Expansions for the distribution and the maximum from distributions with an asymptotically gamma tail when a trend is present
Tóm tắt
We give expansions about the Gumbel distribution in inverse powers of n and log n for M
n
, the maximum of a sample size n or n+1 when the j-th observation is
$\mu (\tfrac{j}
{n}) + e_j
$
, µ is any smooth trend function and the residuals {e
j
} are independent and identically distributed with
$P(e > r) \approx \exp ( - \delta x)x^{d_0 } \sum\limits_{k = 1}^\infty {c_k x^{ - k\beta } } $
as x→∞. We illustrate practical value of the expansions using simulated data sets.
Tài liệu tham khảo
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