误差等相关的信度模型

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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