一类渐近统计量的显式表示  

Explicit expressions for a class of asymptotic statistics

作　　者：李瑞雯 杨士俊 LI Rui-wen;YANG Shi-jun(School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China)* Corresponding Author)

机构地区：[1]浙江工商大学统计与数学学院

出　　处：《高校应用数学学报（A辑）》2019年第3期295-300,共6页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11871430)

摘　　要：设(Xi)i≥1是一列正的独立同分布随机变量,服从指数为α(0<α<1)的Pareto型分布.定义Tn:=X^2/1+X^2/2+…+X^2/n/(X1+X2+…+Xn)^2,且记τk:=limn→∞E(Tn^k).利用组合学方法,渐近矩τk用Bell多项式予以显式表示,并且得到了用对数型Bell多项式的简明表示,简化和完善了文献中的现有结果.Let(Xi)i≥1 be a sequence of positive i.i.d.random variables with regularly varying distribution tail of index 0<α<1 and define Tn:=X^2/1+X^2/2+…+X^2/n/(X1+X2+…+Xn)^2 and τk:=limn→∞E(Tn^k).This paper gives a combinatorial approach to the explicit expression of τk in terms of Bell polynomials and then provides a concise formula in terms of logarithmic polynomials,thereby simplifying and complementing existing results in the literature.

关 键 词：Pareto型分布 渐近统计量 BELL多项式 母函数 

分 类 号：O212.1[理学—概率论与数理统计]