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