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：2
页码：202-217
DOI：10.1007/s13171-011-0014-0
语种：English
出版社：Indian Statistical Institute
摘要：Let M nr be the r th largest of a random sample of size n from a distribution F of exponential power type on R . That is, 1- F ( z ) = O ( x d exp(− x )) as x = ( z/σ ) α → ∞. For example, the exponential, gamma, chi-square, Laplace and normal distributions are of this type. We obtain an asymptotic expansion in powers of u 1 = −log(1 − u ) and u 2 = log u 1, 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 M nr / n 1/ n 1/ α , with the coefficient a polynomial in log log n . We also discuss a possible application to an optimal stopping problem.
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