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页数:11页
时间:2019-06-01
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1、万方数据第5期华东师范大学学报(自然科学版)No.52009年9月JournalofEastChinaNormalUniversity(NaturalScience)Sept.2009ArticleID:1000-5641(2009)05-0118-09CredibilitymodelswitherroruniformdependenceWENLi.rainI,2.WANGWeiI.YUXue—lil(1.DepartmentofStatisticsandActuarialScience,Eas
2、tChinaNormalUniversity,Shanghai200241,China;2.Instituteo/mathematicsandinformationscience,JiangxiNormalUniversity,Jiangxi330022,China)Abstract:Firstly,theerrorswereassumedtobeuniformlydependentinnormal-normalcase8andtheBayespremiumswerederivedinthism
3、odelwhichshowthatitistheex-actcredibility.Secondly,theBiihlmann’Scredibilitymodel8withuniformdependencewerebuilt,andthecorrespondingcredibilityestimatorswerederived.Inaddition,themodelswereextendedtoBiihlmann-Straubcredibilityinwhichthenaturalweights
4、amongcon-tractswereintroduced.However,thecredibilityestimatorsofindividualpremiumunderBiihlmann-Straubmodelhaveonlythegeneralizedformof’’credibility”.Keywords:credibilitypremium;erroruniformdependent;orthogonalprojection;credibilityestimator.CLCnumbe
5、r:0211Documentcode:A误差等相关的信度模型温利民1一,王伟1,俞雪梨1(1.华东师范大学统计与精算学系,上海200241;2.江西师范大学数信学院,南昌江西330022)摘要:首先,在假设误差呈现等相关的正态一正态分布下得至UBayes保费,表明正是精确信度的形式.其次,建立了误差等相关的Biihlmann信度模型,得到了相应的信度估计.在引进了合同之间的自然权重后将该模型推广至lJBiihlmann.Straub信度情形.但是结果表明,在Biihlmann-Straub模型下
6、信度估计仅拥有广义的“信度”形式.关键词:信度保费;误差等相关;正交投影;信度估计.0IntroductionCredibilitytheoryisacommonapproachtocalculateinsurancepremiumbasedonthepolicyholder’spastexperienceandtheexperienceoftheentiregroupofpolicyholders.This收稿日期:2009-02基金项目:华东师范大学优秀博士基金.第一作者:温利民,男,在职博
7、士生,讲师,研究方向为精算数学、统计学.E-mail:wlmjxnu@ecnu.an万方数据第5期温利民,等:误差等相关的信度模型119methodiswidelyusedincommercialpropertyofliabilityinsurance,grouphealth,andlifeinsurance.Thepopularformulasincredibilitytheorytakepremiumasweightedsulnoftheaverageexperienceofthepolic
8、yholderandtheaverageoftheentirecollectionofpolicyholders.Theseformulasareeasytounderstandandsimpletoapplyduetotheirlinearproperties.Incredibilitytheory,let五denotetotalclaimaznountofapolicyholderintheithpolicyperiod.ThedistributionofXidependsontherisk
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