工程数学学报
工程數學學報
공정수학학보
CHINESE JOURNAL OF ENGINEERING MATHEMATICS
2006年
1期
175-181
,共7页
总理赔量%复合Poisson-逆高斯分布%集合风险理论%正态分布%平移Gamma分布
總理賠量%複閤Poisson-逆高斯分佈%集閤風險理論%正態分佈%平移Gamma分佈
총리배량%복합Poisson-역고사분포%집합풍험이론%정태분포%평이Gamma분포
aggregate claims%compound Poisson-inverse gaussian distribution%collective risk theory%normal distribution%translated gamma distribution
本文考虑当理赔次数N的分布为Poisson-逆高斯分布时,相应的总理陪量分布(即复合Poisson-逆高斯分布)的两种近似:正态分布和平移Gamma分布.同时还考虑了当理赔量的分布为下指数分布时复合Poisson-逆高斯分布的尾概率的一种近似计算.
本文攷慮噹理賠次數N的分佈為Poisson-逆高斯分佈時,相應的總理陪量分佈(即複閤Poisson-逆高斯分佈)的兩種近似:正態分佈和平移Gamma分佈.同時還攷慮瞭噹理賠量的分佈為下指數分佈時複閤Poisson-逆高斯分佈的尾概率的一種近似計算.
본문고필당리배차수N적분포위Poisson-역고사분포시,상응적총리배량분포(즉복합Poisson-역고사분포)적량충근사:정태분포화평이Gamma분포.동시환고필료당리배량적분포위하지수분포시복합Poisson-역고사분포적미개솔적일충근사계산.
With the Poisson-inverse Gaussian distribution choice for the distribution of the number of claims, a compound Poisson-inverse Gaussian distribution as the distribution of aggregate claims is considered. The normal distribution and the translated gamma distribution are employed as two kinds of approximations to the compound Poisson-inverse Gaussian distribution under some requirements. Also the approximation to the tail probability of compound Poisson-inverse Gaussian distribution is given when the claim amount distribution is subexponential.
