[1]章 溢,李志龙*.索赔次数的加权信度估计及其统计分析[J].江西师范大学学报(自然科学版),2018,(04):361-365.[doi:10.16357/j.cnki.issn1000-5862.2018.04.07]
　ZHANG Yi,LI Zhilong*.The Weighted Credibility Estimation and Their Statistical Analysis of Claims Number[J].Journal of Jiangxi Normal University:Natural Science Edition,2018,(04):361-365.[doi:10.16357/j.cnki.issn1000-5862.2018.04.07]
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索赔次数的加权信度估计及其统计分析()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2018年04期
页码:
361-365
栏目:
出版日期:
2018-08-20

文章信息/Info

Title:
The Weighted Credibility Estimation and Their Statistical Analysis of Claims Number
文章编号:
1000-5862(2018)04-0361-05
作者:
章 溢; 李志龙*
江西财经大学统计学院,江西 南昌 330013
Author(s):
ZHANG Yi; LI Zhilong*
School of Statistics,Jiangxi University of Finance and Economics,Nanchang Jiangxi 330013,China
关键词:
索赔次数;  风险参数;  信度估计;  结构参数
Keywords:
claims number;  risk parameter;  credibility estimate;  structural parameter
分类号:
O 211.9
DOI:
10.16357/j.cnki.issn1000-5862.2018.04.07
文献标志码:
A
摘要:
利用信度估计的思想研究了索赔次数的信度估计问题,在加权求和损失函数下,最小化期望损失函数得到了索赔次数的概率分布的信度估计.进而,在索赔次数的3大离散分布中分别讨论了风险参数的信度估计,得到了结构参数的估计,并证明了估计的无偏性.最后,利用数值模拟的方法将本文的信度估计与经典的信度估计进行了比较,验证了本文给出的估计的收敛性质.
Abstract:
Using the idea of credibility theory,the credibility estimation of claim number is studied,the credibility estimation of the probability distribution of the claim number is obtained by minimizing the expected weighted sum loss function.Furthermore,credibility estimates of risk parameters are discussed respectively in the three discrete distributions of claim number,and the estimation of structural parameters are obtained.The unbiasedness of estimators are proved.Finally,the credibility estimator is compared with that of the classical Bühlmann estimator by numerical simulation,which verifies the convergence rate of the proposed estimator.

参考文献/References:

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[9] Gerber H U.Credibility for esscher premium[J].Mitleilungen der Vereinigung schweiz Versicher ungsmathematiker,Heft,1980(3):307-312.
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[11] 张林娜,温利民,方婧.聚合风险模型下指数保费的非参数估计[J].西南大学学报:自然科学版,2016,38(5):100-105.
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备注/Memo

备注/Memo:
收稿日期:2018-04-23
基金项目:国家自然科学基金(71761019)和江西省自然科学基金(20171ACB21022)资助项目.
通信作者:李志龙(1977-),男,江西新干人,教授,博士,博士生导师,主要从事随机分析、数理金融和非线性泛函分析等方面的研究.E-mail:lzl771218@sina.com
更新日期/Last Update: 2018-08-20