Two-moment approximations for maxima
成果类型：
Article
署名作者：
Crow, Charles S.; Goldberg, David; Whitt, Ward
署名单位：
Massachusetts Institute of Technology (MIT); Columbia University
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1060.0375
发表日期：
2007
页码：
532-548
关键词：
摘要：
We introduce and investigate approximations for the probability distribution of the maximum of n independent and identically distributed nonnegative random variables, in terms of the number n and the first few moments of the underlying probability distribution, assuming the distribution is unbounded above but does not have a heavy tail. Because the mean of the underlying distribution can immediately be factored out, we focus on the effect of the squared coefficient of variation (SCV, c(2), variance divided by the square of the mean). Our starting point is the classical extreme-value theory for c(2) >= 1 , convolutions of exponentials for c(2) <= 1, sentative distributions with the given SCV-mixtures of exponentials for c(2) >= 1 and gamma for all c(2). We develop approximations for the asymptotic parameters and evaluate their performance. We show that there is a minimum threshold n*, depending on the underlying distribution, with n >= n* required for the asymptotic extreme-value approximations to be effective. The threshold n* tends to increase as c2 increases above one or decreases below one.