论文信息 - Approximation by Penultimate Extreme Value Distributions

Approximation by Penultimate Extreme Value Distributions

In certain cases the distribution of the normalized maximum of a sample can be better approximated by a sequence of different extreme value distributions than by the final one. We show that these cases are somewhat restricted and that the possible improvement is not spectacular.

M. Ivette Gomes | Laurens De Haan

[1] C. Anderson. Contributions to the asymptotic theory of extreme values , 1971 .

[2] M. Ivette Gomes,et al. Penultimate limiting forms in extreme value theory , 1984 .

[3] R. Reiss. Approximate Distributions of Order Statistics , 1989 .

[4] Sidney I. Resnick,et al. On asymptotic normality of the hill estimator , 1998 .

[5] U. Stadtmüller,et al. Generalized regular variation of second order , 1996, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[6] Jonathan P. Cohen. Convergence rates for the ultimate and pentultimate approximations in extreme-value theory , 1982, Advances in Applied Probability.

[7] R. Fisher,et al. Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[8] S. Resnick,et al. Second-Order Regular Variation and Rates of Convergence in Extreme-Value Theory , 1996 .