Bull. Korean Math. Soc. 2008; 45(1): 75-93
Printed March 1, 2008
Copyright © The Korean Mathematical Society.
Fuming Lin, Zuoxiang Peng, and Saralees Nadarajah
Sichuan University of Sciences, Sichuan University of Sciences, and University of Manchester
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 [4] 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
MSC numbers: 60G70
2021; 58(6): 1419-1443
2021; 58(2): 433-444
2017; 54(2): 359-373
2016; 53(5): 1549-1566
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd