mathematics in Practice and Theory, 2009, 39(24): 99-107.
[15] 徐昕, 袁卫, 孟生旺. 负二项回归模型的推广及其在分类费率厘定中的应用[J]. 数理统计与管理, 2010, 29(4): 656-661. Xu X, Yuan W, Meng S W. Generalization of negative binomial regression model and its application to classification ratemaking[J]. Application of Statistics and Management, 2010, 29(4): 656-661.
[16] Aike H. Information theory and an extension of the maximum likelihood principle[C] //Proceedings of the 2nd International Symposium on Information Theory, Akademiai Kiade Budapest, 1973: 267-281.
[17] Shwartz G. Estimating the dimension of a model[J]. Annals of Statistics, 1978(6): 461-464.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(525 KB)
