Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2012; 49(3): 495-510

Printed May 1, 2012

https://doi.org/10.4134/BKMS.2012.49.3.495

Copyright © The Korean Mathematical Society.

Convergence rates for the moments of extremes

Zuoxiang Peng and Saralees Nadarajah

Southwest University, University of Manchester

Abstract

Let $X_{1},X_{2}, \ldots, X_{n}$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.

Keywords: convergence rate of moments, maximum, second order regular variation, second order von Mises condition

MSC numbers: Primary 60G70; Secondary 62E20, 60F05