Expansions for the Distribution and the Maximum from Distributions with an Asymptotically Gamma Tail When a Trend Is Present  

作　　者：Christopher S.WITHERS Saralees NADARAJAH 

机构地区：[1]Industrial Research Limited [2]University of Manchester

出　　处：《Acta Mathematica Sinica,English Series》2015年第3期526-542,共17页数学学报（英文版）

摘　　要：We give expansions about the Gumbel distribution in inverse powers of n and logn for Mn, the maximum of a sample size n or n ＋ 1 when the j-th observation is μ（j/n） ＋ ej, μ is any smooth trend flmction and the residuals {ej} are independent and identically distributed with P（e〉r）≈exp（-δx）x^do ∑k=1 ∞ckx^-kβ as -x→∞. We illustrate practical value of the expansions using simulated data sets.We give expansions about the Gumbel distribution in inverse powers of n and logn for Mn, the maximum of a sample size n or n ＋ 1 when the j-th observation is μ（j/n） ＋ ej, μ is any smooth trend flmction and the residuals {ej} are independent and identically distributed with P（e〉r）≈exp（-δx）x^do ∑k=1 ∞ckx^-kβ as -x→∞. We illustrate practical value of the expansions using simulated data sets.

关 键 词：Bell polynomials EXPANSIONS exponential and gamma tails Gumbel MAXIMUM TREND 

分 类 号：O211.5[理学—概率论与数理统计]