文章基本信息

标题：Expansions for Quantiles and Moments of Extremes for Distributions of Exponential Power Type
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作者：Christopher S. Withers Industrial Research Limited ; Lower Hutt ; New Zealand Saralees Nadarajah University of Manchester, Manchester 等
期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2011
卷号：73
期号：02
页码：202--217
出版社：Indian Statistical Institute
摘要：Let Mnr be the rth largest of a random sample of size n from a distribution F of exponential power type on R. That is, 1..F(z) = O(xd exp(..x)) as x = (z=) ! 1. For example, the exponential, gamma, chi-square, Laplace and normal distributions are of this type. We obtain an asymptotic expansion in powers of u1 = ..log(1 .. u) and u2 = log u1, for the quantile F..1(u) near u = 1. From this, we obtain a double expansion in inverse powers of (log n; n) for the moments of Mnr=n1= , with the coecient a polynomial in log log n. We also discuss a possible application to an optimal stopping problem.
关键词：Extremes, moments optimal stopping, quantiles.