Normalizing constants of a distribution which belongs to the domain of attraction of the Gumbel distribution. (English) Zbl 0617.62050

Takahashi, Rinya

Stat. Probab. Lett. 5, 197-200 (1987).

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

Keywords:

domain of attraction of the Gumbel distribution; inverse Gaussian; gamma; normal; lognormal; von Mises theorem; computing the normalizing constants; tail equivalence

Citations:

Zbl 0381.62039

References:

[1]	David, H. A., Order Statistics (1970), Wiley: Wiley New York · Zbl 0223.62057
[2]	Galambos, J., The Asymptotic Theory of Extreme Order Statistics (1978), Wiley: Wiley New York · Zbl 0381.62039
[3]	Gumbel, E. J., Statistics of Extremes (1958), Columbia University Press: Columbia University Press New York · Zbl 0086.34401
[4]	Haan, L.de, (On Regular Variation and its Application to the Weak Convergence of Sample Extremes, Vol. 32 (1970), Mathematical Centre Tracts: Mathematical Centre Tracts Amsterdam)
[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)