Second order regular variation and its applications to rates of convergence in extreme-value distribution
Bull. Korean Math. Soc. 2008 Vol. 45, No. 1, 75-93 Printed March 1, 2008
Fuming Lin, Zuoxiang Peng, and Saralees Nadarajah Sichuan University of Sciences, Sichuan University of Sciences, and University of Manchester
Abstract : The rate of convergence of the distribution of order statistics to the corresponding extreme-value distribution may be characterized by the uniform and total variation metrics. de Haan and Resnick  derived the convergence rate when the second order generalized regularly varying function has second order derivatives. In this paper, based on the properties of the generalized regular variation and the second order generalized variation and characterized by uniform and total variation metrics, the convergence rates of the distribution of the largest order statistic are obtained under weaker conditions.
Keywords : second order generalized regularly varying function, extreme-value distribution, rate of convergence, total variation metrics