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
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Key words
negative binomial regression /
zero-inflated negative binomial regression /
over-dispersed /
ratemaking
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中图分类号:
O212
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