截断和与次序统计量的联合极限分布  

THE UNIT LIMIT DISTRIBUTIONS OF THE TRUNCATED SUMS AND ORDER STATISTICS

作　　者：程士宏[1] 

机构地区：[1]北京大学

出　　处：《应用数学学报》1993年第1期121-135,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金

摘　　要：§1.引言 设{X_n,n≥1}是iidry序列,具有共同的非退化dfF.对每n≥1,以X_(n,1)≤…≤X_(n,n)。记X_1,……,X_n的次序统计量.如果整数k_n和l_n满足1≤k_n<l_n≤n。Let {X_n,n≥1} be an iid sequence with a nondegenerate df F and X_(n,1)≤……≤X_(n,n) be the order statistics of X_1,…,X_n. Denote S_n~*=X_(n,j) for integ-ers k_(n,1),k_(n,2) satisfying 1≤k_(n,1)<k_(n,2)≤n. Under the conditions that k_(n,1)↑∞, k_(n,1)/n→0, n — k_(n,2)↑∞ and k_(n,2)/n →1, we determine all the limit laws of sequences{(X_(n,k_(n,1)), S_n~*, X_(n,k_(n,2))), n≥1} after normlization and find out the necessary andsufficient conditions of convergence We also discuss some problems on limit distri-butions of S_n~* and ?_n =:S_n~*/(X_(n,k_(n,2))—X_(n,k_(n,1))) in this paper.

关 键 词：截断和 次序统计量 联合分布 

分 类 号：O211.3[理学—概率论与数理统计]