【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。更多还原

【Abstract】 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.更多还原