若干重尾分布族随机和的封闭性和渐进性  

Closure and Asymptotic Behavior for Random Sums of Many Heavy-tailed Distribution Classes

作　　者：刘希军[1] 王岳宝[1] 

机构地区：[1]苏州大学数学科学学院,江苏苏州215006

出　　处：《济南大学学报（自然科学版）》2007年第4期302-305,共4页Journal of University of Jinan(Science and Technology)

基　　金：国家自然科学基金(10671139)

摘　　要：假设G是支撑在(-∞,+∞)上的适正分布,我们定义分布F(x)=sum from n=0 to ∞ pnG*n(x),其中pn,n≥0为R+上的序列,且对某个j≥1,pj>0。研究了在若干重尾分布族(如:正则变换,相容变换等)中F与G之间的关系,即给出支撑在(-∞,+∞)上的若干重尾分布族随机和的封闭性和渐进性,并将其应用到复合泊松分布和复合几何分布。Suppose G is a proper distribution function on(-∞,+∞),and we define F(x)=sum from n=0 to ∞ pnG*n(x),where pn,n≥0 is a sequence on R+,and pj>0 for some j≥1.We study the relations between F and G,that is,we obtains the closure and asymptotic behavior for random sums of many heavy-tailed distribution classes on(-∞,+∞),and apply them to the compound Poisson distribution and the compound geometric distribution.

关 键 词：重尾分布 随机和 复合泊松分布 复合几何分布 

分 类 号：O211[理学—概率论与数理统计]