caa a22 4500 605461627 CHVBK 20210128100244.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10114-015-2003-z doi (NATIONALLICENCE)springer-10.1007/s10114-015-2003-z Expansions for the distribution and the maximum from distributions with an asymptotically gamma tail when a trend is present [Elektronische Daten] [Christopher Withers, Saralees Nadarajah] 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. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Bell polynomials nationallicence expansions nationallicence exponential and gamma tails nationallicence Gumbel nationallicence maximum nationallicence trend nationallicence Withers Christopher Industrial Research Limited, Lower Hutt, New Zealand aut Nadarajah Saralees University of Manchester, M13 9PL, Manchester, UK aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/3(2015-03-01), 526-542 1439-8516 31:3<526 2015 31 10114 https://doi.org/10.1007/s10114-015-2003-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-2003-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Withers Christopher Industrial Research Limited, Lower Hutt, New Zealand aut NATIONALLICENCE 700 1- Nadarajah Saralees University of Manchester, M13 9PL, Manchester, UK aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/3(2015-03-01), 526-542 1439-8516 31:3<526 2015 31 10114