On the rate of convergence in extreme value theory. (English) Zbl 0688.62016
Stability problems for stochastic models, Proc. 11th Int. Semin., Sukhumi/USSR 1987, Lect. Notes Math. 1412, 270-279 (1989).
[For the entire collection see Zbl 0679.00014.]
The author studies essentially an evaluation of the rate of convergence of i.i.d. maxima to the Fréchet distribution, joining the metric approach and the slow variation approach. Some results can be extended to convergence to Gumbel and Weibull distributions. One basic result, stated in the last lines, after Corollary 2.6, gives the expression of the rate of uniform convergence in terms of slowly varying behaviour.
The author studies essentially an evaluation of the rate of convergence of i.i.d. maxima to the Fréchet distribution, joining the metric approach and the slow variation approach. Some results can be extended to convergence to Gumbel and Weibull distributions. One basic result, stated in the last lines, after Corollary 2.6, gives the expression of the rate of uniform convergence in terms of slowly varying behaviour.
Reviewer: J.Tiago de Oliveira
MSC:
| 62E20 | Asymptotic distribution theory in statistics |
| 60F99 | Limit theorems in probability theory |
| 60K10 | Applications of renewal theory (reliability, demand theory, etc.) |
