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Convergence Rate of Extremes for the General Error Distribution

Part of: Distribution theory Limit theorems

Published online by Cambridge University Press:  14 July 2016

Peng Zuoxiang ,
Saralees Nadarajah  and
Lin Fuming
Peng Zuoxiang*
Affiliation:
Southwest University
Saralees Nadarajah*
Affiliation:
University of Manchester
Lin Fuming*
Affiliation:
Sichuan University of Science and Engineering
*
∗Postal address: School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P. R. China.
∗∗Postal address: School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK. Email address: mbbsssn2@manchester.ac.uk
∗∗∗Postal address: Department of Mathematics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, P. R. China.
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Abstract

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Let {Xn, n ≥ 1} be an independent, identically distributed random sequence with each Xn having the general error distribution. In this paper we derive the exact uniform convergence rate of the distribution of the maximum to its extreme value limit.

Keywords

Extreme value distributiongeneral error distributionmaximumuniform convergence rate

MSC classification

Secondary: 62E20: Asymptotic distribution theory 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 3 , September 2010 , pp. 668 - 679
Copyright
Copyright © Applied Probability Trust 2010 

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