The asymptotic distributions of sums of record values for distributions with lognormal-type tails  

作　　者：胡治水 苏淳 王定成 

机构地区：[1]Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China [2]Applied Mathematical Department, University of Electric Science of China, Chengdu 650054, China

出　　处：《Science China Mathematics》2002年第12期1557-1566,共10页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China (Grant No. 10071081), and by Special Foundation of USTC.

摘　　要：LetX 1,X 2,/h. be a sequence of i.i.d. random variables and letX (1) X (2),/h. be the associated record value sequence. We focus on the asymptotic distributions of sums of records, $T_n = \sum\nolimits_{k = 1}^n {X^{\left( k \right)} } $ ,forX 1 ∈LN(γ). In this case, we find that 2 is a strange point for parameter γ. When γ > 2,T n is asymptotically normal, while for 2 > γ > 1, we prove thatT n cannot converge in distribution to any non-degenerate law through common centralizing and normalizing and logT n is asymptotically normal.Let X1,X2,... be a sequence of i.i.d. random variables and let X(1),X(2),... be the associatedrecord value sequence. We focus on the asymptotic distributions of sums of records, Tn=∑nk=1X(k), forX1 ∈ LN(γ). In this case, we find that 2 is a strange point for parameter γ. When γ＞ 2, Tn is asymptoticallynormal, while for 2 ＞γ＞ 1, we prove that Tn cannot converge in distribution to any non-degenerate lawthrough common centralizing and normalizing and log Tn is asymptotically normal.

关 键 词：limit distribution  lognormal  record  REGULAR variable  slowly varying. 

分 类 号：O211[理学—概率论与数理统计]