THE ASYMPTOTIC-DISTRIBUTION OF EXTREME SUMS

• 成果类型: Article
• 署名作者: CSORGO, S; HAEUSLER, E; MASON, DM
• 署名单位: University of Delaware; University of Munich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990451
• 发表日期: 1991
• 页码: 783-811
• 关键词: order-statistics; CONVERGENCE; VALUES

摘要

Let X1,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 integers such that k(n) --> infinity and k(n)/n --> alpha as n --> infinity, where 0 less-than-or-equal-to alpha < 1. We find necessary and sufficient conditions for the existence of normalizing and centering constants A(n) > 0 and C(n) such that the sequence [GRAPHICS] converges in distribution along subsequences of the integers {n} to nondegenerate limits and completely describe the possible subsequential limiting distributions. We also give a necessary and sufficient condition for the existence of A(n) and C(n) such that E(n) be asymptotically normal along a given subsequence, and with suitable A(n) and C(n) determine the limiting distributions of E(n) along the whole sequence {n} when F is in the domain of attraction of an extreme value distribution.