Bulletin of the
Korean Mathematical Society
BKMS

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

Article

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Bull. Korean Math. Soc. 2016; 53(5): 1549-1566

Online first article September 13, 2016      Printed September 30, 2016

https://doi.org/10.4134/BKMS.b150804

Copyright © The Korean Mathematical Society.

Convergence rate of extremes for the generalized short-tailed symmetric distribution

Fuming Lin, Zuoxiang Peng, and Kaizhi Yu

Sichuan University of Science \& Engineering, Southwestern University, Southwestern University of Finance and Economics

Abstract

Denote $M_{n}$ the maximum of $n$ independent and identically distributed variables from the generalized short-tailed symmetric distribution. This paper shows the pointwise convergence rate of the distribution of $M_{n}$ to $\exp(-e^{-x})$ and the supremum-metric-based convergence rate as well.

Keywords: generalized short-tailed symmetric distribution, maximum, extreme value distribution, rate of convergence

MSC numbers: Primary 62E20, 60G70; Secondary 60F15, 60F05