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Normalizing constants of a distribution which belongs to the domain of attraction of the Gumbel distribution. (English) Zbl 0617.62050
The author develops methods of computing the normalizing constants for an extreme to have a limiting distribution. One particular method is based on tail equivalence.
See also J. Villasenor [Bull. Int. Stat. Inst. Contrib. Papers, 43rd Session, Buenos Aires (1981)] and pp. 64-65 and p. 158 in the reviewer’s book ”The asymptotic theory of extreme order statistics.” 2nd ed. Krieger, Melbourne, Fa, (1987; see Zbl 0381.62039 for a review of the first edition).
Reviewer: J.Galambos

MSC:
62G30 Order statistics; empirical distribution functions
60F05 Central limit and other weak theorems
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References:
[1] David, H.A., Order statistics, (1970), Wiley New York · Zbl 0223.62057
[2] Galambos, J., The asymptotic theory of extreme order statistics, (1978), Wiley New York · Zbl 0381.62039
[3] Gumbel, E.J., Statistics of extremes, (1958), Columbia University Press New York · Zbl 0086.34401
[4] Haan, L.de, ()
[5] Resnick, S.I., Tail equivalence and its applications, J. appl. prob., 8, 136-156, (1971) · Zbl 0217.49903
[6] Singpurwalla, N.D., Extreme values from a lognormal law with applications to air pollution problems, Technometrics, 14, 703-711, (1972) · Zbl 0237.62016
[7] Takahashi, R., Remark on stabilizing constants of the extreme statistic, J. Japan statist. soc., 9, 79-86, (1979)
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