THE ASYMPTOTIC-DISTRIBUTION OF INTERMEDIATE SUMS

• 成果类型: Article
• 署名作者: CSORGO, S; MASON, DM
• 署名单位: University of Delaware
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988852
• 发表日期: 1994
• 页码: 145-159
• 关键词: order-statistics

摘要

Let X(1,n) less-than-or-equal-to ... less-than-or-equal-to X(n,n) be the order statistics of n independent random variables with a common distribution function F and let k(n) be positive numbers such that k(n) --> infinity and k(n)/n --> 0 as n --> infinity, and consider the sums I(n)(a, b) = SIGMA(i=[akn]+1)[bkn]X(n+1-i,n) of intermediate order statistics, where 0 < a < b. We find necessary and sufficient conditions for the existence of constants A(n) > 0 arid C(n) such that A(n)-1(I(n)(a,b)-C(n)) converges in distribution along subsequences of the positive integers {n} to nondegenerate limits and completely describe the possible subsequential limiting distributions.