Uniform rates of convergence in extreme-value theory
- 1 March 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 14 (03) , 600-622
- https://doi.org/10.1017/s0001867800020668
Abstract
Rates of convergence are derived for the convergence in distribution of renormalised sample maxima to the appropriate extreme-value distribution. Related questions which are discussed include the estimation of the principal error term and the optimality of the renormalising constants. Throughout the paper a close parallel is drawn with the theory of slow variation with remainder. This theory is used in proving most of the results. Some applications are discussed, including some models of importance in reliability.Keywords
This publication has 9 references indexed in Scilit:
- The penultimate form of approximation to normal extremesAdvances in Applied Probability, 1982
- The Asymptotic Distribution of the Strength of a Series-Parallel System with Equal Load-SharingThe Annals of 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
- Very slowly varying functionsAequationes mathematicae, 1974
- On the distribution and moments of the strength of a bundle of filamentsJournal of Applied Probability, 1970
- Sur La Distribution Limite Du Terme Maximum D'Une Serie AleatoireAnnals of Mathematics, 1943
- Limiting forms of the frequency distribution of the largest or smallest member of a sampleMathematical Proceedings of the Cambridge Philosophical Society, 1928