可换序列变叙项极值的渐近分布

ON LIMITING DISTRIBUTIONS OF ORDER STATISTICS WITH VARIABLE RANKS FROM EXCHANGEABLE SEQUENCES

摘要: 设X_1,n …,X_N,n是可换r. V. 无穷序列的一段,X_1,n^＊≤…≤X_N,n^＊为其顺序统计量,N=N（n）是与这些X_（1,N）独立的正整值r. v.,n=1,2,….当k_n·n^-δ→α(0<α<∞,0<δ<∞)时,本文得出了X_{N-k_n+1m}^＊的渐近分布。

Abstract: Let X_1,n …,X_N,n be a segment of an infinite sequence of exchangeable random variables, X_1,n^＊≤…≤X_N,n^＊ be its order statistics, and N=N（n） be a random variable which is independently distributed of the X＇s, n=1, 2,…. The limit distribution of X_{N-k_n+1m}^＊, different from classical results, is obtained when k_n·n^-δ→α(0<α<∞,0<δ<∞)