The penultimate form of approximation to normal extremes
1982 ◽
Vol 14
(02)
◽
pp. 324-339
◽
Keyword(s):
Let Yn denote the largest of n independent N(0,1) random variables. It is shown that the error in approximating the distribution of Yn by the type III extreme value distribution exp {– (–Ax + B) k }, k > 0, is uniformly of order (log n)–2 if and only if the constants A, B and k satisfy certain conditions. In particular, this holds for the penultimate form of Fisher and Tippett (1928). Furthermore, two sufficient conditions are given so that these results can be extended to a stationary Gaussian sequence.
2013 ◽
Vol 50
(3)
◽
pp. 900-907
◽
1978 ◽
Vol 15
(03)
◽
pp. 552-559
◽
1971 ◽
Vol 8
(01)
◽
pp. 136-156
◽
1970 ◽
Vol 2
(02)
◽
pp. 323-343
◽