Convergence rates for the ultimate and pentultimate approximations in extreme-value theory
- 1 March 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 14 (04) , 833-854
- https://doi.org/10.1017/s000186780002084x
Abstract
Let F be a distribution in the domain of attraction of the type I extreme-value distribution Λ(x). In this paper we derive uniform rates of convergence of Fn to Λfor a large class of distributions F. We also generalise the penultimate approximation of Fisher and Tippett (1928) and show that for many F a type II or type III extreme-value distribution gives a better approximation than the limiting type I distribution.Keywords
This publication has 6 references indexed in Scilit:
- Uniform rates of convergence in extreme-value theoryAdvances in Applied Probability, 1982
- The penultimate form of approximation to normal extremesAdvances in Applied Probability, 1982
- Estimating probabilities for normal extremesAdvances in Applied Probability, 1980
- The rate of convergence in law of the maximum of an exponential sampleStatistica Neerlandica, 1979
- On the rate of convergence of normal extremesJournal of Applied Probability, 1979
- Limiting forms of the frequency distribution of the largest or smallest member of a sampleMathematical Proceedings of the Cambridge Philosophical Society, 1928